Implementation of adiabatic geometric gates with superconducting phase qubits.

PubMed

Peng, Z H; Chu, H F; Wang, Z D; Zheng, D N

2009-01-28

We present an adiabatic geometric quantum computation strategy based on the non-degenerate energy eigenstates in (but not limited to) superconducting phase qubit systems. The fidelity of the designed quantum gate was evaluated in the presence of simulated thermal fluctuations in a superconducting phase qubits circuit and was found to be quite robust against random errors. In addition, it was elucidated that the Berry phase in the designed adiabatic evolution may be detected directly via the quantum state tomography developed for superconducting qubits. We also analyze the effects of control parameter fluctuations on the experimental detection of the Berry phase.

Decrease of Fisher information and the information geometry of evolution equations for quantum mechanical probability amplitudes.

PubMed

Cafaro, Carlo; Alsing, Paul M

2018-04-01

The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is characterized by its decrease along the solutions of the Boltzmann equation for Maxwellian molecules in the two-dimensional case. From a quantum mechanical standpoint, the output state in Grover's quantum search algorithm follows a geodesic path obtained from the Fubini-Study metric on the manifold of Hilbert-space rays. Additionally, Grover's algorithm is specified by constant Fisher information. In this paper, we present an information geometric characterization of the oscillatory or monotonic behavior of statistically parametrized squared probability amplitudes originating from special functional forms of the Fisher information function: constant, exponential decay, and power-law decay. Furthermore, for each case, we compute both the computational speed and the availability loss of the corresponding physical processes by exploiting a convenient Riemannian geometrization of useful thermodynamical concepts. Finally, we briefly comment on the possibility of using the proposed methods of information geometry to help identify a suitable trade-off between speed and thermodynamic efficiency in quantum search algorithms.

Decrease of Fisher information and the information geometry of evolution equations for quantum mechanical probability amplitudes

NASA Astrophysics Data System (ADS)

Cafaro, Carlo; Alsing, Paul M.

2018-04-01

The relevance of the concept of Fisher information is increasing in both statistical physics and quantum computing. From a statistical mechanical standpoint, the application of Fisher information in the kinetic theory of gases is characterized by its decrease along the solutions of the Boltzmann equation for Maxwellian molecules in the two-dimensional case. From a quantum mechanical standpoint, the output state in Grover's quantum search algorithm follows a geodesic path obtained from the Fubini-Study metric on the manifold of Hilbert-space rays. Additionally, Grover's algorithm is specified by constant Fisher information. In this paper, we present an information geometric characterization of the oscillatory or monotonic behavior of statistically parametrized squared probability amplitudes originating from special functional forms of the Fisher information function: constant, exponential decay, and power-law decay. Furthermore, for each case, we compute both the computational speed and the availability loss of the corresponding physical processes by exploiting a convenient Riemannian geometrization of useful thermodynamical concepts. Finally, we briefly comment on the possibility of using the proposed methods of information geometry to help identify a suitable trade-off between speed and thermodynamic efficiency in quantum search algorithms.

Optimal protocols for slowly driven quantum systems.

PubMed

Zulkowski, Patrick R; DeWeese, Michael R

2015-09-01

The design of efficient quantum information processing will rely on optimal nonequilibrium transitions of driven quantum systems. Building on a recently developed geometric framework for computing optimal protocols for classical systems driven in finite time, we construct a general framework for optimizing the average information entropy for driven quantum systems. Geodesics on the parameter manifold endowed with a positive semidefinite metric correspond to protocols that minimize the average information entropy production in finite time. We use this framework to explicitly compute the optimal entropy production for a simple two-state quantum system coupled to a heat bath of bosonic oscillators, which has applications to quantum annealing.

Superadiabatic holonomic quantum computation in cavity QED

NASA Astrophysics Data System (ADS)

Liu, Bao-Jie; Huang, Zhen-Hua; Xue, Zheng-Yuan; Zhang, Xin-Ding

2017-06-01

Adiabatic quantum control is a powerful tool for quantum engineering and a key component in some quantum computation models, where accurate control over the timing of the involved pulses is not needed. However, the adiabatic condition requires that the process be very slow and thus limits its application in quantum computation, where quantum gates are preferred to be fast due to the limited coherent times of the quantum systems. Here, we propose a feasible scheme to implement universal holonomic quantum computation based on non-Abelian geometric phases with superadiabatic quantum control, where the adiabatic manipulation is sped up while retaining its robustness against errors in the timing control. Consolidating the advantages of both strategies, our proposal is thus both robust and fast. The cavity QED system is adopted as a typical example to illustrate the merits where the proposed scheme can be realized in a tripod configuration by appropriately controlling the pulse shapes and their relative strength. To demonstrate the distinct performance of our proposal, we also compare our scheme with the conventional adiabatic strategy.

Room temperature high-fidelity holonomic single-qubit gate on a solid-state spin.

PubMed

Arroyo-Camejo, Silvia; Lazariev, Andrii; Hell, Stefan W; Balasubramanian, Gopalakrishnan

2014-09-12

At its most fundamental level, circuit-based quantum computation relies on the application of controlled phase shift operations on quantum registers. While these operations are generally compromised by noise and imperfections, quantum gates based on geometric phase shifts can provide intrinsically fault-tolerant quantum computing. Here we demonstrate the high-fidelity realization of a recently proposed fast (non-adiabatic) and universal (non-Abelian) holonomic single-qubit gate, using an individual solid-state spin qubit under ambient conditions. This fault-tolerant quantum gate provides an elegant means for achieving the fidelity threshold indispensable for implementing quantum error correction protocols. Since we employ a spin qubit associated with a nitrogen-vacancy colour centre in diamond, this system is based on integrable and scalable hardware exhibiting strong analogy to current silicon technology. This quantum gate realization is a promising step towards viable, fault-tolerant quantum computing under ambient conditions.

Tightening Quantum Speed Limits for Almost All States.

PubMed

Campaioli, Francesco; Pollock, Felix A; Binder, Felix C; Modi, Kavan

2018-02-09

Conventional quantum speed limits perform poorly for mixed quantum states: They are generally not tight and often significantly underestimate the fastest possible evolution speed. To remedy this, for unitary driving, we derive two quantum speed limits that outperform the traditional bounds for almost all quantum states. Moreover, our bounds are significantly simpler to compute as well as experimentally more accessible. Our bounds have a clear geometric interpretation; they arise from the evaluation of the angle between generalized Bloch vectors.

Nongeometric conditional phase shift via adiabatic evolution of dark eigenstates: a new approach to quantum computation.

PubMed

Zheng, Shi-Biao

2005-08-19

We propose a new approach to quantum phase gates via the adiabatic evolution. The conditional phase shift is neither of dynamical nor geometric origin. It arises from the adiabatic evolution of the dark state itself. Taking advantage of the adiabatic passage, this kind of quantum logic gates is robust against moderate fluctuations of experimental parameters. In comparison with the geometric phase gates, it is unnecessary to drive the system to undergo a desired cyclic evolution to obtain a desired solid angle. Thus, the procedure is simplified, and the fidelity may be further improved since the errors in obtaining the required solid angle are avoided. We illustrate such a kind of quantum logic gates in the ion trap system. The idea can also be realized in other systems, opening a new perspective for quantum information processing.

Unification of the family of Garrison-Wright's phases.

PubMed

Cui, Xiao-Dong; Zheng, Yujun

2014-07-24

Inspired by Garrison and Wight's seminal work on complex-valued geometric phases, we generalize the concept of Pancharatnam's "in-phase" in interferometry and further develop a theoretical framework for unification of the abelian geometric phases for a biorthogonal quantum system modeled by a parameterized or time-dependent nonhermitian hamiltonian with a finite and nondegenerate instantaneous spectrum, that is, the family of Garrison-Wright's phases, which will no longer be confined in the adiabatic and nonadiabatic cyclic cases. Besides, we employ a typical example, Bethe-Lamb model, to illustrate how to apply our theory to obtain an explicit result for the Garrison-Wright's noncyclic geometric phase, and also to present its potential applications in quantum computation and information.

Adiabatic gate teleportation.

PubMed

Bacon, Dave; Flammia, Steven T

2009-09-18

The difficulty in producing precisely timed and controlled quantum gates is a significant source of error in many physical implementations of quantum computers. Here we introduce a simple universal primitive, adiabatic gate teleportation, which is robust to timing errors and many control errors and maintains a constant energy gap throughout the computation above a degenerate ground state space. This construction allows for geometric robustness based upon the control of two independent qubit interactions. Further, our piecewise adiabatic evolution easily relates to the quantum circuit model, enabling the use of standard methods from fault-tolerance theory for establishing thresholds.

Differential geometric treewidth estimation in adiabatic quantum computation

NASA Astrophysics Data System (ADS)

Wang, Chi; Jonckheere, Edmond; Brun, Todd

2016-10-01

The D-Wave adiabatic quantum computing platform is designed to solve a particular class of problems—the Quadratic Unconstrained Binary Optimization (QUBO) problems. Due to the particular "Chimera" physical architecture of the D-Wave chip, the logical problem graph at hand needs an extra process called minor embedding in order to be solvable on the D-Wave architecture. The latter problem is itself NP-hard. In this paper, we propose a novel polynomial-time approximation to the closely related treewidth based on the differential geometric concept of Ollivier-Ricci curvature. The latter runs in polynomial time and thus could significantly reduce the overall complexity of determining whether a QUBO problem is minor embeddable, and thus solvable on the D-Wave architecture.

Implementing quantum Ricci curvature

NASA Astrophysics Data System (ADS)

Klitgaard, N.; Loll, R.

2018-05-01

Quantum Ricci curvature has been introduced recently as a new, geometric observable characterizing the curvature properties of metric spaces, without the need for a smooth structure. Besides coordinate invariance, its key features are scalability, computability, and robustness. We demonstrate that these properties continue to hold in the context of nonperturbative quantum gravity, by evaluating the quantum Ricci curvature numerically in two-dimensional Euclidean quantum gravity, defined in terms of dynamical triangulations. Despite the well-known, highly nonclassical properties of the underlying quantum geometry, its Ricci curvature can be matched well to that of a five-dimensional round sphere.

Geometric diffusion of quantum trajectories

PubMed Central

Yang, Fan; Liu, Ren-Bao

2015-01-01

A quantum object can acquire a geometric phase (such as Berry phases and Aharonov–Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects. PMID:26178745

Ultrafast quantum computation in ultrastrongly coupled circuit QED systems.

PubMed

Wang, Yimin; Guo, Chu; Zhang, Guo-Qiang; Wang, Gangcheng; Wu, Chunfeng

2017-03-10

The latest technological progress of achieving the ultrastrong-coupling regime in circuit quantum electrodynamics (QED) systems has greatly promoted the developments of quantum physics, where novel quantum optics phenomena and potential computational benefits have been predicted. Here, we propose a scheme to accelerate the nontrivial two-qubit phase gate in a circuit QED system, where superconducting flux qubits are ultrastrongly coupled to a transmission line resonator (TLR), and two more TLRs are coupled to the ultrastrongly-coupled system for assistant. The nontrivial unconventional geometric phase gate between the two flux qubits is achieved based on close-loop displacements of the three-mode intracavity fields. Moreover, as there are three resonators contributing to the phase accumulation, the requirement of the coupling strength to realize the two-qubit gate can be reduced. Further reduction in the coupling strength to achieve a specific controlled-phase gate can be realized by adding more auxiliary resonators to the ultrastrongly-coupled system through superconducting quantum interference devices. We also present a study of our scheme with realistic parameters considering imperfect controls and noisy environment. Our scheme possesses the merits of ultrafastness and noise-tolerance due to the advantages of geometric phases.

Ultrafast quantum computation in ultrastrongly coupled circuit QED systems

PubMed Central

Wang, Yimin; Guo, Chu; Zhang, Guo-Qiang; Wang, Gangcheng; Wu, Chunfeng

2017-01-01

The latest technological progress of achieving the ultrastrong-coupling regime in circuit quantum electrodynamics (QED) systems has greatly promoted the developments of quantum physics, where novel quantum optics phenomena and potential computational benefits have been predicted. Here, we propose a scheme to accelerate the nontrivial two-qubit phase gate in a circuit QED system, where superconducting flux qubits are ultrastrongly coupled to a transmission line resonator (TLR), and two more TLRs are coupled to the ultrastrongly-coupled system for assistant. The nontrivial unconventional geometric phase gate between the two flux qubits is achieved based on close-loop displacements of the three-mode intracavity fields. Moreover, as there are three resonators contributing to the phase accumulation, the requirement of the coupling strength to realize the two-qubit gate can be reduced. Further reduction in the coupling strength to achieve a specific controlled-phase gate can be realized by adding more auxiliary resonators to the ultrastrongly-coupled system through superconducting quantum interference devices. We also present a study of our scheme with realistic parameters considering imperfect controls and noisy environment. Our scheme possesses the merits of ultrafastness and noise-tolerance due to the advantages of geometric phases. PMID:28281654

Multi-target-qubit unconventional geometric phase gate in a multi-cavity system

NASA Astrophysics Data System (ADS)

Liu, Tong; Cao, Xiao-Zhi; Su, Qi-Ping; Xiong, Shao-Jie; Yang, Chui-Ping

2016-02-01

Cavity-based large scale quantum information processing (QIP) may involve multiple cavities and require performing various quantum logic operations on qubits distributed in different cavities. Geometric-phase-based quantum computing has drawn much attention recently, which offers advantages against inaccuracies and local fluctuations. In addition, multiqubit gates are particularly appealing and play important roles in QIP. We here present a simple and efficient scheme for realizing a multi-target-qubit unconventional geometric phase gate in a multi-cavity system. This multiqubit phase gate has a common control qubit but different target qubits distributed in different cavities, which can be achieved using a single-step operation. The gate operation time is independent of the number of qubits and only two levels for each qubit are needed. This multiqubit gate is generic, e.g., by performing single-qubit operations, it can be converted into two types of significant multi-target-qubit phase gates useful in QIP. The proposal is quite general, which can be used to accomplish the same task for a general type of qubits such as atoms, NV centers, quantum dots, and superconducting qubits.

Multi-target-qubit unconventional geometric phase gate in a multi-cavity system.

PubMed

Liu, Tong; Cao, Xiao-Zhi; Su, Qi-Ping; Xiong, Shao-Jie; Yang, Chui-Ping

2016-02-22

Cavity-based large scale quantum information processing (QIP) may involve multiple cavities and require performing various quantum logic operations on qubits distributed in different cavities. Geometric-phase-based quantum computing has drawn much attention recently, which offers advantages against inaccuracies and local fluctuations. In addition, multiqubit gates are particularly appealing and play important roles in QIP. We here present a simple and efficient scheme for realizing a multi-target-qubit unconventional geometric phase gate in a multi-cavity system. This multiqubit phase gate has a common control qubit but different target qubits distributed in different cavities, which can be achieved using a single-step operation. The gate operation time is independent of the number of qubits and only two levels for each qubit are needed. This multiqubit gate is generic, e.g., by performing single-qubit operations, it can be converted into two types of significant multi-target-qubit phase gates useful in QIP. The proposal is quite general, which can be used to accomplish the same task for a general type of qubits such as atoms, NV centers, quantum dots, and superconducting qubits.

Generalized Geometric Quantum Speed Limits

NASA Astrophysics Data System (ADS)

Pires, Diego Paiva; Cianciaruso, Marco; Céleri, Lucas C.; Adesso, Gerardo; Soares-Pinto, Diogo O.

2016-04-01

The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.

The geometrical structure of quantum theory as a natural generalization of information geometry

NASA Astrophysics Data System (ADS)

Reginatto, Marcel

2015-01-01

Quantum mechanics has a rich geometrical structure which allows for a geometrical formulation of the theory. This formalism was introduced by Kibble and later developed by a number of other authors. The usual approach has been to start from the standard description of quantum mechanics and identify the relevant geometrical features that can be used for the reformulation of the theory. Here this procedure is inverted: the geometrical structure of quantum theory is derived from information geometry, a geometrical structure that may be considered more fundamental, and the Hilbert space of the standard formulation of quantum mechanics is constructed using geometrical quantities. This suggests that quantum theory has its roots in information geometry.

Quantum coherence behaviors of fermionic system in non-inertial frame

NASA Astrophysics Data System (ADS)

Huang, Zhiming; Situ, Haozhen

2018-04-01

In this paper, we analyze the quantum coherence behaviors of a single qubit in the relativistic regime beyond the single-mode approximation. Firstly, we investigate the freezing condition of quantum coherence in fermionic system. We also study the quantum coherence tradeoff between particle and antiparticle sector. It is found that there exists quantum coherence transfer between particle and antiparticle sector, but the coherence lost in particle sector is not entirely compensated by the coherence generation of antiparticle sector. Besides, we emphatically discuss the cohering power and decohering power of Unruh channel with respect to the computational basis. It is shown that cohering power is vanishing and decohering power is dependent of the choice of Unruh mode and acceleration. Finally, we compare the behaviors of quantum coherence with geometric quantum discord and entanglement in relativistic setup. Our results show that this quantifiers in two region converge at infinite acceleration limit, which implies that this measures become independent of Unruh modes beyond the single-mode approximations. It is also demonstrated that the robustness of quantum coherence and geometric quantum discord are better than entanglement under the influence of acceleration, since entanglement undergoes sudden death.

Impact of geometric, thermal and tunneling effects on nano-transistors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Langhua; Chen, Duan, E-mail: dchen10@uncc.edu; Wei, Guo-Wei

Electronic transistors are fundamental building blocks of large scale integrated circuits in modern advanced electronic equipments, and their sizes have been down-scaled to nanometers. Modeling and simulations in the framework of quantum dynamics have emerged as important tools to study functional characteristics of these nano-devices. This work explores the effects of geometric shapes of semiconductor–insulator interfaces, phonon–electron interactions, and quantum tunneling of three-dimensional (3D) nano-transistors. First, we propose a two-scale energy functional to describe the electron dynamics in a dielectric continuum of device material. Coupled governing equations, i.e., Poisson–Kohn–Sham (PKS) equations, are derived by the variational principle. Additionally, it ismore » found that at a given channel cross section area and gate voltage, the geometry that has the smallest perimeter of the channel cross section offers the largest channel current, which indicates that ultra-thin nanotransistors may not be very efficient in practical applications. Moreover, we introduce a new method to evaluate quantum tunneling effects in nanotransistors without invoking the comparison of classical and quantum predictions. It is found that at a given channel cross section area and gate voltage, the geometry that has the smallest perimeter of the channel cross section has the smallest quantum tunneling ratio, which indicates that geometric defects can lead to higher geometric confinement and larger quantum tunneling effect. Furthermore, although an increase in the phonon–electron interaction strength reduces channel current, it does not have much impact to the quantum tunneling ratio. Finally, advanced numerical techniques, including second order elliptic interface methods, have been applied to ensure computational accuracy and reliability of the present PKS simulation.« less

The geometrical structure of quantum theory as a natural generalization of information geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reginatto, Marcel

2015-01-13

Quantum mechanics has a rich geometrical structure which allows for a geometrical formulation of the theory. This formalism was introduced by Kibble and later developed by a number of other authors. The usual approach has been to start from the standard description of quantum mechanics and identify the relevant geometrical features that can be used for the reformulation of the theory. Here this procedure is inverted: the geometrical structure of quantum theory is derived from information geometry, a geometrical structure that may be considered more fundamental, and the Hilbert space of the standard formulation of quantum mechanics is constructed usingmore » geometrical quantities. This suggests that quantum theory has its roots in information geometry.« less

Gauge freedom in observables and Landsberg's nonadiabatic geometric phase: Pumping spectroscopy of interacting open quantum systems

NASA Astrophysics Data System (ADS)

Pluecker, T.; Wegewijs, M. R.; Splettstoesser, J.

2017-04-01

We set up a general density-operator approach to geometric steady-state pumping through slowly driven open quantum systems. This approach applies to strongly interacting systems that are weakly coupled to multiple reservoirs at high temperature, illustrated by an Anderson quantum dot. Pumping gives rise to a nonadiabatic geometric phase that can be described by a framework originally developed for classical dissipative systems by Landsberg. This geometric phase is accumulated by the transported observable (charge, spin, energy) and not by the quantum state. It thus differs radically from the adiabatic Berry-Simon phase, even when generalizing it to mixed states, following Sarandy and Lidar. As a key feature, our geometric formulation of pumping stays close to a direct physical intuition (i) by tying gauge transformations to calibration of the meter registering the transported observable and (ii) by deriving a geometric connection from a driving-frequency expansion of the current. Furthermore, our approach provides a systematic and efficient way to compute the geometric pumping of various observables, including charge, spin, energy, and heat. These insights seem to be generalizable beyond the present paper's working assumptions (e.g., Born-Markov limit) to more general open-system evolutions involving memory and strong-coupling effects due to low-temperature reservoirs as well. Our geometric curvature formula reveals a general experimental scheme for performing geometric transport spectroscopy that enhances standard nonlinear spectroscopies based on measurements for static parameters. We indicate measurement strategies for separating the useful geometric pumping contribution to transport from nongeometric effects. A large part of the paper is devoted to an explicit comparison with the Sinitsyn-Nemenmann full-counting-statistics (FCS) approach to geometric pumping, restricting attention to the first moments of the pumped observable. Covering all key aspects, gauge freedom, pumping connection, curvature, and gap condition, we argue that our approach is physically more transparent and, importantly, simpler for practical calculations. In particular, this comparison allows us to clarify how in the FCS approach an "adiabatic" approximation leads to a manifestly nonadiabatic result involving a finite retardation time of the response to parameter driving.

Interband emission energy in a dilute nitride quaternary semiconductor quantum dot for longer wavelength applications

NASA Astrophysics Data System (ADS)

Mageshwari, P. Uma; Peter, A. John; Lee, Chang Woo; Duque, C. A.

2016-07-01

Excitonic properties are studied in a strained Ga1-xInxNyAs1-y/GaAs cylindrical quantum dot. The optimum condition for the desired band alignment for emitting wavelength 1.55 μm is investigated using band anticrossing model and the model solid theory. The band gap and the band discontinuities of a Ga1-xInxNyAs1-y/GaAs quantum dot on GaAs are computed with the geometrical confinement effect. The binding energy of the exciton, the oscillator strength and its radiative life time for the optimum condition are found taking into account the spatial confinement effect. The effects of geometrical confinement and the nitrogen incorporation on the interband emission energy are brought out. The result shows that the desired band alignment for emitting wavelength 1.55 μm is achieved for the inclusion of alloy contents, y=0.0554% and x=0.339% in Ga1-xInxNyAs1-y/GaAs quantum dot. And the incorporation of nitrogen and indium shows the red-shift and the geometrical confinement shows the blue-shift. And it can be applied for fibre optical communication networks.

JOURNAL SCOPE GUIDELINES: Paper classification scheme

NASA Astrophysics Data System (ADS)

2005-06-01

This scheme is used to clarify the journal's scope and enable authors and readers to more easily locate the appropriate section for their work. For each of the sections listed in the scope statement we suggest some more detailed subject areas which help define that subject area. These lists are by no means exhaustive and are intended only as a guide to the type of papers we envisage appearing in each section. We acknowledge that no classification scheme can be perfect and that there are some papers which might be placed in more than one section. We are happy to provide further advice on paper classification to authors upon request (please email jphysa@iop.org). 1. Statistical physics numerical and computational methods statistical mechanics, phase transitions and critical phenomena quantum condensed matter theory Bose-Einstein condensation strongly correlated electron systems exactly solvable models in statistical mechanics lattice models, random walks and combinatorics field-theoretical models in statistical mechanics disordered systems, spin glasses and neural networks nonequilibrium systems network theory 2. Chaotic and complex systems nonlinear dynamics and classical chaos fractals and multifractals quantum chaos classical and quantum transport cellular automata granular systems and self-organization pattern formation biophysical models 3. Mathematical physics combinatorics algebraic structures and number theory matrix theory classical and quantum groups, symmetry and representation theory Lie algebras, special functions and orthogonal polynomials ordinary and partial differential equations difference and functional equations integrable systems soliton theory functional analysis and operator theory inverse problems geometry, differential geometry and topology numerical approximation and analysis geometric integration computational methods 4. Quantum mechanics and quantum information theory coherent states eigenvalue problems supersymmetric quantum mechanics scattering theory relativistic quantum mechanics semiclassical approximations foundations of quantum mechanics and measurement theory entanglement and quantum nonlocality geometric phases and quantum tomography quantum tunnelling decoherence and open systems quantum cryptography, communication and computation theoretical quantum optics 5. Classical and quantum field theory quantum field theory gauge and conformal field theory quantum electrodynamics and quantum chromodynamics Casimir effect integrable field theory random matrix theory applications in field theory string theory and its developments classical field theory and electromagnetism metamaterials 6. Fluid and plasma theory turbulence fundamental plasma physics kinetic theory magnetohydrodynamics and multifluid descriptions strongly coupled plasmas one-component plasmas non-neutral plasmas astrophysical and dusty plasmas

Quantum correlations of helicity entangled states in non-inertial frames beyond single mode approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Harsij, Zeynab, E-mail: z.harsij@ph.iut.ac.ir; Mirza, Behrouz, E-mail: b.mirza@cc.iut.ac.ir

A helicity entangled tripartite state is considered in which the degree of entanglement is preserved in non-inertial frames. It is shown that Quantum Entanglement remains observer independent. As another measure of quantum correlation, Quantum Discord has been investigated. It is explicitly shown that acceleration has no effect on the degree of quantum correlation for the bipartite and tripartite helicity entangled states. Geometric Quantum Discord as a Hilbert–Schmidt distance is computed for helicity entangled states. It is shown that living in non-inertial frames does not make any influence on this distance, either. In addition, the analysis has been extended beyond singlemore » mode approximation to show that acceleration does not have any impact on the quantum features in the limit beyond the single mode. As an interesting result, while the density matrix depends on the right and left Unruh modes, the Negativity as a measure of Quantum Entanglement remains constant. Also, Quantum Discord does not change beyond single mode approximation. - Highlights: • The helicity entangled states here are observer independent in non-inertial frames. • It is explicitly shown that Quantum Discord for these states is observer independent. • Geometric Quantum Discord is also not affected by acceleration increase. • Extending to beyond single mode does not change the degree of entanglement. • Beyond single mode approximation the degree of Quantum Discord is also preserved.« less

Physics of lateral triple quantum-dot molecules with controlled electron numbers.

PubMed

Hsieh, Chang-Yu; Shim, Yun-Pil; Korkusinski, Marek; Hawrylak, Pawel

2012-11-01

We review the recent progress in theory and experiments with lateral triple quantum dots with controlled electron numbers down to one electron in each dot. The theory covers electronic and spin properties as a function of topology, number of electrons, gate voltage and external magnetic field. The orbital Hund's rules and Nagaoka ferromagnetism, magnetic frustration and chirality, interplay of quantum interference and electron-electron interactions and geometrical phases are described and related to charging and transport spectroscopy. Fabrication techniques and recent experiments are covered, as well as potential applications of triple quantum-dot molecule in coherent control, spin manipulation and quantum computation.

Sudden change of geometric quantum discord in finite temperature reservoirs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hu, Ming-Liang, E-mail: mingliang0301@163.com; Sun, Jian

2015-03-15

We investigate sudden change (SC) behaviors of the distance-based measures of geometric quantum discords (GQDs) for two non-interacting qubits subject to the two-sided and the one-sided thermal reservoirs. We found that the GQDs defined by different distances exhibit different SCs, and thus the SCs are the combined result of the chosen discord measure and the property of a state. We also found that the thermal reservoir may generate states having different orderings related to different GQDs. These inherent differences of the GQDs reveal that they are incompatible in characterizing quantum correlations both quantitatively and qualitatively. - Highlights: • Comparable studymore » of different distance-based geometric quantum discords. • Evolution of the geometric quantum discords in finite temperature reservoirs. • Different geometric quantum discords exhibit distinct sudden changes. • Nonunique states ordering imposed by different geometric quantum discords.« less

Quantum correlations for bipartite continuous-variable systems

NASA Astrophysics Data System (ADS)

Ma, Ruifen; Hou, Jinchuan; Qi, Xiaofei; Wang, Yangyang

2018-04-01

Two quantum correlations Q and Q_P for (m+n)-mode continuous-variable systems are introduced in terms of average distance between the reduced states under the local Gaussian positive operator-valued measurements, and analytical formulas of these quantum correlations for bipartite Gaussian states are provided. It is shown that the product states do not contain these quantum correlations, and conversely, all (m+n)-mode Gaussian states with zero quantum correlations are product states. Generally, Q≥ Q_{P}, but for the symmetric two-mode squeezed thermal states, these quantum correlations are the same and a computable formula is given. In addition, Q is compared with Gaussian geometric discord for symmetric squeezed thermal states.

Quantum Adiabatic Brachistochrone

NASA Astrophysics Data System (ADS)

Rezakhani, A. T.; Kuo, W.-J.; Hamma, A.; Lidar, D. A.; Zanardi, P.

2009-08-01

We formulate a time-optimal approach to adiabatic quantum computation (AQC). A corresponding natural Riemannian metric is also derived, through which AQC can be understood as the problem of finding a geodesic on the manifold of control parameters. This geometrization of AQC is demonstrated through two examples, where we show that it leads to improved performance of AQC, and sheds light on the roles of entanglement and curvature of the control manifold in algorithmic performance.

Quantum adiabatic brachistochrone.

PubMed

Rezakhani, A T; Kuo, W-J; Hamma, A; Lidar, D A; Zanardi, P

2009-08-21

We formulate a time-optimal approach to adiabatic quantum computation (AQC). A corresponding natural Riemannian metric is also derived, through which AQC can be understood as the problem of finding a geodesic on the manifold of control parameters. This geometrization of AQC is demonstrated through two examples, where we show that it leads to improved performance of AQC, and sheds light on the roles of entanglement and curvature of the control manifold in algorithmic performance.

Complex quantum network geometries: Evolution and phase transitions

NASA Astrophysics Data System (ADS)

Bianconi, Ginestra; Rahmede, Christoph; Wu, Zhihao

2015-08-01

Networks are topological and geometric structures used to describe systems as different as the Internet, the brain, or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e., simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a nonequilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped, respectively, to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks, including small-world property, high clustering coefficient, high modularity, and scale-free degree distribution. Moreover, they can be distinguished between the Fermi-Dirac network and the Bose-Einstein network obeying, respectively, the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally, we comment on the relation between quantum complex network geometries, spin networks, and triangulations.

Complex quantum network geometries: Evolution and phase transitions.

PubMed

Bianconi, Ginestra; Rahmede, Christoph; Wu, Zhihao

2015-08-01

Networks are topological and geometric structures used to describe systems as different as the Internet, the brain, or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e., simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a nonequilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped, respectively, to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks, including small-world property, high clustering coefficient, high modularity, and scale-free degree distribution. Moreover, they can be distinguished between the Fermi-Dirac network and the Bose-Einstein network obeying, respectively, the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally, we comment on the relation between quantum complex network geometries, spin networks, and triangulations.

Non-adiabatic quantum reactive scattering in hyperspherical coordinates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kendrick, Brian K.

A new electronically non-adiabatic quantum reactive scattering methodology is presented based on a time-independent coupled channel formalism and the adiabatically adjusting principal axis hyperspherical coordinates of Pack and Parker [J. Chem. Phys. 87, 3888 (1987)]. The methodology computes the full state-to-state scattering matrix for A + B 2(v, j) ↔ AB(v', j') + B and A + AB(v, j) → A + AB(v', j') reactions that involve two coupled electronic states which exhibit a conical intersection. The methodology accurately treats all six degrees of freedom relative to the center-of-mass which includes non-zero total angular momentum J and identical particle exchangemore » symmetry. The new methodology is applied to the ultracold hydrogen exchange reaction for which large geometric phase effects have been recently reported [B. K. Kendrick et al., Phys. Rev. Lett. 115, 153201 (2015)]. Rate coefficients for the H/D + HD(v = 4, j = 0) → H/D + HD(v', j') reactions are reported for collision energies between 1 μK and 100 K (total energy ≈1.9 eV). A new diabatic potential energy matrix is developed based on the Boothroyd, Keogh, Martin, and Peterson (BKMP2) and double many body expansion plus single-polynomial (DSP) adiabatic potential energy surfaces for the ground and first excited electronic states of H 3, respectively. The rate coefficients computed using the new non-adiabatic methodology and diabatic potential matrix reproduce the recently reported rates that include the geometric phase and are computed using a single adiabatic ground electronic state potential energy surface (BKMP2). The dramatic enhancement and suppression of the ultracold rates due to the geometric phase are confirmed as well as its effects on several shape resonances near 1 K. In conclusion, the results reported here represent the first fully non-adiabatic quantum reactive scattering calculation for an ultracold reaction and validate the importance of the geometric phase on the Wigner threshold behavior.« less

Non-adiabatic quantum reactive scattering in hyperspherical coordinates

NASA Astrophysics Data System (ADS)

Kendrick, Brian K.

2018-01-01

A new electronically non-adiabatic quantum reactive scattering methodology is presented based on a time-independent coupled channel formalism and the adiabatically adjusting principal axis hyperspherical coordinates of Pack and Parker [J. Chem. Phys. 87, 3888 (1987)]. The methodology computes the full state-to-state scattering matrix for A + B2(v , j) ↔ AB(v ', j') + B and A + AB(v , j) → A + AB(v ', j') reactions that involve two coupled electronic states which exhibit a conical intersection. The methodology accurately treats all six degrees of freedom relative to the center-of-mass which includes non-zero total angular momentum J and identical particle exchange symmetry. The new methodology is applied to the ultracold hydrogen exchange reaction for which large geometric phase effects have been recently reported [B. K. Kendrick et al., Phys. Rev. Lett. 115, 153201 (2015)]. Rate coefficients for the H/D + HD(v = 4, j = 0) → H/D + HD(v ', j') reactions are reported for collision energies between 1 μK and 100 K (total energy ≈1.9 eV). A new diabatic potential energy matrix is developed based on the Boothroyd, Keogh, Martin, and Peterson (BKMP2) and double many body expansion plus single-polynomial (DSP) adiabatic potential energy surfaces for the ground and first excited electronic states of H3, respectively. The rate coefficients computed using the new non-adiabatic methodology and diabatic potential matrix reproduce the recently reported rates that include the geometric phase and are computed using a single adiabatic ground electronic state potential energy surface (BKMP2). The dramatic enhancement and suppression of the ultracold rates due to the geometric phase are confirmed as well as its effects on several shape resonances near 1 K. The results reported here represent the first fully non-adiabatic quantum reactive scattering calculation for an ultracold reaction and validate the importance of the geometric phase on the Wigner threshold behavior.

Non-adiabatic quantum reactive scattering in hyperspherical coordinates

DOE PAGES

Kendrick, Brian K.

2018-01-28

A new electronically non-adiabatic quantum reactive scattering methodology is presented based on a time-independent coupled channel formalism and the adiabatically adjusting principal axis hyperspherical coordinates of Pack and Parker [J. Chem. Phys. 87, 3888 (1987)]. The methodology computes the full state-to-state scattering matrix for A + B 2(v, j) ↔ AB(v', j') + B and A + AB(v, j) → A + AB(v', j') reactions that involve two coupled electronic states which exhibit a conical intersection. The methodology accurately treats all six degrees of freedom relative to the center-of-mass which includes non-zero total angular momentum J and identical particle exchangemore » symmetry. The new methodology is applied to the ultracold hydrogen exchange reaction for which large geometric phase effects have been recently reported [B. K. Kendrick et al., Phys. Rev. Lett. 115, 153201 (2015)]. Rate coefficients for the H/D + HD(v = 4, j = 0) → H/D + HD(v', j') reactions are reported for collision energies between 1 μK and 100 K (total energy ≈1.9 eV). A new diabatic potential energy matrix is developed based on the Boothroyd, Keogh, Martin, and Peterson (BKMP2) and double many body expansion plus single-polynomial (DSP) adiabatic potential energy surfaces for the ground and first excited electronic states of H 3, respectively. The rate coefficients computed using the new non-adiabatic methodology and diabatic potential matrix reproduce the recently reported rates that include the geometric phase and are computed using a single adiabatic ground electronic state potential energy surface (BKMP2). The dramatic enhancement and suppression of the ultracold rates due to the geometric phase are confirmed as well as its effects on several shape resonances near 1 K. In conclusion, the results reported here represent the first fully non-adiabatic quantum reactive scattering calculation for an ultracold reaction and validate the importance of the geometric phase on the Wigner threshold behavior.« less

A Theoretical Mechanism of Szilard Engine Function in Nucleic Acids and the Implications for Quantum Coherence in Biological Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matthew Mihelic, F.

2010-12-22

Nucleic acids theoretically possess a Szilard engine function that can convert the energy associated with the Shannon entropy of molecules for which they have coded recognition, into the useful work of geometric reconfiguration of the nucleic acid molecule. This function is logically reversible because its mechanism is literally and physically constructed out of the information necessary to reduce the Shannon entropy of such molecules, which means that this information exists on both sides of the theoretical engine, and because information is retained in the geometric degrees of freedom of the nucleic acid molecule, a quantum gate is formed through whichmore » multi-state nucleic acid qubits can interact. Entangled biophotons emitted as a consequence of symmetry breaking nucleic acid Szilard engine (NASE) function can be used to coordinate relative positioning of different nucleic acid locations, both within and between cells, thus providing the potential for quantum coherence of an entire biological system. Theoretical implications of understanding biological systems as such 'quantum adaptive systems' include the potential for multi-agent based quantum computing, and a better understanding of systemic pathologies such as cancer, as being related to a loss of systemic quantum coherence.« less

A Theoretical Mechanism of Szilard Engine Function in Nucleic Acids and the Implications for Quantum Coherence in Biological Systems

NASA Astrophysics Data System (ADS)

Matthew Mihelic, F.

2010-12-01

Nucleic acids theoretically possess a Szilard engine function that can convert the energy associated with the Shannon entropy of molecules for which they have coded recognition, into the useful work of geometric reconfiguration of the nucleic acid molecule. This function is logically reversible because its mechanism is literally and physically constructed out of the information necessary to reduce the Shannon entropy of such molecules, which means that this information exists on both sides of the theoretical engine, and because information is retained in the geometric degrees of freedom of the nucleic acid molecule, a quantum gate is formed through which multi-state nucleic acid qubits can interact. Entangled biophotons emitted as a consequence of symmetry breaking nucleic acid Szilard engine (NASE) function can be used to coordinate relative positioning of different nucleic acid locations, both within and between cells, thus providing the potential for quantum coherence of an entire biological system. Theoretical implications of understanding biological systems as such "quantum adaptive systems" include the potential for multi-agent based quantum computing, and a better understanding of systemic pathologies such as cancer, as being related to a loss of systemic quantum coherence.

Non-Abelian Geometric Phases Carried by the Quantum Noise Matrix

NASA Astrophysics Data System (ADS)

Bharath, H. M.; Boguslawski, Matthew; Barrios, Maryrose; Chapman, Michael

2017-04-01

Topological phases of matter are characterized by topological order parameters that are built using Berry's geometric phase. Berry's phase is the geometric information stored in the overall phase of a quantum state. We show that geometric information is also stored in the second and higher order spin moments of a quantum spin system, captured by a non-abelian geometric phase. The quantum state of a spin-S system is uniquely characterized by its spin moments up to order 2S. The first-order spin moment is the spin vector, and the second-order spin moment represents the spin fluctuation tensor, i.e., the quantum noise matrix. When the spin vector is transported along a loop in the Bloch ball, we show that the quantum noise matrix picks up a geometric phase. Considering spin-1 systems, we formulate this geometric phase as an SO(3) operator. Geometric phases are usually interpreted in terms of the solid angle subtended by the loop at the center. However, solid angles are not well defined for loops that pass through the center. Here, we introduce a generalized solid angle which is well defined for all loops inside the Bloch ball, in terms of which, we interpret the SO(3) geometric phase. This geometric phase can be used to characterize topological spin textures in cold atomic clouds.

Universal Adiabatic Quantum Computing using Double Quantum Dot Charge Qubits

NASA Astrophysics Data System (ADS)

Ryan-Anderson, Ciaran; Jacobson, N. Tobias; Landahl, Andrew

Adiabatic quantum computation (AQC) provides one path to achieving universal quantum computing in experiment. Computation in the AQC model occurs by starting with an easy to prepare groundstate of some simple Hamiltonian and then adiabatically evolving the Hamiltonian to obtain the groundstate of a final, more complex Hamiltonian. It has been shown that the circuit model can be mapped to AQC Hamiltonians and, thus, AQC can be made universal. Further, these Hamiltonians can be made planar and two-local. We propose using double quantum dot charge qubits (DQDs) to implement such universal AQC Hamiltonians. However, the geometry and restricted set of interactions of DQDs make the application of even these 2-local planar Hamiltonians non-trivial. We present a construction tailored to DQDs to overcome the geometric and interaction contraints and allow for universal AQC. These constraints are dealt with in this construction by making use of perturbation gadgets, which introduce ancillary qubits to mediate interactions. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.

Control landscapes are almost always trap free: a geometric assessment

NASA Astrophysics Data System (ADS)

Russell, Benjamin; Rabitz, Herschel; Wu, Re-Bing

2017-05-01

A proof is presented that almost all closed, finite dimensional quantum systems have trap free (i.e. free from local optima) landscapes for a large and physically general class of circumstances, which includes qubit evolutions in quantum computing. This result offers an explanation for why gradient-based methods succeed so frequently in quantum control. The role of singular controls is analyzed using geometric tools in the case of the control of the propagator, and thus in the case of observables as well. Singular controls have been implicated as a source of landscape traps. The conditions under which singular controls can introduce traps, and thus interrupt the progress of a control optimization, are discussed and a geometrical characterization of the issue is presented. It is shown that a control being singular is not sufficient to cause control optimization progress to halt, and sufficient conditions for a trap free landscape are presented. It is further shown that the local surjectivity (full rank) assumption of landscape analysis can be refined to the condition that the end-point map is transverse to each of the level sets of the fidelity function. This mild condition is shown to be sufficient for a quantum system’s landscape to be trap free. The control landscape is shown to be trap free for all but a null set of Hamiltonians using a geometric technique based on the parametric transversality theorem. Numerical evidence confirming this analysis is also presented. This new result is the analogue of the work of Altifini, wherein it was shown that controllability holds for all but a null set of quantum systems in the dipole approximation. These collective results indicate that the availability of adequate control resources remains the most physically relevant issue for achieving high fidelity control performance while also avoiding landscape traps.

Quantum entanglement properties of geometrical and topological quantum gates

NASA Astrophysics Data System (ADS)

Sezer, Hasan Cavit; Duy, Hoang Ngoc; Heydari, Hoshang

2011-03-01

In this paper we will investigate the action of holonomic and topological quantum gates on different classes of four qubit states. In particular, we review the construction of holonomic quantum gate based on geometric phase and topological quantum gate based on braid group. Then, we investigate the entanglement properties of three different classes of four-qubit states based on geometric invariants. The result shows that entanglement properties of the two most generic classes of four-qubit states can be controlled by holonomic and topological quantum gate..

FIRST Quantum-(1980)-Computing DISCOVERY in Siegel-Rosen-Feynman-...A.-I. Neural-Networks: Artificial(ANN)/Biological(BNN) and Siegel FIRST Semantic-Web and Siegel FIRST ``Page''-``Brin'' ``PageRank'' PRE-Google Search-Engines!!!

NASA Astrophysics Data System (ADS)

Rosen, Charles; Siegel, Edward Carl-Ludwig; Feynman, Richard; Wunderman, Irwin; Smith, Adolph; Marinov, Vesco; Goldman, Jacob; Brine, Sergey; Poge, Larry; Schmidt, Erich; Young, Frederic; Goates-Bulmer, William-Steven; Lewis-Tsurakov-Altshuler, Thomas-Valerie-Genot; Ibm/Exxon Collaboration; Google/Uw Collaboration; Microsoft/Amazon Collaboration; Oracle/Sun Collaboration; Ostp/Dod/Dia/Nsa/W.-F./Boa/Ubs/Ub Collaboration

2013-03-01

Belew[Finding Out About, Cambridge(2000)] and separately full-decade pre-Page/Brin/Google FIRST Siegel-Rosen(Machine-Intelligence/Atherton)-Feynman-Smith-Marinov(Guzik Enterprises/Exxon-Enterprises/A.-I./Santa Clara)-Wunderman(H.-P.) [IBM Conf. on Computers and Mathematics, Stanford(1986); APS Mtgs.(1980s): Palo Alto/Santa Clara/San Francisco/...(1980s) MRS Spring-Mtgs.(1980s): Palo Alto/San Jose/San Francisco/...(1980-1992) FIRST quantum-computing via Bose-Einstein quantum-statistics(BEQS) Bose-Einstein CONDENSATION (BEC) in artificial-intelligence(A-I) artificial neural-networks(A-N-N) and biological neural-networks(B-N-N) and Siegel[J. Noncrystalline-Solids 40, 453(1980); Symp. on Fractals..., MRS Fall-Mtg., Boston(1989)-5-papers; Symp. on Scaling..., (1990); Symp. on Transport in Geometric-Constraint (1990)

Moving walls and geometric phases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Facchi, Paolo, E-mail: paolo.facchi@ba.infn.it; INFN, Sezione di Bari, I-70126 Bari; Garnero, Giancarlo, E-mail: giancarlo.garnero@uniba.it

2016-09-15

We unveil the existence of a non-trivial Berry phase associated to the dynamics of a quantum particle in a one dimensional box with moving walls. It is shown that a suitable choice of boundary conditions has to be made in order to preserve unitarity. For these boundary conditions we compute explicitly the geometric phase two-form on the parameter space. The unboundedness of the Hamiltonian describing the system leads to a natural prescription of renormalization for divergent contributions arising from the boundary.

Distribution of geometric quantum discord in photon-added coherent states

NASA Astrophysics Data System (ADS)

Daoud, M.; Kaydi, W.; El Hadfi, H.

2015-12-01

In this paper, we examine the influence of photon excitation on the monogamy property of quantum discord in tripartite coherent states of Greenberger-Horne-Zeilinger (GHZ) type. The Hilbert-Schmidt norm is used as quantifier of pairwise quantum correlations. The geometric quantum discord in all bipartite subsystems are explicitly given. We show that the geometric discord is monogamous for any photon excitation order.

Quantum realization of the bilinear interpolation method for NEQR.

PubMed

Zhou, Ri-Gui; Hu, Wenwen; Fan, Ping; Ian, Hou

2017-05-31

In recent years, quantum image processing is one of the most active fields in quantum computation and quantum information. Image scaling as a kind of image geometric transformation has been widely studied and applied in the classical image processing, however, the quantum version of which does not exist. This paper is concerned with the feasibility of the classical bilinear interpolation based on novel enhanced quantum image representation (NEQR). Firstly, the feasibility of the bilinear interpolation for NEQR is proven. Then the concrete quantum circuits of the bilinear interpolation including scaling up and scaling down for NEQR are given by using the multiply Control-Not operation, special adding one operation, the reverse parallel adder, parallel subtractor, multiplier and division operations. Finally, the complexity analysis of the quantum network circuit based on the basic quantum gates is deduced. Simulation result shows that the scaled-up image using bilinear interpolation is clearer and less distorted than nearest interpolation.

Geometry of quantum Hall states: Gravitational anomaly and transport coefficients

DOE Office of Scientific and Technical Information (OSTI.GOV)

Can, Tankut, E-mail: tcan@scgp.stonybrook.edu; Laskin, Michael; Wiegmann, Paul B.

2015-11-15

We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly. We develop a general method to compute correlation functions of FQH states in a curved space, where local transformation properties of these states are examined through local geometric variations. We introduce the notion of a generating functional and relate it to geometric invariant functionals recently studied in geometry. We develop two complementary methods to study the geometry of the FQHE. One method is based on iteratingmore » a Ward identity, while the other is based on a field theoretical formulation of the FQHE through a path integral formalism.« less

Hydrogenic molecular transitions in double concentric quantum donuts by changing geometrical parameters

NASA Astrophysics Data System (ADS)

Ospina-Londoño, D. A.; Fulla, M. R.; Marín, J. H.

2013-03-01

In this work it is considered a versatile model to study two different ionization processes starting from a D20 homonuclear hydrogenic molecule confined in double concentric quantum donuts. Very narrow quantum donut circular cross sections are considered to separate the radial and angular variables in the D20 Hamiltonian by using the well-known adiabatic approximation D20 total energy as a function of the inter donor spacing and the outer donut center line radius is calculated. The salient features of an artificial D20 hydrogenic molecule such as the dissociation energy and the equilibrium length are strongly dependent on the quantum donut geometrical parameters. By increasing systematically the quantum donut outer center line radius, it is possible to understand a first ionization process: D20→D2++e-. A second ionization process D20→D-+D+ can be carried out by fixing the first donor position and gradually moving away the second one. The results obtained in this study are in good agreement with those previously obtained in the limiting cases of very large inter donor separation. The model proposed here is computationally economical and provides a realistic description of both ionization processes and the few-particle system confined in double concentric quantum donuts.

Geometric measure of pairwise quantum discord for superpositions of multipartite generalized coherent states

NASA Astrophysics Data System (ADS)

Daoud, M.; Ahl Laamara, R.

2012-07-01

We give the explicit expressions of the pairwise quantum correlations present in superpositions of multipartite coherent states. A special attention is devoted to the evaluation of the geometric quantum discord. The dynamics of quantum correlations under a dephasing channel is analyzed. A comparison of geometric measure of quantum discord with that of concurrence shows that quantum discord in multipartite coherent states is more resilient to dissipative environments than is quantum entanglement. To illustrate our results, we consider some special superpositions of Weyl-Heisenberg, SU(2) and SU(1,1) coherent states which interpolate between Werner and Greenberger-Horne-Zeilinger states.

Quantum geometric phase in Majorana's stellar representation: mapping onto a many-body Aharonov-Bohm phase.

PubMed

Bruno, Patrick

2012-06-15

The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of finite-dimensional quantum systems is studied. It is shown that a pure quantum state in a (2J+1)-dimensional Hilbert space (or, equivalently, of a spin-J system) can be mapped onto the partition function of a gas of independent Dirac strings moving on a sphere and subject to the Coulomb repulsion of 2J fixed test charges (the Majorana stars) characterizing the quantum state. The geometric phase may be viewed as the Aharonov-Bohm phase acquired by the Majorana stars as they move through the gas of Dirac strings. Expressions for the geometric connection and curvature, for the metric tensor, as well as for the multipole moments (dipole, quadrupole, etc.), are given in terms of the Majorana stars. Finally, the geometric formulation of the quantum dynamics is presented and its application to systems with exotic ordering such as spin nematics is outlined.

Quantum Geometric Phase in Majorana's Stellar Representation: Mapping onto a Many-Body Aharonov-Bohm Phase

NASA Astrophysics Data System (ADS)

Bruno, Patrick

2012-06-01

The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of finite-dimensional quantum systems is studied. It is shown that a pure quantum state in a (2J+1)-dimensional Hilbert space (or, equivalently, of a spin-J system) can be mapped onto the partition function of a gas of independent Dirac strings moving on a sphere and subject to the Coulomb repulsion of 2J fixed test charges (the Majorana stars) characterizing the quantum state. The geometric phase may be viewed as the Aharonov-Bohm phase acquired by the Majorana stars as they move through the gas of Dirac strings. Expressions for the geometric connection and curvature, for the metric tensor, as well as for the multipole moments (dipole, quadrupole, etc.), are given in terms of the Majorana stars. Finally, the geometric formulation of the quantum dynamics is presented and its application to systems with exotic ordering such as spin nematics is outlined.

Universal freezing of quantum correlations within the geometric approach

PubMed Central

Cianciaruso, Marco; Bromley, Thomas R.; Roga, Wojciech; Lo Franco, Rosario; Adesso, Gerardo

2015-01-01

Quantum correlations in a composite system can be measured by resorting to a geometric approach, according to which the distance from the state of the system to a suitable set of classically correlated states is considered. Here we show that all distance functions, which respect natural assumptions of invariance under transposition, convexity, and contractivity under quantum channels, give rise to geometric quantifiers of quantum correlations which exhibit the peculiar freezing phenomenon, i.e., remain constant during the evolution of a paradigmatic class of states of two qubits each independently interacting with a non-dissipative decohering environment. Our results demonstrate from first principles that freezing of geometric quantum correlations is independent of the adopted distance and therefore universal. This finding paves the way to a deeper physical interpretation and future practical exploitation of the phenomenon for noisy quantum technologies. PMID:26053239

Gauge Gravity and Electroweak Theory

NASA Astrophysics Data System (ADS)

Hestenes, David

2008-09-01

Reformulation of the Dirac equation in terms of the real Spacetime Algebra (STA) reveals hidden geometric structure, including a geometric role for the unit imaginary as generator of rotations in a spacelike plane. The STA and the real Dirac equation play essential roles in a new Gauge Theory Gravity (GTG) version of General Relativity (GR). Besides clarifying the conceptual foundations of GR and facilitating complex computations, GTG opens up new possibilities for a unified gauge theory of gravity and quantum mechanics, including spacetime geometry of electroweak interactions. The Weinberg-Salam model fits perfectly into this geometric framework, and a promising variant that replaces chiral states with Majorana states is formulated to incorporate zitterbewegung in electron states.

Gouy Phase Radial Mode Sorter for Light: Concepts and Experiments.

PubMed

Gu, Xuemei; Krenn, Mario; Erhard, Manuel; Zeilinger, Anton

2018-03-09

We present an in principle lossless sorter for radial modes of light, using accumulated Gouy phases. The experimental setups have been found by a computer algorithm, and can be intuitively understood in a geometric way. Together with the ability to sort angular-momentum modes, we now have access to the complete two-dimensional transverse plane of light. The device can readily be used in multiplexing classical information. On a quantum level, it is an analog of the Stern-Gerlach experiment-significant for the discussion of fundamental concepts in quantum physics. As such, it can be applied in high-dimensional and multiphotonic quantum experiments.

Gouy Phase Radial Mode Sorter for Light: Concepts and Experiments

NASA Astrophysics Data System (ADS)

Gu, Xuemei; Krenn, Mario; Erhard, Manuel; Zeilinger, Anton

2018-03-01

We present an in principle lossless sorter for radial modes of light, using accumulated Gouy phases. The experimental setups have been found by a computer algorithm, and can be intuitively understood in a geometric way. Together with the ability to sort angular-momentum modes, we now have access to the complete two-dimensional transverse plane of light. The device can readily be used in multiplexing classical information. On a quantum level, it is an analog of the Stern-Gerlach experiment—significant for the discussion of fundamental concepts in quantum physics. As such, it can be applied in high-dimensional and multiphotonic quantum experiments.

Extended Quantum Field Theory, Index Theory, and the Parity Anomaly

NASA Astrophysics Data System (ADS)

Müller, Lukas; Szabo, Richard J.

2018-06-01

We use techniques from functorial quantum field theory to provide a geometric description of the parity anomaly in fermionic systems coupled to background gauge and gravitational fields on odd-dimensional spacetimes. We give an explicit construction of a geometric cobordism bicategory which incorporates general background fields in a stack, and together with the theory of symmetric monoidal bicategories we use it to provide the concrete forms of invertible extended quantum field theories which capture anomalies in both the path integral and Hamiltonian frameworks. Specialising this situation by using the extension of the Atiyah-Patodi-Singer index theorem to manifolds with corners due to Loya and Melrose, we obtain a new Hamiltonian perspective on the parity anomaly. We compute explicitly the 2-cocycle of the projective representation of the gauge symmetry on the quantum state space, which is defined in a parity-symmetric way by suitably augmenting the standard chiral fermionic Fock spaces with Lagrangian subspaces of zero modes of the Dirac Hamiltonian that naturally appear in the index theorem. We describe the significance of our constructions for the bulk-boundary correspondence in a large class of time-reversal invariant gauge-gravity symmetry-protected topological phases of quantum matter with gapless charged boundary fermions, including the standard topological insulator in 3 + 1 dimensions.

Quantum correlations of helicity entangled states in non-inertial frames beyond single mode approximation

NASA Astrophysics Data System (ADS)

Harsij, Zeynab; Mirza, Behrouz

2014-12-01

A helicity entangled tripartite state is considered in which the degree of entanglement is preserved in non-inertial frames. It is shown that Quantum Entanglement remains observer independent. As another measure of quantum correlation, Quantum Discord has been investigated. It is explicitly shown that acceleration has no effect on the degree of quantum correlation for the bipartite and tripartite helicity entangled states. Geometric Quantum Discord as a Hilbert-Schmidt distance is computed for helicity entangled states. It is shown that living in non-inertial frames does not make any influence on this distance, either. In addition, the analysis has been extended beyond single mode approximation to show that acceleration does not have any impact on the quantum features in the limit beyond the single mode. As an interesting result, while the density matrix depends on the right and left Unruh modes, the Negativity as a measure of Quantum Entanglement remains constant. Also, Quantum Discord does not change beyond single mode approximation.

Particle creation in (2+1) circular dust collapse

NASA Astrophysics Data System (ADS)

Gutti, Sashideep; Singh, T. P.

2007-09-01

We investigate the quantum particle creation during the circularly symmetric collapse of a 2+1 dust cloud, for the cases when the cosmological constant is either zero or negative. We derive the Ford-Parker formula for the 2+1 case, which can be used to compute the radiated quantum flux in the geometric optics approximation. It is shown that no particles are created when the collapse ends in a naked singularity, unlike in the 3+1 case. When the collapse ends in a Banados-Teitelboim-Zanelli black hole, we recover the expected Hawking radiation.

Competing ν = 5/2 fractional quantum Hall states in confined geometry.

PubMed

Fu, Hailong; Wang, Pengjie; Shan, Pujia; Xiong, Lin; Pfeiffer, Loren N; West, Ken; Kastner, Marc A; Lin, Xi

2016-11-01

Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either Abelian or non-Abelian statistics. Recent experiments suggest that the tunneling exponents are more consistent with an Abelian state rather than a non-Abelian state. Here, we present edge-current-tunneling experiments in geometrically confined quantum point contacts, which indicate that Abelian and non-Abelian states compete at filling factor 5/2. Our results are consistent with a transition from an Abelian state to a non-Abelian state in a single quantum point contact when the confinement is tuned. Our observation suggests that there is an intrinsic non-Abelian 5/2 ground state but that the appropriate confinement is necessary to maintain it. This observation is important not only for understanding the physics of the 5/2 state but also for the design of future topological quantum computation devices.

Application of fermionic marginal constraints to hybrid quantum algorithms

NASA Astrophysics Data System (ADS)

Rubin, Nicholas C.; Babbush, Ryan; McClean, Jarrod

2018-05-01

Many quantum algorithms, including recently proposed hybrid classical/quantum algorithms, make use of restricted tomography of the quantum state that measures the reduced density matrices, or marginals, of the full state. The most straightforward approach to this algorithmic step estimates each component of the marginal independently without making use of the algebraic and geometric structure of the marginals. Within the field of quantum chemistry, this structure is termed the fermionic n-representability conditions, and is supported by a vast amount of literature on both theoretical and practical results related to their approximations. In this work, we introduce these conditions in the language of quantum computation, and utilize them to develop several techniques to accelerate and improve practical applications for quantum chemistry on quantum computers. As a general result, we demonstrate how these marginals concentrate to diagonal quantities when measured on random quantum states. We also show that one can use fermionic n-representability conditions to reduce the total number of measurements required by more than an order of magnitude for medium sized systems in chemistry. As a practical demonstration, we simulate an efficient restoration of the physicality of energy curves for the dilation of a four qubit diatomic hydrogen system in the presence of three distinct one qubit error channels, providing evidence these techniques are useful for pre-fault tolerant quantum chemistry experiments.

Experimental realization of non-adiabatic universal quantum gates using geometric Landau-Zener-Stückelberg interferometry

PubMed Central

Wang, Li; Tu, Tao; Gong, Bo; Zhou, Cheng; Guo, Guang-Can

2016-01-01

High fidelity universal gates for quantum bits form an essential ingredient of quantum information processing. In particular, geometric gates have attracted attention because they have a higher intrinsic resistance to certain errors. However, their realization remains a challenge because of the need for complicated quantum control on a multi-level structure as well as meeting the adiabatic condition within a short decoherence time. Here, we demonstrate non-adiabatic quantum operations for a two-level system by applying a well-controlled geometric Landau-Zener-Stückelberg interferometry. By characterizing the gate quality, we also investigate the operation in the presence of realistic dephasing. Furthermore, the result provides an essential model suitable for understanding an interplay of geometric phase and Landau-Zener-Stückelberg process which are well explored separately. PMID:26738875

Signatures of bifurcation on quantum correlations: Case of the quantum kicked top

NASA Astrophysics Data System (ADS)

Bhosale, Udaysinh T.; Santhanam, M. S.

2017-01-01

Quantum correlations reflect the quantumness of a system and are useful resources for quantum information and computational processes. Measures of quantum correlations do not have a classical analog and yet are influenced by classical dynamics. In this work, by modeling the quantum kicked top as a multiqubit system, the effect of classical bifurcations on measures of quantum correlations such as the quantum discord, geometric discord, and Meyer and Wallach Q measure is studied. The quantum correlation measures change rapidly in the vicinity of a classical bifurcation point. If the classical system is largely chaotic, time averages of the correlation measures are in good agreement with the values obtained by considering the appropriate random matrix ensembles. The quantum correlations scale with the total spin of the system, representing its semiclassical limit. In the vicinity of trivial fixed points of the kicked top, the scaling function decays as a power law. In the chaotic limit, for large total spin, quantum correlations saturate to a constant, which we obtain analytically, based on random matrix theory, for the Q measure. We also suggest that it can have experimental consequences.

Geometric construction of quantum hall clustering Hamiltonians

DOE PAGES

Lee, Ching Hua; Papić, Zlatko; Thomale, Ronny

2015-10-08

In this study, many fractional quantum Hall wave functions are known to be unique highest-density zero modes of certain “pseudopotential” Hamiltonians. While a systematic method to construct such parent Hamiltonians has been available for the infinite plane and sphere geometries, the generalization to manifolds where relative angular momentum is not an exact quantum number, i.e., the cylinder or torus, remains an open problem. This is particularly true for non-Abelian states, such as the Read-Rezayi series (in particular, the Moore-Read and Read-Rezayi Z 3 states) and more exotic nonunitary (Haldane-Rezayi and Gaffnian) or irrational (Haffnian) states, whose parent Hamiltonians involve complicatedmore » many-body interactions. Here, we develop a universal geometric approach for constructing pseudopotential Hamiltonians that is applicable to all geometries. Our method straightforwardly generalizes to the multicomponent SU(n) cases with a combination of spin or pseudospin (layer, subband, or valley) degrees of freedom. We demonstrate the utility of our approach through several examples, some of which involve non-Abelian multicomponent states whose parent Hamiltonians were previously unknown, and we verify the results by numerically computing their entanglement properties.« less

Geometric Algebra for Physicists

NASA Astrophysics Data System (ADS)

Doran, Chris; Lasenby, Anthony

2007-11-01

Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.

Black holes as quantum gravity condensates

NASA Astrophysics Data System (ADS)

Oriti, Daniele; Pranzetti, Daniele; Sindoni, Lorenzo

2018-03-01

We model spherically symmetric black holes within the group field theory formalism for quantum gravity via generalized condensate states, involving sums over arbitrarily refined graphs (dual to three-dimensional triangulations). The construction relies heavily on both the combinatorial tools of random tensor models and the quantum geometric data of loop quantum gravity, both part of the group field theory formalism. Armed with the detailed microscopic structure, we compute the entropy associated with the black hole horizon, which turns out to be equivalently the Boltzmann entropy of its microscopic degrees of freedom and the entanglement entropy between the inside and outside regions. We recover the area law under very general conditions, as well as the Bekenstein-Hawking formula. The result is also shown to be generically independent of any specific value of the Immirzi parameter.

Imaginary geometric phases of quantum trajectories in high-order terahertz sideband generation

NASA Astrophysics Data System (ADS)

Yang, Fan; Liu, Ren-Bao

2014-03-01

Quantum evolution of particles under strong fields can be described by a small number of quantum trajectories that satisfy the stationary phase condition in the Dirac-Feynmann path integral. The quantum trajectories are the key concept to understand the high-order terahertz siedeband generation (HSG) in semiconductors. Due to the nontrivial ``vacuum'' states of band materials, the quantum trajectories of optically excited electron-hole pairs in semiconductors can accumulate geometric phases under the driving of an elliptically polarized THz field. We find that the geometric phase of the stationary trajectory is generally complex with both real and imaginary parts. In monolayer MoS2, the imaginary parts of the geometric phase leads to a changing of the polarization ellipticity of the sideband. We further show that the imaginary part originates from the quantum interference of many trajectories with different phases. Thus the observation of the polarization ellipticity of the sideband shall be a good indication of the quantum nature of the stationary trajectory. This work is supported by Hong Kong RGC/GRF 401512 and the CUHK Focused Investments Scheme.

Entanglement in Quantum-Classical Hybrid

NASA Technical Reports Server (NTRS)

Zak, Michail

2011-01-01

It is noted that the phenomenon of entanglement is not a prerogative of quantum systems, but also occurs in other, non-classical systems such as quantum-classical hybrids, and covers the concept of entanglement as a special type of global constraint imposed upon a broad class of dynamical systems. Application of hybrid systems for physics of life, as well as for quantum-inspired computing, has been outlined. In representing the Schroedinger equation in the Madelung form, there is feedback from the Liouville equation to the Hamilton-Jacobi equation in the form of the quantum potential. Preserving the same topology, the innovators replaced the quantum potential with other types of feedback, and investigated the property of these hybrid systems. A function of probability density has been introduced. Non-locality associated with a global geometrical constraint that leads to an entanglement effect was demonstrated. Despite such a quantum like characteristic, the hybrid can be of classical scale and all the measurements can be performed classically. This new emergence of entanglement sheds light on the concept of non-locality in physics.

Stimulated Raman adiabatic passage in a three-level superconducting circuit

PubMed Central

Kumar, K. S.; Vepsäläinen, A.; Danilin, S.; Paraoanu, G. S.

2016-01-01

The adiabatic manipulation of quantum states is a powerful technique that opened up new directions in quantum engineering—enabling tests of fundamental concepts such as geometrical phases and topological transitions, and holding the promise of alternative models of quantum computation. Here we benchmark the stimulated Raman adiabatic passage for circuit quantum electrodynamics by employing the first three levels of a transmon qubit. In this ladder configuration, we demonstrate a population transfer efficiency >80% between the ground state and the second excited state using two adiabatic Gaussian-shaped control microwave pulses. By doing quantum tomography at successive moments during the Raman pulses, we investigate the transfer of the population in time domain. Furthermore, we show that this protocol can be reversed by applying a third adiabatic pulse, we study a hybrid nondiabatic–adiabatic sequence, and we present experimental results for a quasi-degenerate intermediate level. PMID:26902454

Stimulated Raman adiabatic passage in a three-level superconducting circuit.

PubMed

Kumar, K S; Vepsäläinen, A; Danilin, S; Paraoanu, G S

2016-02-23

The adiabatic manipulation of quantum states is a powerful technique that opened up new directions in quantum engineering--enabling tests of fundamental concepts such as geometrical phases and topological transitions, and holding the promise of alternative models of quantum computation. Here we benchmark the stimulated Raman adiabatic passage for circuit quantum electrodynamics by employing the first three levels of a transmon qubit. In this ladder configuration, we demonstrate a population transfer efficiency >80% between the ground state and the second excited state using two adiabatic Gaussian-shaped control microwave pulses. By doing quantum tomography at successive moments during the Raman pulses, we investigate the transfer of the population in time domain. Furthermore, we show that this protocol can be reversed by applying a third adiabatic pulse, we study a hybrid nondiabatic-adiabatic sequence, and we present experimental results for a quasi-degenerate intermediate level.

Quantum electric-dipole liquid on a triangular lattice.

PubMed

Shen, Shi-Peng; Wu, Jia-Chuan; Song, Jun-Da; Sun, Xue-Feng; Yang, Yi-Feng; Chai, Yi-Sheng; Shang, Da-Shan; Wang, Shou-Guo; Scott, James F; Sun, Young

2016-02-04

Geometric frustration and quantum fluctuations may prohibit the formation of long-range ordering even at the lowest temperature, and therefore liquid-like ground states could be expected. A good example is the quantum spin liquid in frustrated magnets. Geometric frustration and quantum fluctuations can happen beyond magnetic systems. Here we propose that quantum electric-dipole liquids, analogues of quantum spin liquids, could emerge in frustrated dielectrics where antiferroelectrically coupled electric dipoles reside on a triangular lattice. The quantum paraelectric hexaferrite BaFe12O19 with geometric frustration represents a promising candidate for the proposed electric-dipole liquid. We present a series of experimental lines of evidence, including dielectric permittivity, heat capacity and thermal conductivity measured down to 66 mK, to reveal the existence of an unusual liquid-like quantum phase in BaFe12O19, characterized by itinerant low-energy excitations with a small gap. The possible quantum liquids of electric dipoles in frustrated dielectrics open up a fresh playground for fundamental physics.

Helicity conservation under quantum reconnection of vortex rings.

PubMed

Zuccher, Simone; Ricca, Renzo L

2015-12-01

Here we show that under quantum reconnection, simulated by using the three-dimensional Gross-Pitaevskii equation, self-helicity of a system of two interacting vortex rings remains conserved. By resolving the fine structure of the vortex cores, we demonstrate that the total length of the vortex system reaches a maximum at the reconnection time, while both writhe helicity and twist helicity remain separately unchanged throughout the process. Self-helicity is computed by two independent methods, and topological information is based on the extraction and analysis of geometric quantities such as writhe, total torsion, and intrinsic twist of the reconnecting vortex rings.

Experimental verification of steerability via geometric Bell-like inequalities

NASA Astrophysics Data System (ADS)

Li, Jian; Wang, Cen-Yang; Liu, Tong-Jun; Wang, Qin

2018-03-01

Quantum steering is one form of quantum correlations interpolating between entanglement and Bell nonlocality, which in some cases can be detected by various steering inequalities. Recently, a remarkable and useful steerability criterion via geometric Bell-like inequalities was established [M. Zukowski, A. Dutta, and Z. Yin, Phys. Rev. A 91, 032107 (2015), 10.1103/PhysRevA.91.032107]. We report an experimental investigation of this steering criterion and verify the geometric Bell-like steering inequality experimentally by using of the Werner states. The results demonstrate that the geometric Bell-like steering inequality is a convenient tool to detect quantum steering both theoretically and practically.

Compactness Aromaticity of Atoms in Molecules

PubMed Central

Putz, Mihai V.

2010-01-01

A new aromaticity definition is advanced as the compactness formulation through the ratio between atoms-in-molecule and orbital molecular facets of the same chemical reactivity property around the pre- and post-bonding stabilization limit, respectively. Geometrical reactivity index of polarizability was assumed as providing the benchmark aromaticity scale, since due to its observable character; with this occasion new Hydrogenic polarizability quantum formula that recovers the exact value of 4.5 a03 for Hydrogen is provided, where a0 is the Bohr radius; a polarizability based–aromaticity scale enables the introduction of five referential aromatic rules (Aroma 1 to 5 Rules). With the help of these aromatic rules, the aromaticity scales based on energetic reactivity indices of electronegativity and chemical hardness were computed and analyzed within the major semi-empirical and ab initio quantum chemical methods. Results show that chemical hardness based-aromaticity is in better agreement with polarizability based-aromaticity than the electronegativity-based aromaticity scale, while the most favorable computational environment appears to be the quantum semi-empirical for the first and quantum ab initio for the last of them, respectively. PMID:20480020

Quantum image encryption based on restricted geometric and color transformations

NASA Astrophysics Data System (ADS)

Song, Xian-Hua; Wang, Shen; Abd El-Latif, Ahmed A.; Niu, Xia-Mu

2014-08-01

A novel encryption scheme for quantum images based on restricted geometric and color transformations is proposed. The new strategy comprises efficient permutation and diffusion properties for quantum image encryption. The core idea of the permutation stage is to scramble the codes of the pixel positions through restricted geometric transformations. Then, a new quantum diffusion operation is implemented on the permutated quantum image based on restricted color transformations. The encryption keys of the two stages are generated by two sensitive chaotic maps, which can ensure the security of the scheme. The final step, measurement, is built by the probabilistic model. Experiments conducted on statistical analysis demonstrate that significant improvements in the results are in favor of the proposed approach.

Nonlinear dynamics of laser systems with elements of a chaos: Advanced computational code

NASA Astrophysics Data System (ADS)

Buyadzhi, V. V.; Glushkov, A. V.; Khetselius, O. Yu; Kuznetsova, A. A.; Buyadzhi, A. A.; Prepelitsa, G. P.; Ternovsky, V. B.

2017-10-01

A general, uniform chaos-geometric computational approach to analysis, modelling and prediction of the non-linear dynamics of quantum and laser systems (laser and quantum generators system etc) with elements of the deterministic chaos is briefly presented. The approach is based on using the advanced generalized techniques such as the wavelet analysis, multi-fractal formalism, mutual information approach, correlation integral analysis, false nearest neighbour algorithm, the Lyapunov’s exponents analysis, and surrogate data method, prediction models etc There are firstly presented the numerical data on the topological and dynamical invariants (in particular, the correlation, embedding, Kaplan-York dimensions, the Lyapunov’s exponents, Kolmogorov’s entropy and other parameters) for laser system (the semiconductor GaAs/GaAlAs laser with a retarded feedback) dynamics in a chaotic and hyperchaotic regimes.

On the role of dealing with quantum coherence in amplitude amplification

NASA Astrophysics Data System (ADS)

Rastegin, Alexey E.

2018-07-01

Amplitude amplification is one of primary tools in building algorithms for quantum computers. This technique generalizes key ideas of the Grover search algorithm. Potentially useful modifications are connected with changing phases in the rotation operations and replacing the intermediate Hadamard transform with arbitrary unitary one. In addition, arbitrary initial distribution of the amplitudes may be prepared. We examine trade-off relations between measures of quantum coherence and the success probability in amplitude amplification processes. As measures of coherence, the geometric coherence and the relative entropy of coherence are considered. In terms of the relative entropy of coherence, complementarity relations with the success probability seem to be the most expository. The general relations presented are illustrated within several model scenarios of amplitude amplification processes.

INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY: Efficient One-Step Generation of Cluster State with Charge Qubits in Circuit QED

NASA Astrophysics Data System (ADS)

Wang, Yi-Min; Li, Cheng-Zu

2010-01-01

We propose theoretical schemes to generate highly entangled cluster state with superconducting qubits in a circuit QED architecture. Charge qubits are located inside a superconducting transmission line, which serves as a quantum data bus. We show that large clusters state can be efficiently generated in just one step with the long-range Ising-like unitary operators. The quantum operations which are generally realized by two coupling mechanisms: either voltage coupling or current coupling, depend only on global geometric features and are insensitive not only to the thermal state of the transmission line but also to certain random operation errors. Thus high-fidelity one-way quantum computation can be achieved.

Hall viscosity and geometric response in the Chern-Simons matrix model of the Laughlin states

NASA Astrophysics Data System (ADS)

Lapa, Matthew F.; Hughes, Taylor L.

2018-05-01

We study geometric aspects of the Laughlin fractional quantum Hall (FQH) states using a description of these states in terms of a matrix quantum mechanics model known as the Chern-Simons matrix model (CSMM). This model was proposed by Polychronakos as a regularization of the noncommutative Chern-Simons theory description of the Laughlin states proposed earlier by Susskind. Both models can be understood as describing the electrons in a FQH state as forming a noncommutative fluid, i.e., a fluid occupying a noncommutative space. Here, we revisit the CSMM in light of recent work on geometric response in the FQH effect, with the goal of determining whether the CSMM captures this aspect of the physics of the Laughlin states. For this model, we compute the Hall viscosity, Hall conductance in a nonuniform electric field, and the Hall viscosity in the presence of anisotropy (or intrinsic geometry). Our calculations show that the CSMM captures the guiding center contribution to the known values of these quantities in the Laughlin states, but lacks the Landau orbit contribution. The interesting correlations in a Laughlin state are contained entirely in the guiding center part of the state/wave function, and so we conclude that the CSMM accurately describes the most important aspects of the physics of the Laughlin FQH states, including the Hall viscosity and other geometric properties of these states, which are of current interest.

Experimental limits on the fidelity of adiabatic geometric phase gates in a single solid-state spin qubit

DOE PAGES

Zhang, Kai; Nusran, N. M.; Slezak, B. R.; ...

2016-05-17

While it is often thought that the geometric phase is less sensitive to fluctuations in the control fields, a very general feature of adiabatic Hamiltonians is the unavoidable dynamic phase that accompanies the geometric phase. The effect of control field noise during adiabatic geometric quantum gate operations has not been probed experimentally, especially in the canonical spin qubit system that is of interest for quantum information. We present measurement of the Berry phase and carry out adiabatic geometric phase gate in a single solid-state spin qubit associated with the nitrogen-vacancy center in diamond. We manipulate the spin qubit geometrically bymore » careful application of microwave radiation that creates an effective rotating magnetic field, and observe the resulting Berry phase signal via spin echo interferometry. Our results show that control field noise at frequencies higher than the spin echo clock frequency causes decay of the quantum phase, and degrades the fidelity of the geometric phase gate to the classical threshold after a few (~10) operations. This occurs in spite of the geometric nature of the state preparation, due to unavoidable dynamic contributions. In conclusion, we have carried out systematic analysis and numerical simulations to study the effects of the control field noise and imperfect driving waveforms on the quantum phase gate.« less

Experimental limits on the fidelity of adiabatic geometric phase gates in a single solid-state spin qubit

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Kai; Nusran, N. M.; Slezak, B. R.

While it is often thought that the geometric phase is less sensitive to fluctuations in the control fields, a very general feature of adiabatic Hamiltonians is the unavoidable dynamic phase that accompanies the geometric phase. The effect of control field noise during adiabatic geometric quantum gate operations has not been probed experimentally, especially in the canonical spin qubit system that is of interest for quantum information. We present measurement of the Berry phase and carry out adiabatic geometric phase gate in a single solid-state spin qubit associated with the nitrogen-vacancy center in diamond. We manipulate the spin qubit geometrically bymore » careful application of microwave radiation that creates an effective rotating magnetic field, and observe the resulting Berry phase signal via spin echo interferometry. Our results show that control field noise at frequencies higher than the spin echo clock frequency causes decay of the quantum phase, and degrades the fidelity of the geometric phase gate to the classical threshold after a few (~10) operations. This occurs in spite of the geometric nature of the state preparation, due to unavoidable dynamic contributions. In conclusion, we have carried out systematic analysis and numerical simulations to study the effects of the control field noise and imperfect driving waveforms on the quantum phase gate.« less

Solving quantum optimal control problems using Clebsch variables and Lin constraints

NASA Astrophysics Data System (ADS)

Delgado-Téllez, M.; Ibort, A.; Rodríguez de la Peña, T.

2018-01-01

Clebsch variables (and Lin constraints) are applied to the study of a class of optimal control problems for affine-controlled quantum systems. The optimal control problem will be modelled with controls defined on an auxiliary space where the dynamical group of the system acts freely. The reciprocity between both theories: the classical theory defined by the objective functional and the quantum system, is established by using a suitable version of Lagrange’s multipliers theorem and a geometrical interpretation of the constraints of the system as defining a subspace of horizontal curves in an associated bundle. It is shown how the solutions of the variational problem defined by the objective functional determine solutions of the quantum problem. Then a new way of obtaining explicit solutions for a family of optimal control problems for affine-controlled quantum systems (finite or infinite dimensional) is obtained. One of its main advantages, is the the use of Clebsch variables allows to compute such solutions from solutions of invariant problems that can often be computed explicitly. This procedure can be presented as an algorithm that can be applied to a large class of systems. Finally, some simple examples, spin control, a simple quantum Hamiltonian with an ‘Elroy beanie’ type classical model and a controlled one-dimensional quantum harmonic oscillator, illustrating the main features of the theory, will be discussed.

Impact of nonlinear effective interactions on group field theory quantum gravity condensates

NASA Astrophysics Data System (ADS)

Pithis, Andreas G. A.; Sakellariadou, Mairi; Tomov, Petar

2016-09-01

We present the numerical analysis of effectively interacting group field theory models in the context of the group field theory quantum gravity condensate analog of the Gross-Pitaevskii equation for real Bose-Einstein condensates including combinatorially local interaction terms. Thus, we go beyond the usually considered construction for free models. More precisely, considering such interactions in a weak regime, we find solutions for which the expectation value of the number operator N is finite, as in the free case. When tuning the interaction to the strongly nonlinear regime, however, we obtain solutions for which N grows and eventually blows up, which is reminiscent of what one observes for real Bose-Einstein condensates, where a strong interaction regime can only be realized at high density. This behavior suggests the breakdown of the Bogoliubov ansatz for quantum gravity condensates and the need for non-Fock representations to describe the system when the condensate constituents are strongly correlated. Furthermore, we study the expectation values of certain geometric operators imported from loop quantum gravity in the free and interacting cases. In particular, computing solutions around the nontrivial minima of the interaction potentials, one finds, already in the weakly interacting case, a nonvanishing condensate population for which the spectra are dominated by the lowest nontrivial configuration of the quantum geometry. This result indicates that the condensate may indeed consist of many smallest building blocks giving rise to an effectively continuous geometry, thus suggesting the interpretation of the condensate phase to correspond to a geometric phase.

The geometric semantics of algebraic quantum mechanics.

PubMed

Cruz Morales, John Alexander; Zilber, Boris

2015-08-06

In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Quantum Computer Circuit Analysis and Design

DTIC Science & Technology

2009-02-01

is a first order nonlinear differential matrix equation of the Lax type. This report gives derivations of the Levi - Civita connection, Riemann...directions on the manifold not easily simulated by local gates. In this way, basic differential geometric concepts such as the Levi - Civita connection...and two - body terms, and Q(H) contains more than two - body terms. Thus ),()( HQHPH  (1) in which P and Q are superoperators (matrices) acting on

The Butterfly and the Photon:. New Perspectives on Unpredictability, and the Notion of Casual Reality, in Quantum Physics

NASA Astrophysics Data System (ADS)

Palmer, T. N.

2012-12-01

This essay discusses a proposal that draws together the three great revolutionary theories of 20th Century physics: quantum theory, relativity theory and chaos theory. Motivated by the Bohmian notion of implicate order, and what in chaos theory would be described as a strange attractor, the proposal attributes special ontological significance to certain non-computable, dynamically invariant state-space geometries for the universe as a whole. Studying the phenomenon of quantum interference, it is proposed to understand quantum wave-particle duality, and indeed classical electromagnetism, in terms of particles in space time and waves on this state space geometry. Studying the EPR experiment, the acausal constraints that this invariant geometry provides on spatially distant degrees of freedom, provides a way for the underlying dynamics to be consistent with the Bell theorem, yet be relativistically covariant ("nonlocality without nonlocality"). It is suggested that the physical basis for such non-computable geometries lies in properties of gravity with the information irreversibility implied by black hole no-hair theorems being crucial. In conclusion it is proposed that quantum theory may be emergent from an extended theory of gravity which is geometric not only in space time, but also in state space. Such a notion would undermine most current attempts to "quantise gravity".

Contact geometry and quantum mechanics

NASA Astrophysics Data System (ADS)

Herczeg, Gabriel; Waldron, Andrew

2018-06-01

We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime". We show that this covariant starting point makes quantization into a purely geometric flatness condition. This makes quantum mechanics purely geometric, and possibly even topological. Our approach is especially useful for time-dependent problems and systems subject to ambiguities in choices of clock or observer. As a byproduct, we give a derivation and generalization of the Wigner functions of standard quantum mechanics.

Hilbert-Schmidt Measure of Pairwise Quantum Discord for Three-Qubit X States

NASA Astrophysics Data System (ADS)

Daoud, M.; Laamara, R. Ahl; Seddik, S.

2015-10-01

The Hilbert-Schmidt distance between a mixed three-qubit state and its closest state is used to quantify the amount of pairwise quantum correlations in a tripartite system. Analytical expressions of geometric quantum discord are derived. A particular attention is devoted to two special classes of three-qubit X states. They include three-qubit states of W, GHZ and Bell type. We also discuss the monogamy property of geometric quantum discord in some mixed three-qubit systems.

Aspects of perturbation theory in quantum mechanics: The BenderWuMATHEMATICA® package

NASA Astrophysics Data System (ADS)

Sulejmanpasic, Tin; Ünsal, Mithat

2018-07-01

We discuss a general setup which allows the study of the perturbation theory of an arbitrary, locally harmonic 1D quantum mechanical potential as well as its multi-variable (many-body) generalization. The latter may form a prototype for regularized quantum field theory. We first generalize the method of Bender-Wu,and derive exact recursion relations which allow the determination of the perturbative wave-function and energy corrections to an arbitrary order, at least in principle. For 1D systems, we implement these equations in an easy to use MATHEMATICA® package we call BenderWu. Our package enables quick home-computer computation of high orders of perturbation theory (about 100 orders in 10-30 s, and 250 orders in 1-2 h) and enables practical study of a large class of problems in Quantum Mechanics. We have two hopes concerning the BenderWu package. One is that due to resurgence, large amount of non-perturbative information, such as non-perturbative energies and wave-functions (e.g. WKB wave functions), can in principle be extracted from the perturbative data. We also hope that the package may be used as a teaching tool, providing an effective bridge between perturbation theory and non-perturbative physics in textbooks. Finally, we show that for the multi-variable case, the recursion relation acquires a geometric character, and has a structure which allows parallelization to computer clusters.

CNOT sequences for heterogeneous spin qubit architectures in a noisy environment

NASA Astrophysics Data System (ADS)

Ferraro, Elena; Fanciulli, Marco; de Michielis, Marco

Explicit CNOT gate sequences for two-qubits mixed architectures are presented in view of applications for large-scale quantum computation. Different kinds of coded spin qubits are combined allowing indeed the favorable physical properties of each to be employed. The building blocks for such composite systems are qubit architectures based on the electronic spin in electrostatically defined semiconductor quantum dots. They are the single quantum dot spin qubit, the double quantum dot singlet-triplet qubit and the double quantum dot hybrid qubit. The effective Hamiltonian models expressed by only exchange interactions between pair of electrons are exploited in different geometrical configurations. A numerical genetic algorithm that takes into account the realistic physical parameters involved is adopted. Gate operations are addressed by modulating the tunneling barriers and the energy offsets between different couple of quantum dots. Gate infidelities are calculated considering limitations due to unideal control of gate sequence pulses, hyperfine interaction and unwanted charge coupling. Second affiliation: Dipartimento di Scienza dei Materiali, University of Milano Bicocca, Via R. Cozzi, 55, 20126 Milano, Italy.

Geometrical Phases in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Christian, Joy Julius

In quantum mechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantum mechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a truly quantum regime, and allows, for the first time, the measurements of such phases associated with arbitrary non-cyclic evolutions of entangled linear-momentum photon -states. This non-classical manifestation of the geometrical phases is due to the entangled character of linear-momentum photon-states of two correlated photons produced by parametric down-conversion in non-linear crystals. Finally, the non-local aspect of the geometrical phase is contrasted with the fundamental non-locality of quantum mechanics due to the entangled character of quantum states.

Enzymatic Kinetic Isotope Effects from Path-Integral Free Energy Perturbation Theory.

PubMed

Gao, J

2016-01-01

Path-integral free energy perturbation (PI-FEP) theory is presented to directly determine the ratio of quantum mechanical partition functions of different isotopologs in a single simulation. Furthermore, a double averaging strategy is used to carry out the practical simulation, separating the quantum mechanical path integral exactly into two separate calculations, one corresponding to a classical molecular dynamics simulation of the centroid coordinates, and another involving free-particle path-integral sampling over the classical, centroid positions. An integrated centroid path-integral free energy perturbation and umbrella sampling (PI-FEP/UM, or simply, PI-FEP) method along with bisection sampling was summarized, which provides an accurate and fast convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. The PI-FEP method is illustrated by a number of applications, to highlight the computational precision and accuracy, the rule of geometrical mean in kinetic isotope effects, enhanced nuclear quantum effects in enzyme catalysis, and protein dynamics on temperature dependence of kinetic isotope effects. © 2016 Elsevier Inc. All rights reserved.

Optimization of topological quantum algorithms using Lattice Surgery is hard

NASA Astrophysics Data System (ADS)

Herr, Daniel; Nori, Franco; Devitt, Simon

The traditional method for computation in the surface code or the Raussendorf model is the creation of holes or ''defects'' within the encoded lattice of qubits which are manipulated via topological braiding to enact logic gates. However, this is not the only way to achieve universal, fault-tolerant computation. In this work we turn attention to the Lattice Surgery representation, which realizes encoded logic operations without destroying the intrinsic 2D nearest-neighbor interactions sufficient for braided based logic and achieves universality without using defects for encoding information. In both braided and lattice surgery logic there are open questions regarding the compilation and resource optimization of quantum circuits. Optimization in braid-based logic is proving to be difficult to define and the classical complexity associated with this problem has yet to be determined. In the context of lattice surgery based logic, we can introduce an optimality condition, which corresponds to a circuit with lowest amount of physical qubit requirements, and prove that the complexity of optimizing the geometric (lattice surgery) representation of a quantum circuit is NP-hard.

Quantum Hall states and conformal field theory on a singular surface

NASA Astrophysics Data System (ADS)

Can, T.; Wiegmann, P.

2017-12-01

In Can et al (2016 Phys. Rev. Lett. 117), quantum Hall states on singular surfaces were shown to possess an emergent conformal symmetry. In this paper, we develop this idea further and flesh out details on the emergent conformal symmetry in holomorphic adiabatic states, which we define in the paper. We highlight the connection between the universal features of geometric transport of quantum Hall states and holomorphic dimension of primary fields in conformal field theory. In parallel we compute the universal finite-size corrections to the free energy of a critical system on a hyperbolic sphere with conical and cusp singularities, thus extending the result of Cardy and Peschel for critical systems on a flat cone (Cardy and Peschel 1988 Nucl. Phys. B 300 377-92), and the known results for critical systems on polyhedra and flat branched Riemann surfaces.

Optimal ancilla-free Pauli+V circuits for axial rotations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blass, Andreas; Bocharov, Alex; Gurevich, Yuri

We address the problem of optimal representation of single-qubit rotations in a certain unitary basis consisting of the so-called V gates and Pauli matrices. The V matrices were proposed by Lubotsky, Philips, and Sarnak [Commun. Pure Appl. Math. 40, 401–420 (1987)] as a purely geometric construct in 1987 and recently found applications in quantum computation. They allow for exceptionally simple quantum circuit synthesis algorithms based on quaternionic factorization. We adapt the deterministic-search technique initially proposed by Ross and Selinger to synthesize approximating Pauli+V circuits of optimal depth for single-qubit axial rotations. Our synthesis procedure based on simple SL{sub 2}(ℤ) geometrymore » is almost elementary.« less

Modeling Electronic Quantum Transport with Machine Learning

DOE PAGES

Lopez Bezanilla, Alejandro; von Lilienfeld Toal, Otto A.

2014-06-11

We present a machine learning approach to solve electronic quantum transport equations of one-dimensional nanostructures. The transmission coefficients of disordered systems were computed to provide training and test data sets to the machine. The system’s representation encodes energetic as well as geometrical information to characterize similarities between disordered configurations, while the Euclidean norm is used as a measure of similarity. Errors for out-of-sample predictions systematically decrease with training set size, enabling the accurate and fast prediction of new transmission coefficients. The remarkable performance of our model to capture the complexity of interference phenomena lends further support to its viability inmore » dealing with transport problems of undulatory nature.« less

Geometry of the Adiabatic Theorem

ERIC Educational Resources Information Center

Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas

2012-01-01

We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…

Geometric and Topological Methods for Quantum Field Theory

NASA Astrophysics Data System (ADS)

Cardona, Alexander; Contreras, Iván.; Reyes-Lega, Andrés. F.

2013-05-01

Introduction; 1. A brief introduction to Dirac manifolds Henrique Bursztyn; 2. Differential geometry of holomorphic vector bundles on a curve Florent Schaffhauser; 3. Paths towards an extension of Chern-Weil calculus to a class of infinite dimensional vector bundles Sylvie Paycha; 4. Introduction to Feynman integrals Stefan Weinzierl; 5. Iterated integrals in quantum field theory Francis Brown; 6. Geometric issues in quantum field theory and string theory Luis J. Boya; 7. Geometric aspects of the standard model and the mysteries of matter Florian Scheck; 8. Absence of singular continuous spectrum for some geometric Laplacians Leonardo A. Cano García; 9. Models for formal groupoids Iván Contreras; 10. Elliptic PDEs and smoothness of weakly Einstein metrics of Hölder regularity Andrés Vargas; 11. Regularized traces and the index formula for manifolds with boundary Alexander Cardona and César Del Corral; Index.

Geometric descriptions of entangled states by auxiliary varieties

NASA Astrophysics Data System (ADS)

Holweck, Frédéric; Luque, Jean-Gabriel; Thibon, Jean-Yves

2012-10-01

The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an open subset of an algebraic variety built by classical geometric constructions (tangent lines, secant lines) from the set of separable states. In this setting, we describe well-known classifications of multipartite entanglement such as 2 × 2 × (n + 1), for n ⩾ 1, quantum systems and a new description with the 2 × 3 × 3 quantum system. Our results complete the approach of Miyake and make stronger connections with recent work of algebraic geometers. Moreover, for the quantum systems detailed in this paper, we propose an algorithm, based on the classical theory of invariants, to decide to which subvariety of the Hilbert space a given state belongs.

Importance of geometric phase effects in ultracold chemistry

DOE PAGES

Hazra, Jisha; Kendrick, Brian K.; Balakrishnan, Naduvalath

2015-08-28

Here, it is demonstrated that the inclusion of the geometric phase has an important effect on ultracold chemical reaction rates. The effect appears in rotationally and vibrationally resolved integral cross sections as well as cross sections summed over all product quantum states. The effect arises from interference between scattering amplitudes of two reaction pathways: a direct path and a looping path that encircle the conical intersection between the two lowest adiabatic electronic potential energy surfaces. It is magnified when the two scattering amplitudes have comparable magnitude and they scatter into the same angular region which occurs in the isotropic scatteringmore » characteristic of the ultracold regime (s-wave scattering). Results are presented for the O + OH → H + O 2 reaction for total angular momentum quantum number J = 0–5. Large geometric phase effects occur for collision energies below 0.1 K, but the effect vanishes at higher energies when contributions from different partial waves are included. It is also qualitatively demonstrated that the geometric phase effect can be modulated by applying an external electric field allowing the possibility of quantum control of chemical reactions in the ultracold regime. In this case, the geometric phase plays the role of a “quantum switch” which can turn the reaction “on” or “off”.« less

Holonomic Quantum Control by Coherent Optical Excitation in Diamond.

PubMed

Zhou, Brian B; Jerger, Paul C; Shkolnikov, V O; Heremans, F Joseph; Burkard, Guido; Awschalom, David D

2017-10-06

Although geometric phases in quantum evolution are historically overlooked, their active control now stimulates strategies for constructing robust quantum technologies. Here, we demonstrate arbitrary single-qubit holonomic gates from a single cycle of nonadiabatic evolution, eliminating the need to concatenate two separate cycles. Our method varies the amplitude, phase, and detuning of a two-tone optical field to control the non-Abelian geometric phase acquired by a nitrogen-vacancy center in diamond over a coherent excitation cycle. We demonstrate the enhanced robustness of detuned gates to excited-state decoherence and provide insights for optimizing fast holonomic control in dissipative quantum systems.

Aspects of Geodesical Motion with Fisher-Rao Metric: Classical and Quantum

NASA Astrophysics Data System (ADS)

Ciaglia, Florio M.; Cosmo, Fabio Di; Felice, Domenico; Mancini, Stefano; Marmo, Giuseppe; Pérez-Pardo, Juan M.

The purpose of this paper is to exploit the geometric structure of quantum mechanics and of statistical manifolds to study the qualitative effect that the quantum properties have in the statistical description of a system. We show that the end points of geodesics in the classical setting coincide with the probability distributions that minimise Shannon’s entropy, i.e. with distributions of zero dispersion. In the quantum setting this happens only for particular initial conditions, which in turn correspond to classical submanifolds. This result can be interpreted as a geometric manifestation of the uncertainty principle.

Holonomic Quantum Control by Coherent Optical Excitation in Diamond

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, Brian B.; Jerger, Paul C.; Shkolnikov, V. O.

Although geometric phases in quantum evolution are historically overlooked, their active control now stimulates strategies for constructing robust quantum technologies. Here, we demonstrate arbitrary singlequbit holonomic gates from a single cycle of nonadiabatic evolution, eliminating the need to concatenate two separate cycles. Our method varies the amplitude, phase, and detuning of a two-tone optical field to control the non-Abelian geometric phase acquired by a nitrogen-vacancy center in diamond over a coherent excitation cycle. We demonstrate the enhanced robustness of detuned gates to excited-state decoherence and provide insights for optimizing fast holonomic control in dissipative quantum systems.

EPRL/FK asymptotics and the flatness problem

NASA Astrophysics Data System (ADS)

Oliveira, José Ricardo

2018-05-01

Spin foam models are an approach to quantum gravity based on the concept of sum over states, which aims to describe quantum spacetime dynamics in a way that its parent framework, loop quantum gravity, has not as of yet succeeded. Since these models’ relation to classical Einstein gravity is not explicit, an important test of their viabilitiy is the study of asymptotics—the classical theory should be obtained in a limit where quantum effects are negligible, taken to be the limit of large triangle areas in a triangulated manifold with boundary. In this paper we will briefly introduce the EPRL/FK spin foam model and known results about its asymptotics, proceeding then to describe a practical computation of spin foam and semiclassical geometric data for a simple triangulation with only one interior triangle. The results are used to comment on the ‘flatness problem’—a hypothesis raised by Bonzom (2009 Phys. Rev. D 80 064028) suggesting that EPRL/FK’s classical limit only describes flat geometries in vacuum.

A Non-Abelian Geometric Phase for Spin Systems

NASA Astrophysics Data System (ADS)

H M, Bharath; Boguslawski, Matthew; Barrios, Maryrose; Chapman, Michael

Berry's geometric phase has been used to characterize topological phase transitions. Recent works have addressed the question of whether generalizations of Berry's phase to mixed states can be used to characterize topological phase transitions. Berry's phase is essentially the geometric information stored in the overall phase of a quantum system. Here, we show that geometric information is also stored in the higher order spin moments of a quantum spin system. In particular, we show that when the spin vector of a quantum spin system with a spin 1 or higher is transported along a closed path inside the Bloch ball, the tensor of second moments picks up a geometric phase in the form of an SO(3) operator. Geometrically interpreting this phase is tantamount to defining a steradian angle for closed paths inside the Bloch ball. Typically the steradian angle is defined by projecting the path onto the surface of the Bloch ball. However, paths that pass through the center cannot be projected onto the surface. We show that the steradian angles of all paths, including those that pass through the center can be defined by projecting them onto a real projective plane, instead of a sphere. This steradian angle is equal to the geometric phase picked up by a spin system.

Unitary easy quantum groups: Geometric aspects

NASA Astrophysics Data System (ADS)

Banica, Teodor

2018-03-01

We discuss the classification problem for the unitary easy quantum groups, under strong axioms, of noncommutative geometric nature. Our main results concern the intermediate easy quantum groups ON ⊂ G ⊂ UN+ . To any such quantum group we associate its Schur-Weyl twist G ¯ , two noncommutative spheres S , S ¯ , a noncommutative torus T, and a quantum reflection group K. Studying (S , S ¯ , T , K , G , G ¯) leads then to some natural axioms, which can be used in order to investigate G itself. We prove that the main examples are covered by our formalism, and we conjecture that in what concerns the case UN ⊂ G ⊂ UN+ , our axioms should restrict the list of known examples.

Binding energy and photoionization cross-section of hydrogen-like donor impurity in strongly oblate ellipsoidal quantum dot

NASA Astrophysics Data System (ADS)

Hayrapetyan, D. B.; Ohanyan, G. L.; Baghdasaryan, D. A.; Sarkisyan, H. A.; Baskoutas, S.; Kazaryan, E. M.

2018-01-01

Hydrogen-like donor impurity states in strongly oblate ellipsoidal quantum dot have been studied. The hydrogen-like donor impurity states are investigated within the framework of variational method. The trial wave function constructed on the base of wave functions of the system without impurity. The dependence of the energy and binding energy for the ground and first excited states on the geometrical parameters of the ellipsoidal quantum dot and on the impurity position have been calculated. The behavior of the oscillator strength for different angles of incident light and geometrical parameters have been revealed. Photoionization cross-section of the electron transitions from the impurity ground state to the size-quantized ground and first excited states have been studied. The effects of impurity position and the geometrical parameters of the ellipsoidal quantum dot on the photoionization cross section dependence on the photon energy have been considered.

Vibronic eigenstates and the geometric phase effect in the 2E″ state of NO3.

PubMed

Eisfeld, Wolfgang; Viel, Alexandra

2017-01-21

The 2 E″ state of NO 3 , a prototype for the Jahn-Teller effect, has been an enigma and a challenge for a long time for both experiment and theory. We present a detailed theoretical study of the vibronic quantum dynamics in this electronic state, uncovering the effects of tunnelling, geometric phase, and symmetry. To this end, 45 vibronic levels of NO 3 in the 2 E″ state are determined accurately and analyzed thoroughly. The computation is based on a high quality diabatic potential representation of the two-sheeted surface of the 2 E″ state developed by us [W. Eisfeld et al., J. Chem. Phys. 140, 224109 (2014)] and on the multi-configuration time dependent Hartree approach. The vibrational eigenstates of the NO 3 - anion are determined and analyzed as well to gain a deeper understanding of the symmetry properties of such D 3h symmetric systems. To this end, 61 eigenstates of the NO 3 - anion ground state are computed using the single sheeted potential surface of the 1 A 1 state published in the same reference quoted above. The assignments of both the vibrational and vibronic levels are discussed. A simple model is proposed to rationalize the computed NO 3 spectrum strongly influenced by the Jahn-Teller couplings, the associated geometric phase effect, and the tunnelling. Comparison with the available spectroscopic data is also presented.

Gravity at a Quantum Condensate

NASA Astrophysics Data System (ADS)

Atanasov, Victor

2017-07-01

Provided a quantum superconducting condensate is allowed to occupy a curved hyper-plane of space-time, a geometric potential from the kinetic term arises. An energy conservation relation involving the geometric field at every material point in the superconductor can be demonstrated. The induced three-dimensional scalar curvature is directly related to the wavefunction/order parameter of the quantum condensate thus pointing the way to a possible experimental procedure to artificially induce curvature of space-time via change in the electric/probability current density.

Characterizing and quantifying frustration in quantum many-body systems.

PubMed

Giampaolo, S M; Gualdi, G; Monras, A; Illuminati, F

2011-12-23

We present a general scheme for the study of frustration in quantum systems. We introduce a universal measure of frustration for arbitrary quantum systems and we relate it to a class of entanglement monotones via an exact inequality. If all the (pure) ground states of a given Hamiltonian saturate the inequality, then the system is said to be inequality saturating. We introduce sufficient conditions for a quantum spin system to be inequality saturating and confirm them with extensive numerical tests. These conditions provide a generalization to the quantum domain of the Toulouse criteria for classical frustration-free systems. The models satisfying these conditions can be reasonably identified as geometrically unfrustrated and subject to frustration of purely quantum origin. Our results therefore establish a unified framework for studying the intertwining of geometric and quantum contributions to frustration.

Revised Geometric Measure of Entanglement in Infinite Dimensional Multipartite Quantum Systems

NASA Astrophysics Data System (ADS)

Wang, Yinzhu; Wang, Danxia; Huang, Li

2018-05-01

In Cao and Wang (J. Phys.: Math. Theor. 40, 3507-3542, 2007), the revised geometric measure of entanglement (RGME) for states in finite dimensional bipartite quantum systems was proposed. Furthermore, in Cao and Wang (Commun. Theor. Phys. 51(4), 613-620, 2009), the authors obtained the revised geometry measure of entanglement for multipartite states including three-qubit GHZ state, W state, and the generalized Smolin state in the presence of noise and the two-mode squeezed thermal state, and defined the Gaussian geometric entanglement measure. In this paper, we generalize the RGME to infinite dimensional multipartite quantum systems, and prove that this measure satisfies some necessary properties as a well-defined entanglement measure, including monotonicity under local operations and classical communications.

Quantum no-singularity theorem from geometric flows

NASA Astrophysics Data System (ADS)

Alsaleh, Salwa; Alasfar, Lina; Faizal, Mir; Ali, Ahmed Farag

2018-04-01

In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects.

Vibronic Coupling Investigation to Compute Phosphorescence Spectra of Pt(II) Complexes.

PubMed

Vazart, Fanny; Latouche, Camille; Bloino, Julien; Barone, Vincenzo

2015-06-01

The present paper reports a comprehensive quantum mechanical investigation on the luminescence properties of several mono- and dinuclear platinum(II) complexes. The electronic structures and geometric parameters are briefly analyzed together with the absorption bands of all complexes. In all cases agreement with experiment is remarkable. Next, emission (phosphorescence) spectra from the first triplet states have been investigated by comparing different computational approaches and taking into account also vibronic effects. Once again, agreement with experiment is good, especially using unrestricted electronic computations coupled to vibronic contributions. Together with the intrinsic interest of the results, the robustness and generality of the approach open the opportunity for computationally oriented chemists to provide accurate results for the screening of large targets which could be of interest in molecular materials design.

Geometry of discrete quantum computing

NASA Astrophysics Data System (ADS)

Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr; Tai, Yu-Tsung

2013-05-01

Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2n infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields \\mathbf {F}_{p^2} (based on primes p congruent to 3 (mod4)) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space \\mathbf {CP}^{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p + 1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to \\mathbf {DCP}^{2^{n}-1}, the discrete analogue of the complex projective space, which has p^{2^{n}-1} (p-1)\\,\\prod _{k=1}^{n-1} ( p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field \\mathbf {F}_{p^2} have pn(p - 1)n unentangled states (the product of the tally for a single qubit) with purity 1, and they have pn + 1(p - 1)(p + 1)n - 1 maximally entangled states with purity zero.

Stimulated Raman adiabatic control of a nuclear spin in diamond

NASA Astrophysics Data System (ADS)

Coto, Raul; Jacques, Vincent; Hétet, Gabriel; Maze, Jerónimo R.

2017-08-01

Coherent manipulation of nuclear spins is a highly desirable tool for both quantum metrology and quantum computation. However, most of the current techniques to control nuclear spins lack fast speed, impairing their robustness against decoherence. Here, based on stimulated Raman adiabatic passage, and its modification including shortcuts to adiabaticity, we present a fast protocol for the coherent manipulation of nuclear spins. Our proposed Λ scheme is implemented in the microwave domain and its excited-state relaxation can be optically controlled through an external laser excitation. These features allow for the initialization of a nuclear spin starting from a thermal state. Moreover we show how to implement Raman control for performing Ramsey spectroscopy to measure the dynamical and geometric phases acquired by nuclear spins.

Quantum speed limits: from Heisenberg’s uncertainty principle to optimal quantum control

NASA Astrophysics Data System (ADS)

Deffner, Sebastian; Campbell, Steve

2017-11-01

One of the most widely known building blocks of modern physics is Heisenberg’s indeterminacy principle. Among the different statements of this fundamental property of the full quantum mechanical nature of physical reality, the uncertainty relation for energy and time has a special place. Its interpretation and its consequences have inspired continued research efforts for almost a century. In its modern formulation, the uncertainty relation is understood as setting a fundamental bound on how fast any quantum system can evolve. In this topical review we describe important milestones, such as the Mandelstam-Tamm and the Margolus-Levitin bounds on the quantum speed limit, and summarise recent applications in a variety of current research fields—including quantum information theory, quantum computing, and quantum thermodynamics amongst several others. To bring order and to provide an access point into the many different notions and concepts, we have grouped the various approaches into the minimal time approach and the geometric approach, where the former relies on quantum control theory, and the latter arises from measuring the distinguishability of quantum states. Due to the volume of the literature, this topical review can only present a snapshot of the current state-of-the-art and can never be fully comprehensive. Therefore, we highlight but a few works hoping that our selection can serve as a representative starting point for the interested reader.

Diamagnetic susceptibility of a hydrogenic donor in a group IV-VI quantum dot-quantum well heterostructure

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saravanamoorthy, S. N.; Peter, A. John, E-mail: a.john.peter@gmail.com

2016-05-23

Electronic properties of a hydrogenic donor impurity in a CdSe/Pb{sub 0.8}Cd{sub 0.2}Se/CdSe quantum dot quantum well system are investigated for various radii of core with shell materials. Confined energies are obtained taking into account the geometrical size of the system and thereby the donor binding energies are found. The diamagnetic susceptibility is estimated for a confined shallow donor in the well system. The results show that the diamagnetic susceptibility strongly depends on core and shell radii and it is more sensitive to variations of the geometrical size of the well material.

High quantum efficiency photocathode simulation for the investigation of novel structured designs

DOE PAGES

MacPhee, A. G.; Nagel, S. R.; Bell, P. M.; ...

2014-09-02

A computer model in CST Studio Suite has been developed to evaluate several novel geometrically enhanced photocathode designs. This work was aimed at identifying a structure that would increase the total electron yield by a factor of two or greater in the 1–30 keV range. The modeling software was used to simulate the electric field and generate particle tracking for several potential structures. The final photocathode structure has been tailored to meet a set of detector performance requirements, namely, a spatial resolution of <40 μm and a temporal spread of 1–10 ps. As a result, we present the details ofmore » the geometrically enhanced photocathode model and resulting static field and electron emission characteristics.« less

Robustness against parametric noise of nonideal holonomic gates

NASA Astrophysics Data System (ADS)

Lupo, Cosmo; Aniello, Paolo; Napolitano, Mario; Florio, Giuseppe

2007-07-01

Holonomic gates for quantum computation are commonly considered to be robust against certain kinds of parametric noise, the cause of this robustness being the geometric character of the transformation achieved in the adiabatic limit. On the other hand, the effects of decoherence are expected to become more and more relevant when the adiabatic limit is approached. Starting from the system described by Florio [Phys. Rev. A 73, 022327 (2006)], here we discuss the behavior of nonideal holonomic gates at finite operational time, i.e., long before the adiabatic limit is reached. We have considered several models of parametric noise and studied the robustness of finite-time gates. The results obtained suggest that the finite-time gates present some effects of cancellation of the perturbations introduced by the noise which mimic the geometrical cancellation effect of standard holonomic gates. Nevertheless, a careful analysis of the results leads to the conclusion that these effects are related to a dynamical instead of a geometrical feature.

A note on the Poisson bracket of 2d smeared fluxes in loop quantum gravity

NASA Astrophysics Data System (ADS)

Cattaneo, Alberto S.; Perez, Alejandro

2017-05-01

We show that the non-Abelian nature of geometric fluxes—the corner-stone in the definition of quantum geometry in the framework of loop quantum gravity (LQG)—follows directly form the continuum canonical commutations relations of gravity in connection variables and the validity of the Gauss law. The present treatment simplifies previous formulations and thus identifies more clearly the root of the discreteness of geometric operators in LQG. Our statement generalizes to arbitrary gauge theories and relies only on the validity of the Gauss law.

Geometric descriptions of entangled states by auxiliary varieties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Holweck, Frederic; Luque, Jean-Gabriel; Thibon, Jean-Yves

2012-10-15

The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an open subset of an algebraic variety built by classical geometric constructions (tangent lines, secant lines) from the set of separable states. In this setting, we describe well-known classifications of multipartite entanglement such as 2 Multiplication-Sign 2 Multiplication-Sign (n+ 1), for n Greater-Than-Or-Slanted-Equal-To 1, quantum systems and a new description with the 2 Multiplication-Sign 3 Multiplication-Sign 3 quantum system. Our results complete themore » approach of Miyake and make stronger connections with recent work of algebraic geometers. Moreover, for the quantum systems detailed in this paper, we propose an algorithm, based on the classical theory of invariants, to decide to which subvariety of the Hilbert space a given state belongs.« less

On the geometrization of quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tavernelli, Ivano, E-mail: ita@zurich.ibm.com

Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schrödinger equations (SE). Despite the success of this representation of the quantum world a wave–particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie–Bohm theory according to which a pilot-wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantum mechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is inducedmore » by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space–time, as it is the case for gravitation in the general relativity.« less

Investigation of anticancer properties of caffeinated complexes via computational chemistry methods

NASA Astrophysics Data System (ADS)

Sayin, Koray; Üngördü, Ayhan

2018-03-01

Computational investigations were performed for 1,3,7-trimethylpurine-2,6-dione, 3,7-dimethylpurine-2,6-dione, their Ru(II) and Os(III) complexes. B3LYP/6-311 ++G(d,p)(LANL2DZ) level was used in numerical calculations. Geometric parameters, IR spectrum, 1H-, 13C and 15N NMR spectrum were examined in detail. Additionally, contour diagram of frontier molecular orbitals (FMOs), molecular electrostatic potential (MEP) maps, MEP contour and some quantum chemical descriptors were used in the determination of reactivity rankings and active sites. The electron density on the surface was similar to each other in studied complexes. Quantum chemical descriptors were investigated and the anticancer activity of complexes were more than cisplatin and their ligands. Additionally, molecular docking calculations were performed in water between related complexes and a protein (ID: 3WZE). The most interact complex was found as Os complex. The interaction energy was calculated as 342.9 kJ/mol.

Information geometry of Gaussian channels

DOE Office of Scientific and Technical Information (OSTI.GOV)

Monras, Alex; CNR-INFM Coherentia, Napoli; CNISM Unita di Salerno

2010-06-15

We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The resulting metric inherits several desirable properties from the Bures-Fisher metric and is operationally motivated by distinguishability considerations: It serves as an upper bound to the attainable quantum Fisher information for the channel parameters using Gaussian states, under generic constraints on the physically available resources. Our approach naturally includes the use of entangled Gaussian probe states. We prove that the metric enjoys some desirablemore » properties like stability and covariance. As a by-product, we also obtain some general results in Gaussian channel estimation that are the continuous-variable analogs of previously known results in finite dimensions. We prove that optimal probe states are always pure and bounded in the number of ancillary modes, even in the presence of constraints on the reduced state input in the channel. This has experimental and computational implications. It limits the complexity of optimal experimental setups for channel estimation and reduces the computational requirements for the evaluation of the metric: Indeed, we construct a converging algorithm for its computation. We provide explicit formulas for computing the multiparametric quantum Fisher information for dissipative channels probed with arbitrary Gaussian states and provide the optimal observables for the estimation of the channel parameters (e.g., bath couplings, squeezing, and temperature).« less

Quantum correlations are weaved by the spinors of the Euclidean primitives

PubMed Central

2018-01-01

The exceptional Lie group E8 plays a prominent role in both mathematics and theoretical physics. It is the largest symmetry group associated with the most general possible normed division algebra, namely, that of the non-associative real octonions, which—thanks to their non-associativity—form the only possible closed set of spinors (or rotors) that can parallelize the 7-sphere. By contrast, here we show how a similar 7-sphere also arises naturally from the algebraic interplay of the graded Euclidean primitives, such as points, lines, planes and volumes, which characterize the three-dimensional conformal geometry of the ambient physical space, set within its eight-dimensional Clifford-algebraic representation. Remarkably, the resulting algebra remains associative, and allows us to understand the origins and strengths of all quantum correlations locally, in terms of the geometry of the compactified physical space, namely, that of a quaternionic 3-sphere, S3, with S7 being its algebraic representation space. Every quantum correlation can thus be understood as a correlation among a set of points of this S7, computed using manifestly local spinors within S3, thereby extending the stringent bounds of ±2 set by Bell inequalities to the bounds of ±22 on the strengths of all possible strong correlations, in the same quantitatively precise manner as that predicted within quantum mechanics. The resulting geometrical framework thus overcomes Bell’s theorem by producing a strictly deterministic and realistic framework that allows a locally causal understanding of all quantum correlations, without requiring either remote contextuality or backward causation. We demonstrate this by first proving a general theorem concerning the geometrical origins of the correlations predicted by arbitrarily entangled quantum states, and then reproducing the correlations predicted by the EPR-Bohm and the GHZ states. The raison d’être of strong correlations turns out to be the Möbius-like twists in the Hopf bundles of S3 and S7. PMID:29893385

Canonical methods in classical and quantum gravity: An invitation to canonical LQG

NASA Astrophysics Data System (ADS)

Reyes, Juan D.

2018-04-01

Loop Quantum Gravity (LQG) is a candidate quantum theory of gravity still under construction. LQG was originally conceived as a background independent canonical quantization of Einstein’s general relativity theory. This contribution provides some physical motivations and an overview of some mathematical tools employed in canonical Loop Quantum Gravity. First, Hamiltonian classical methods are reviewed from a geometric perspective. Canonical Dirac quantization of general gauge systems is sketched next. The Hamiltonian formultation of gravity in geometric ADM and connection-triad variables is then presented to finally lay down the canonical loop quantization program. The presentation is geared toward advanced undergradute or graduate students in physics and/or non-specialists curious about LQG.

BFV quantization on hermitian symmetric spaces

NASA Astrophysics Data System (ADS)

Fradkin, E. S.; Linetsky, V. Ya.

1995-02-01

Gauge-invariant BFV approach to geometric quantization is applied to the case of hermitian symmetric spaces G/ H. In particular, gauge invariant quantization on the Lobachevski plane and sphere is carried out. Due to the presence of symmetry, master equations for the first-class constraints, quantum observables and physical quantum states are exactly solvable. BFV-BRST operator defines a flat G-connection in the Fock bundle over G/ H. Physical quantum states are covariantly constant sections with respect to this connection and are shown to coincide with the generalized coherent states for the group G. Vacuum expectation values of the quantum observables commuting with the quantum first-class constraints reduce to the covariant symbols of Berezin. The gauge-invariant approach to quantization on symplectic manifolds synthesizes geometric, deformation and Berezin quantization approaches.

Analysis of two-player quantum games in an EPR setting using Clifford's geometric algebra.

PubMed

Chappell, James M; Iqbal, Azhar; Abbott, Derek

2012-01-01

The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR) type setting is investigated using the mathematical formalism of geometric algebra (GA). The main advantage of this framework is that the players' strategy sets remain identical to the ones in the classical mixed-strategy version of the game, and hence the quantum game becomes a proper extension of the classical game, avoiding a criticism of other quantum game frameworks. We produce a general solution for two-player games, and as examples, we analyze the games of Prisoners' Dilemma and Stag Hunt in the EPR setting. The use of GA allows a quantum-mechanical analysis without the use of complex numbers or the Dirac Bra-ket notation, and hence is more accessible to the non-physicist.

Analysis of Two-Player Quantum Games in an EPR Setting Using Clifford's Geometric Algebra

PubMed Central

Chappell, James M.; Iqbal, Azhar; Abbott, Derek

2012-01-01

The framework for playing quantum games in an Einstein-Podolsky-Rosen (EPR) type setting is investigated using the mathematical formalism of geometric algebra (GA). The main advantage of this framework is that the players' strategy sets remain identical to the ones in the classical mixed-strategy version of the game, and hence the quantum game becomes a proper extension of the classical game, avoiding a criticism of other quantum game frameworks. We produce a general solution for two-player games, and as examples, we analyze the games of Prisoners' Dilemma and Stag Hunt in the EPR setting. The use of GA allows a quantum-mechanical analysis without the use of complex numbers or the Dirac Bra-ket notation, and hence is more accessible to the non-physicist. PMID:22279525

Gaussian geometric discord in terms of Hellinger distance

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suciu, Serban, E-mail: serban.suciu@theory.nipne.ro; Isar, Aurelian

2015-12-07

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we address the quantification of general non-classical correlations in Gaussian states of continuous variable systems from a geometric perspective. We give a description of the Gaussian geometric discord by using the Hellinger distance as a measure for quantum correlations between two non-interacting non-resonant bosonic modes embedded in a thermal environment. We evaluate the Gaussian geometric discord by taking two-mode squeezed thermal states as initial states of the system and show that it has finite values between 0 and 1 and that it decays asymptoticallymore » to zero in time under the effect of the thermal bath.« less

Simulations of relativistic quantum plasmas using real-time lattice scalar QED

NASA Astrophysics Data System (ADS)

Shi, Yuan; Xiao, Jianyuan; Qin, Hong; Fisch, Nathaniel J.

2018-05-01

Real-time lattice quantum electrodynamics (QED) provides a unique tool for simulating plasmas in the strong-field regime, where collective plasma scales are not well separated from relativistic-quantum scales. As a toy model, we study scalar QED, which describes self-consistent interactions between charged bosons and electromagnetic fields. To solve this model on a computer, we first discretize the scalar-QED action on a lattice, in a way that respects geometric structures of exterior calculus and U(1)-gauge symmetry. The lattice scalar QED can then be solved, in the classical-statistics regime, by advancing an ensemble of statistically equivalent initial conditions in time, using classical field equations obtained by extremizing the discrete action. To demonstrate the capability of our numerical scheme, we apply it to two example problems. The first example is the propagation of linear waves, where we recover analytic wave dispersion relations using numerical spectrum. The second example is an intense laser interacting with a one-dimensional plasma slab, where we demonstrate natural transition from wakefield acceleration to pair production when the wave amplitude exceeds the Schwinger threshold. Our real-time lattice scheme is fully explicit and respects local conservation laws, making it reliable for long-time dynamics. The algorithm is readily parallelized using domain decomposition, and the ensemble may be computed using quantum parallelism in the future.

Further Evidence in Support of the Universal Nilpotent Grammatical Computational Paradigm of Quantum Physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marcer, Peter J.; Rowlands, Peter

2010-12-22

Further evidence is presented in favour of the computational paradigm, conceived and constructed by Rowlands and Diaz, as detailed in Rowlands' book Zero to Infinity (2007), and in particular the authors' paper 'The Grammatical Universe: the Laws of Thermodynamics and Quantum Entanglement'. The paradigm, which has isomorphic group and algebraic quantum mechanical language interpretations, not only predicts the well-established facts of quantum physics, the periodic table, chemistry / valence and of molecular biology, whose understanding it extends; it also provides an elegant, simple solution to the unresolved quantum measurement problem. In this fundamental paradigm, all the computational constructs / predictionsmore » that emerge, follow from the simple fact, that, as in quantum mechanics, the wave function is defined only up to an arbitrary fixed phase. This fixed phase provides a simple physical understanding of the quantum vacuum in quantum field theory, where only relative phases, known to be able to encode 3+1 relativistic space-time geometries, can be measured. It is the arbitrary fixed measurement standard, against which everything that follows is to be measured, even though the standard itself cannot be, since nothing exists against which to measure it. The standard, as an arbitrary fixed reference phase, functions as the holographic basis for a self-organized universal quantum process of emergent novel fermion states of matter where, following each emergence, the arbitrary standard is re-fixed anew so as to provide a complete history / holographic record or hologram of the current fixed past, advancing an unending irreversible evolution, such as is the evidence of our senses. The fermion states, in accord with the Pauli exclusion principle, each correspond to a unique nilpotent symbol in the infinite alphabet (which specifies the grammar in this nilpotent universal computational rewrite system (NUCRS) paradigm); and the alphabet, as Hill and Rowlands hypothesize on substantial evidence [26], includes that of the RNA / DNA genetic code and, as holographic phase encodings / holograms, the 4D geometries of all living systems as self-organised grammatical computational rewrite machines / machinery. Human brains, natural grammatical (written symbol) languages, 4D geometric self-awareness and a totally new emergent property of matter, human consciousness, can thus with some measure of confidence be postulated as further genetic consequences which follow from this self-organizing fundamental rewrite NUCRS construction. For it, like natural language, possesses a semantics and not just a syntax, where the initial symbol, i.e. the arbitrary fixed phase measurement standard, is able to function as the template for the blueprints of the emergent 4D relativistic real and virtual geometries to come, in a 'from the Self Creation to the creation of the human self' computational rewrite process evolution.« less

Further Evidence in Support of the Universal Nilpotent Grammatical Computational Paradigm of Quantum Physics

NASA Astrophysics Data System (ADS)

Marcer, Peter J.; Rowlands, Peter

2010-12-01

Further evidence is presented in favour of the computational paradigm, conceived and constructed by Rowlands and Diaz, as detailed in Rowlands' book Zero to Infinity (2007) [2], and in particular the authors' paper `The Grammatical Universe: the Laws of Thermodynamics and Quantum Entanglement' [1]. The paradigm, which has isomorphic group and algebraic quantum mechanical language interpretations, not only predicts the well-established facts of quantum physics, the periodic table, chemistry / valence and of molecular biology, whose understanding it extends; it also provides an elegant, simple solution to the unresolved quantum measurement problem. In this fundamental paradigm, all the computational constructs / predictions that emerge, follow from the simple fact, that, as in quantum mechanics, the wave function is defined only up to an arbitrary fixed phase. This fixed phase provides a simple physical understanding of the quantum vacuum in quantum field theory, where only relative phases, known to be able to encode 3+1 relativistic space-time geometries, can be measured. It is the arbitrary fixed measurement standard, against which everything that follows is to be measured, even though the standard itself cannot be, since nothing exists against which to measure it. The standard, as an arbitrary fixed reference phase, functions as the holographic basis for a self-organized universal quantum process of emergent novel fermion states of matter where, following each emergence, the arbitrary standard is re-fixed anew so as to provide a complete history / holographic record or hologram of the current fixed past, advancing an unending irreversible evolution, such as is the evidence of our senses. The fermion states, in accord with the Pauli exclusion principle, each correspond to a unique nilpotent symbol in the infinite alphabet (which specifies the grammar in this nilpotent universal computational rewrite system (NUCRS) paradigm); and the alphabet, as Hill and Rowlands hypothesize on substantial evidence [26], includes that of the RNA / DNA genetic code and, as holographic phase encodings / holograms, the 4D geometries of all living systems as self-organised grammatical computational rewrite machines / machinery. Human brains, natural grammatical (written symbol) languages, 4D geometric self-awareness and a totally new emergent property of matter, human consciousness, can thus with some measure of confidence be postulated as further genetic consequences which follow from this self-organizing fundamental rewrite NUCRS construction. For it, like natural language, possesses a semantics and not just a syntax, where the initial symbol, i.e. the arbitrary fixed phase measurement standard, is able to function as the template for the blueprints of the emergent 4D relativistic real and virtual geometries to come, in a `from the Self Creation to the creation of the human self' computational rewrite process evolution.

Information Graph Flow: A Geometric Approximation of Quantum and Statistical Systems

NASA Astrophysics Data System (ADS)

Vanchurin, Vitaly

2018-05-01

Given a quantum (or statistical) system with a very large number of degrees of freedom and a preferred tensor product factorization of the Hilbert space (or of a space of distributions) we describe how it can be approximated with a very low-dimensional field theory with geometric degrees of freedom. The geometric approximation procedure consists of three steps. The first step is to construct weighted graphs (we call information graphs) with vertices representing subsystems (e.g., qubits or random variables) and edges representing mutual information (or the flow of information) between subsystems. The second step is to deform the adjacency matrices of the information graphs to that of a (locally) low-dimensional lattice using the graph flow equations introduced in the paper. (Note that the graph flow produces very sparse adjacency matrices and thus might also be used, for example, in machine learning or network science where the task of graph sparsification is of a central importance.) The third step is to define an emergent metric and to derive an effective description of the metric and possibly other degrees of freedom. To illustrate the procedure we analyze (numerically and analytically) two information graph flows with geometric attractors (towards locally one- and two-dimensional lattices) and metric perturbations obeying a geometric flow equation. Our analysis also suggests a possible approach to (a non-perturbative) quantum gravity in which the geometry (a secondary object) emerges directly from a quantum state (a primary object) due to the flow of the information graphs.

Information Graph Flow: A Geometric Approximation of Quantum and Statistical Systems

NASA Astrophysics Data System (ADS)

Vanchurin, Vitaly

2018-06-01

Given a quantum (or statistical) system with a very large number of degrees of freedom and a preferred tensor product factorization of the Hilbert space (or of a space of distributions) we describe how it can be approximated with a very low-dimensional field theory with geometric degrees of freedom. The geometric approximation procedure consists of three steps. The first step is to construct weighted graphs (we call information graphs) with vertices representing subsystems (e.g., qubits or random variables) and edges representing mutual information (or the flow of information) between subsystems. The second step is to deform the adjacency matrices of the information graphs to that of a (locally) low-dimensional lattice using the graph flow equations introduced in the paper. (Note that the graph flow produces very sparse adjacency matrices and thus might also be used, for example, in machine learning or network science where the task of graph sparsification is of a central importance.) The third step is to define an emergent metric and to derive an effective description of the metric and possibly other degrees of freedom. To illustrate the procedure we analyze (numerically and analytically) two information graph flows with geometric attractors (towards locally one- and two-dimensional lattices) and metric perturbations obeying a geometric flow equation. Our analysis also suggests a possible approach to (a non-perturbative) quantum gravity in which the geometry (a secondary object) emerges directly from a quantum state (a primary object) due to the flow of the information graphs.

Accelerated quantum control using superadiabatic dynamics in a solid-state lambda system

DOE PAGES

Zhou, Brian B.; Baksic, Alexandre; Ribeiro, Hugo; ...

2016-11-28

Adiabatic evolutions find widespread utility in applications to quantum state engineering1 , geometric quantum computation2 , and quantum simulation3 . Although offering desirable robustness to experimental imperfections, adiabatic techniques are susceptible to decoherence during their long operation time. A recent strategy termed ‘shortcuts to adiabaticity’ 4–10 (STA) aims to circumvent this trade-off by designing fast dynamics to reproduce the results of infinitely slow, adiabatic processes. Here, as a realization of this strategy, we implement ‘superadiabatic’ transitionless driving11 (SATD) to speed up stimulated Raman adiabatic passage1,12–15 (STIRAP) in a solid-state lambda (Λ) system. Utilizing optical transitions to a dissipative excited statemore » in the nitrogen vacancy (NV) center in diamond, we demonstrate the accelerated performance of different shortcut trajectories for population transfer and for the transfer and initialization of coherent superpositions. We reveal that SATD protocols exhibit robustness to dissipation and experimental uncertainty, and can be optimized when these effects are present. These results motivate STA as a promising tool for controlling open quantum systems comprising individual or hybrid nanomechanical, superconducting, and photonic elements in the solid state12–17.« less

CatSim: a new computer assisted tomography simulation environment

NASA Astrophysics Data System (ADS)

De Man, Bruno; Basu, Samit; Chandra, Naveen; Dunham, Bruce; Edic, Peter; Iatrou, Maria; McOlash, Scott; Sainath, Paavana; Shaughnessy, Charlie; Tower, Brendon; Williams, Eugene

2007-03-01

We present a new simulation environment for X-ray computed tomography, called CatSim. CatSim provides a research platform for GE researchers and collaborators to explore new reconstruction algorithms, CT architectures, and X-ray source or detector technologies. The main requirements for this simulator are accurate physics modeling, low computation times, and geometrical flexibility. CatSim allows simulating complex analytic phantoms, such as the FORBILD phantoms, including boxes, ellipsoids, elliptical cylinders, cones, and cut planes. CatSim incorporates polychromaticity, realistic quantum and electronic noise models, finite focal spot size and shape, finite detector cell size, detector cross-talk, detector lag or afterglow, bowtie filtration, finite detector efficiency, non-linear partial volume, scatter (variance-reduced Monte Carlo), and absorbed dose. We present an overview of CatSim along with a number of validation experiments.

Are Quantum Models for Order Effects Quantum?

NASA Astrophysics Data System (ADS)

Moreira, Catarina; Wichert, Andreas

2017-12-01

The application of principles of Quantum Mechanics in areas outside of physics has been getting increasing attention in the scientific community in an emergent disciplined called Quantum Cognition. These principles have been applied to explain paradoxical situations that cannot be easily explained through classical theory. In quantum probability, events are characterised by a superposition state, which is represented by a state vector in a N-dimensional vector space. The probability of an event is given by the squared magnitude of the projection of this superposition state into the desired subspace. This geometric approach is very useful to explain paradoxical findings that involve order effects, but do we really need quantum principles for models that only involve projections? This work has two main goals. First, it is still not clear in the literature if a quantum projection model has any advantage towards a classical projection. We compared both models and concluded that the Quantum Projection model achieves the same results as its classical counterpart, because the quantum interference effects play no role in the computation of the probabilities. Second, it intends to propose an alternative relativistic interpretation for rotation parameters that are involved in both classical and quantum models. In the end, instead of interpreting these parameters as a similarity measure between questions, we propose that they emerge due to the lack of knowledge concerned with a personal basis state and also due to uncertainties towards the state of world and towards the context of the questions.

Geometric description of modular and weak values in discrete quantum systems using the Majorana representation

NASA Astrophysics Data System (ADS)

Cormann, Mirko; Caudano, Yves

2017-07-01

We express modular and weak values of observables of three- and higher-level quantum systems in their polar form. The Majorana representation of N-level systems in terms of symmetric states of N  -  1 qubits provides us with a description on the Bloch sphere. With this geometric approach, we find that modular and weak values of observables of N-level quantum systems can be factored in N  -  1 contributions. Their modulus is determined by the product of N  -  1 ratios involving projection probabilities between qubits, while their argument is deduced from a sum of N  -  1 solid angles on the Bloch sphere. These theoretical results allow us to study the geometric origin of the quantum phase discontinuity around singularities of weak values in three-level systems. We also analyze the three-box paradox (Aharonov and Vaidman 1991 J. Phys. A: Math. Gen. 24 2315-28) from the point of view of a bipartite quantum system. In the Majorana representation of this paradox, an observer comes to opposite conclusions about the entanglement state of the particles that were successfully pre- and postselected.

Inexact trajectory planning and inverse problems in the Hamilton–Pontryagin framework

PubMed Central

Burnett, Christopher L.; Holm, Darryl D.; Meier, David M.

2013-01-01

We study a trajectory-planning problem whose solution path evolves by means of a Lie group action and passes near a designated set of target positions at particular times. This is a higher-order variational problem in optimal control, motivated by potential applications in computational anatomy and quantum control. Reduction by symmetry in such problems naturally summons methods from Lie group theory and Riemannian geometry. A geometrically illuminating form of the Euler–Lagrange equations is obtained from a higher-order Hamilton–Pontryagin variational formulation. In this context, the previously known node equations are recovered with a new interpretation as Legendre–Ostrogradsky momenta possessing certain conservation properties. Three example applications are discussed as well as a numerical integration scheme that follows naturally from the Hamilton–Pontryagin principle and preserves the geometric properties of the continuous-time solution. PMID:24353467

BFV approach to geometric quantization

NASA Astrophysics Data System (ADS)

Fradkin, E. S.; Linetsky, V. Ya.

1994-12-01

A gauge-invariant approach to geometric quantization is developed. It yields a complete quantum description for dynamical systems with non-trivial geometry and topology of the phase space. The method is a global version of the gauge-invariant approach to quantization of second-class constraints developed by Batalin, Fradkin and Fradkina (BFF). Physical quantum states and quantum observables are respectively described by covariantly constant sections of the Fock bundle and the bundle of hermitian operators over the phase space with a flat connection defined by the nilpotent BVF-BRST operator. Perturbative calculation of the first non-trivial quantum correction to the Poisson brackets leads to the Chevalley cocycle known in deformation quantization. Consistency conditions lead to a topological quantization condition with metaplectic anomaly.

Geometric Defects in Quantum Hall States

NASA Astrophysics Data System (ADS)

Gromov, Andrey

I will describe a geometric analogue of Laughlin quasiholes in fractional quantum Hall (FQH) states. These ``quasiholes'' are generated by an insertion of quantized fluxes of curvature - which can be modeled by branch points of a certain Riemann surface - and, consequently, are related to genons. Unlike quasiholes, the genons are not excitations, but extrinsic defects. Fusion of genons describes the response of an FQH state to a process that changes (effective) topology of the physical space. These defects are abelian for IQH states and non-abelian for FQH states. I will explain how to calculate an electric charge, geometric spin and adiabatic mutual statistics of the these defects. Leo Kadanoff Fellowship.

Ordering states with various coherence measures

NASA Astrophysics Data System (ADS)

Yang, Long-Mei; Chen, Bin; Fei, Shao-Ming; Wang, Zhi-Xi

2018-04-01

Quantum coherence is one of the most significant theories in quantum physics. Ordering states with various coherence measures is an intriguing task in quantification theory of coherence. In this paper, we study this problem by use of four important coherence measures—the l_1 norm of coherence, the relative entropy of coherence, the geometric measure of coherence and the modified trace distance measure of coherence. We show that each pair of these measures give a different ordering of qudit states when d≥3. However, for single-qubit states, the l_1 norm of coherence and the geometric coherence provide the same ordering. We also show that the relative entropy of coherence and the geometric coherence give a different ordering for single-qubit states. Then we partially answer the open question proposed in Liu et al. (Quantum Inf Process 15:4189, 2016) whether all the coherence measures give a different ordering of states.

Quantization of geometric phase with integer and fractional topological characterization in a quantum Ising chain with long-range interaction.

PubMed

Sarkar, Sujit

2018-04-12

An attempt is made to study and understand the behavior of quantization of geometric phase of a quantum Ising chain with long range interaction. We show the existence of integer and fractional topological characterization for this model Hamiltonian with different quantization condition and also the different quantized value of geometric phase. The quantum critical lines behave differently from the perspective of topological characterization. The results of duality and its relation to the topological quantization is presented here. The symmetry study for this model Hamiltonian is also presented. Our results indicate that the Zak phase is not the proper physical parameter to describe the topological characterization of system with long range interaction. We also present quite a few exact solutions with physical explanation. Finally we present the relation between duality, symmetry and topological characterization. Our work provides a new perspective on topological quantization.

Geometric Computation of Human Gyrification Indexes from Magnetic Resonance Images

DTIC Science & Technology

2009-04-01

GEOMETRIC COMPUTATION OF HUMAN GYRIFICATION INDEXES FROM MAGNETIC RESONANCE IMAGES By Shu Su Tonya White Marcus Schmidt Chiu-Yen Kao and Guillermo...00-2009 to 00-00-2009 4. TITLE AND SUBTITLE Geometric Computation of Human Gyrification Indexes from Magnetic Resonance Images 5a. CONTRACT NUMBER... Geometric Computation of Gyrification Indexes Chiu-Yen Kao 1 Geometric Computation of Human Gyrification

Geometric reduction of dynamical nonlocality in nanoscale quantum circuits.

PubMed

Strambini, E; Makarenko, K S; Abulizi, G; de Jong, M P; van der Wiel, W G

2016-01-06

Nonlocality is a key feature discriminating quantum and classical physics. Quantum-interference phenomena, such as Young's double slit experiment, are one of the clearest manifestations of nonlocality, recently addressed as dynamical to specify its origin in the quantum equations of motion. It is well known that loss of dynamical nonlocality can occur due to (partial) collapse of the wavefunction due to a measurement, such as which-path detection. However, alternative mechanisms affecting dynamical nonlocality have hardly been considered, although of crucial importance in many schemes for quantum information processing. Here, we present a fundamentally different pathway of losing dynamical nonlocality, demonstrating that the detailed geometry of the detection scheme is crucial to preserve nonlocality. By means of a solid-state quantum-interference experiment we quantify this effect in a diffusive system. We show that interference is not only affected by decoherence, but also by a loss of dynamical nonlocality based on a local reduction of the number of quantum conduction channels of the interferometer. With our measurements and theoretical model we demonstrate that this mechanism is an intrinsic property of quantum dynamics. Understanding the geometrical constraints protecting nonlocality is crucial when designing quantum networks for quantum information processing.

One-norm geometric quantum discord and critical point estimation in the XY spin chain

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cheng, Chang-Cheng; Wang, Yao; Guo, Jin-Liang, E-mail: guojinliang80@163.com

2016-11-15

In contrast with entanglement and quantum discord (QD), we investigate the thermal quantum correlation in terms of Schatten one-norm geometric quantum discord (GQD) in the XY spin chain, and analyze their capabilities in detecting the critical point of quantum phase transition. We show that the one-norm GQD can reveal more properties about quantum correlation between two spins, especially for the long-range quantum correlation at finite temperature. Under the influences of site distance, anisotropy and temperature, one-norm GQD and its first derivative make it possible to detect the critical point efficiently for a general XY spin chain. - Highlights: • Comparingmore » with entanglement and QD, one-norm GQD is more robust versus the temperature. • One-norm GQD is more efficient in characterization of long-range quantum correlation between two distant qubits. • One-norm GQD performs well in highlighting the critical point of QPT at zero or low finite temperature. • One-norm GQD has a number of advantages over QD in detecting the critical point of the spin chain.« less

Aharonov–Anandan quantum phases and Landau quantization associated with a magnetic quadrupole moment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fonseca, I.C.; Bakke, K., E-mail: kbakke@fisica.ufpb.br

The arising of geometric quantum phases in the wave function of a moving particle possessing a magnetic quadrupole moment is investigated. It is shown that an Aharonov–Anandan quantum phase (Aharonov and Anandan, 1987) can be obtained in the quantum dynamics of a moving particle with a magnetic quadrupole moment. In particular, it is obtained as an analogue of the scalar Aharonov–Bohm effect for a neutral particle (Anandan, 1989). Besides, by confining the quantum particle to a hard-wall confining potential, the dependence of the energy levels on the geometric quantum phase is discussed and, as a consequence, persistent currents can arisemore » from this dependence. Finally, an analogue of the Landau quantization is discussed. -- Highlights: •Scalar Aharonov–Bohm effect for a particle possessing a magnetic quadrupole moment. •Aharonov–Anandan quantum phase for a particle with a magnetic quadrupole moment. •Dependence of the energy levels on the Aharonov–Anandan quantum phase. •Landau quantization associated with a particle possessing a magnetic quadrupole moment.« less

Molecular mechanism of NDMA formation from N,N-dimethylsulfamide during ozonation: quantum chemical insights into a bromide-catalyzed pathway.

PubMed

Trogolo, Daniela; Mishra, Brijesh Kumar; Heeb, Michèle B; von Gunten, Urs; Arey, J Samuel

2015-04-07

During ozonation of drinking water, the fungicide metabolite N,N-dimethylsulfamide (DMS) can be transformed into a highly toxic product, N-nitrosodimethylamine (NDMA). We used quantum chemical computations and stopped-flow experiments to evaluate a chemical mechanism proposed previously to describe this transformation. Stopped-flow experiments indicate a pK(a) = 10.4 for DMS. Experiments show that hypobromous acid (HOBr), generated by ozone oxidation of naturally occurring bromide, brominates the deprotonated DMS(-) anion with a near-diffusion controlled rate constant (7.1 ± 0.6 × 10(8) M(-1) s(-1)), forming Br-DMS(-) anion. According to quantum chemical calculations, Br-DMS has a pK(a) ∼ 9.0 and thus remains partially deprotonated at neutral pH. The anionic Br-DMS(-) bromamine can react with ozone with a high rate constant (10(5 ± 2.5) M(-1) s(-1)), forming the reaction intermediate (BrNO)(SO2)N(CH3)2(-). This intermediate resembles a loosely bound complex between an electrophilic nitrosyl bromide (BrNO) molecule and an electron-rich dimethylaminosulfinate ((SO2)N(CH3)2(-)) fragment, based on inspection of computed natural charges and geometric parameters. This fragile complex undergoes immediate (10(10 ± 2.5) s(-1)) reaction by two branches: an exothermic channel that produces NDMA, and an entropy-driven channel giving non-NDMA products. Computational results bring new insights into the electronic nature, chemical equilibria, and kinetics of the elementary reactions of this pathway, enabled by computed energies of structures that are not possible to access experimentally.

Controlling geometric phase optically in a single spin in diamond

NASA Astrophysics Data System (ADS)

Yale, Christopher G.

Geometric phase, or Berry phase, is an intriguing quantum mechanical phenomenon that arises from the cyclic evolution of a quantum state. Unlike dynamical phases, which rely on the time and energetics of the interaction, the geometric phase is determined solely by the geometry of the path travelled in parameter space. As such, it is robust to certain types of noise that preserve the area enclosed by the path, and shows promise for the development of fault-tolerant logic gates. Here, we demonstrate the optical control of geometric phase within a solid-state spin qubit, the nitrogen-vacancy center in diamond. Using stimulated Raman adiabatic passage (STIRAP), we evolve a coherent dark state along `tangerine slice' trajectories on the Bloch sphere and probe these paths through time-resolved state tomography. We then measure the accumulated geometric phase through phase reference to a third ground spin state. In addition, we examine the limits of this control due to adiabatic breakdown as well as the longer timescale effect of far-detuned optical fields. Finally, we intentionally introduce noise into the experimental control parameters, and measure the distributions of the resulting phases to probe the resilience of the phase to differing types of noise. We also examine this robustness as a function of traversal time as well as the noise amplitude. Through these studies, we demonstrate that geometric phase is a promising route toward fault-tolerant quantum information processing. This work is supported by the AFOSR, the NSF, and the German Research Foundation.

Application of classical simulations for the computation of vibrational properties of free molecules.

PubMed

Tikhonov, Denis S; Sharapa, Dmitry I; Schwabedissen, Jan; Rybkin, Vladimir V

2016-10-12

In this study, we investigate the ability of classical molecular dynamics (MD) and Monte-Carlo (MC) simulations for modeling the intramolecular vibrational motion. These simulations were used to compute thermally-averaged geometrical structures and infrared vibrational intensities for a benchmark set previously studied by gas electron diffraction (GED): CS 2 , benzene, chloromethylthiocyanate, pyrazinamide and 9,12-I 2 -1,2-closo-C 2 B 10 H 10 . The MD sampling of NVT ensembles was performed using chains of Nose-Hoover thermostats (NH) as well as the generalized Langevin equation thermostat (GLE). The performance of the theoretical models based on the classical MD and MC simulations was compared with the experimental data and also with the alternative computational techniques: a conventional approach based on the Taylor expansion of potential energy surface, path-integral MD and MD with quantum-thermal bath (QTB) based on the generalized Langevin equation (GLE). A straightforward application of the classical simulations resulted, as expected, in poor accuracy of the calculated observables due to the complete neglect of quantum effects. However, the introduction of a posteriori quantum corrections significantly improved the situation. The application of these corrections for MD simulations of the systems with large-amplitude motions was demonstrated for chloromethylthiocyanate. The comparison of the theoretical vibrational spectra has revealed that the GLE thermostat used in this work is not applicable for this purpose. On the other hand, the NH chains yielded reasonably good results.

Universal holonomic single quantum gates over a geometric spin with phase-modulated polarized light.

PubMed

Ishida, Naoki; Nakamura, Takaaki; Tanaka, Touta; Mishima, Shota; Kano, Hiroki; Kuroiwa, Ryota; Sekiguchi, Yuhei; Kosaka, Hideo

2018-05-15

We demonstrate universal non-adiabatic non-abelian holonomic single quantum gates over a geometric electron spin with phase-modulated polarized light and 93% average fidelity. This allows purely geometric rotation around an arbitrary axis by any angle defined by light polarization and phase using a degenerate three-level Λ-type system in a negatively charged nitrogen-vacancy center in diamond. Since the control light is completely resonant to the ancillary excited state, the demonstrated holonomic gate not only is fast with low power, but also is precise without the dynamical phase being subject to control error and environmental noise. It thus allows pulse shaping for further fidelity.

Thermodynamic studies of different black holes with modifications of entropy

NASA Astrophysics Data System (ADS)

Haldar, Amritendu; Biswas, Ritabrata

2018-02-01

In recent years, the thermodynamic properties of black holes are topics of interests. We investigate the thermodynamic properties like surface gravity and Hawking temperature on event horizon of regular black holes viz. Hayward Class and asymptotically AdS (Anti-de Sitter) black holes. We also analyze the thermodynamic volume and naive geometric volume of asymptotically AdS black holes and show that the entropy of these black holes is simply the ratio of the naive geometric volume to thermodynamic volume. We plot the different graphs and interpret them physically. We derive the `cosmic-Censorship-Inequality' for both type of black holes. Moreover, we calculate the thermal heat capacity of aforesaid black holes and study their stabilities in different regimes. Finally, we compute the logarithmic correction to the entropy for both the black holes considering the quantum fluctuations around the thermal equilibrium and study the corresponding thermodynamics.

Control of the spin geometric phase in semiconductor quantum rings.

PubMed

Nagasawa, Fumiya; Frustaglia, Diego; Saarikoski, Henri; Richter, Klaus; Nitta, Junsaku

2013-01-01

Since the formulation of the geometric phase by Berry, its relevance has been demonstrated in a large variety of physical systems. However, a geometric phase of the most fundamental spin-1/2 system, the electron spin, has not been observed directly and controlled independently from dynamical phases. Here we report experimental evidence on the manipulation of an electron spin through a purely geometric effect in an InGaAs-based quantum ring with Rashba spin-orbit coupling. By applying an in-plane magnetic field, a phase shift of the Aharonov-Casher interference pattern towards the small spin-orbit-coupling regions is observed. A perturbation theory for a one-dimensional Rashba ring under small in-plane fields reveals that the phase shift originates exclusively from the modulation of a pure geometric-phase component of the electron spin beyond the adiabatic limit, independently from dynamical phases. The phase shift is well reproduced by implementing two independent approaches, that is, perturbation theory and non-perturbative transport simulations.

An Introduction to Geometric Algebra with some Preliminary Thoughts on the Geometric Meaning of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Horn, Martin Erik

2014-10-01

It is still a great riddle to me why Wolfgang Pauli and P.A.M. Dirac had not fully grasped the meaning of their own mathematical constructions. They invented magnificent, fantastic and very important mathematical features of modern physics, but they only delivered half of the interpretations of their own inventions. Of course, Pauli matrices and Dirac matrices represent operators, which Pauli and Dirac discussed in length. But this is only part of the true meaning behind them, as the non-commutative ideas of Grassmann, Clifford, Hamilton and Cartan allow a second, very far reaching interpretation of Pauli and Dirac matrices. An introduction to this alternative interpretation will be discussed. Some applications of this view on Pauli and Dirac matrices are given, e.g. a geometric algebra picture of the plane wave solution of the Maxwell equation, a geometric algebra picture of special relativity, a toy model of SU(3) symmetry, and some only very preliminary thoughts about a possible geometric meaning of quantum mechanics.

Molecular structure, spectroscopic studies and first-order molecular hyperpolarizabilities of ferulic acid by density functional study

NASA Astrophysics Data System (ADS)

Sebastian, S.; Sundaraganesan, N.; Manoharan, S.

2009-10-01

Quantum chemical calculations of energies, geometrical structure and vibrational wavenumbers of ferulic acid (FA) (4-hydroxy-3-methoxycinnamic acid) were carried out by using density functional (DFT/B3LYP/BLYP) method with 6-31G(d,p) as basis set. The optimized geometrical parameters obtained by DFT calculations are in good agreement with single crystal XRD data. The vibrational spectral data obtained from solid phase FT-IR and FT-Raman spectra are assigned based on the results of the theoretical calculations. The observed spectra are found to be in good agreement with calculated values. The electric dipole moment ( μ) and the first hyperpolarizability ( β) values of the investigated molecule have been computed using ab initio quantum mechanical calculations. The calculation results also show that the FA molecule might have microscopic nonlinear optical (NLO) behavior with non-zero values. A detailed interpretation of the infrared and Raman spectra of FA was also reported. The energy and oscillator strength calculated by time-dependent density functional theory (TD-DFT) results complements with the experimental findings. The calculated HOMO and LUMO energies shows that charge transfer occur within the molecule. The theoretical FT-IR and FT-Raman spectra for the title molecule have been constructed.

Generalized centripetal force law and quantization of motion constrained on 2D surfaces

NASA Astrophysics Data System (ADS)

Liu, Q. H.; Zhang, J.; Lian, D. K.; Hu, L. D.; Li, Z.

2017-03-01

For a particle of mass μ moves on a 2D surface f(x) = 0 embedded in 3D Euclidean space of coordinates x, there is an open and controversial problem whether the Dirac's canonical quantization scheme for the constrained motion allows for the geometric potential that has been experimentally confirmed. We note that the Dirac's scheme hypothesizes that the symmetries indicated by classical brackets among positions x and momenta p and Hamiltonian Hc remain in quantum mechanics, i.e., the following Dirac brackets [ x ,Hc ] D and [ p ,Hc ] D holds true after quantization, in addition to the fundamental ones [ x , x ] D, [ x , p ] D and [ p , p ] D. This set of hypotheses implies that the Hamiltonian operator is simultaneously determined during the quantization. The quantum mechanical relations corresponding to the classical mechanical ones p / μ =[ x ,Hc ] D directly give the geometric momenta. The time t derivative of the momenta p ˙ =[ p ,Hc ] D in classical mechanics is in fact the generalized centripetal force law for particle on the 2D surface, which in quantum mechanics permits both the geometric momenta and the geometric potential.

Probing the geometry of the Laughlin state

DOE PAGES

Johri, Sonika; Papic, Z.; Schmitteckert, P.; ...

2016-02-05

It has recently been pointed out that phases of matter with intrinsic topological order, like the fractional quantum Hall states, have an extra dynamical degree of freedom that corresponds to quantum geometry. Here we perform extensive numerical studies of the geometric degree of freedom for the simplest example of fractional quantumHall states—the filling v = 1/3 Laughlin state.We perturb the system by a smooth, spatially dependent metric deformation and measure the response of the Hall fluid, finding it to be proportional to the Gaussian curvature of the metric. Further, we generalize the concept of coherent states to formulate the bulkmore » off-diagonal long range order for the Laughlin state, and compute the deformations of the metric in the vicinity of the edge of the system. We introduce a ‘pair amplitude’ operator and show that it can be used to numerically determine the intrinsic metric of the Laughlin state. Furthermore, these various probes are applied to several experimentally relevant settings that can expose the quantum geometry of the Laughlin state, in particular to systems with mass anisotropy and in the presence of an electric field gradient.« less

Reaching Agreement in Quantum Hybrid Networks.

PubMed

Shi, Guodong; Li, Bo; Miao, Zibo; Dower, Peter M; James, Matthew R

2017-07-20

We consider a basic quantum hybrid network model consisting of a number of nodes each holding a qubit, for which the aim is to drive the network to a consensus in the sense that all qubits reach a common state. Projective measurements are applied serving as control means, and the measurement results are exchanged among the nodes via classical communication channels. In this way the quantum-opeartion/classical-communication nature of hybrid quantum networks is captured, although coherent states and joint operations are not taken into consideration in order to facilitate a clear and explicit analysis. We show how to carry out centralized optimal path planning for this network with all-to-all classical communications, in which case the problem becomes a stochastic optimal control problem with a continuous action space. To overcome the computation and communication obstacles facing the centralized solutions, we also develop a distributed Pairwise Qubit Projection (PQP) algorithm, where pairs of nodes meet at a given time and respectively perform measurements at their geometric average. We show that the qubit states are driven to a consensus almost surely along the proposed PQP algorithm, and that the expected qubit density operators converge to the average of the network's initial values.

Interplay between topology, gauge fields and gravity

NASA Astrophysics Data System (ADS)

Corichi Rodriguez Gil, Alejandro

In this thesis we consider several physical systems that illustrate an interesting interplay between quantum theory, connections and knot theory. It can be divided into two parts. In the first one, we consider the quantization of the free Maxwell field. We show that there is an important role played by knot theory, and in particular the Gauss linking number, in the quantum theory. This manifestation is twofold. The first occurs at the level of the algebra of observables given by fluxes of electric and magnetic field across surfaces. The commutator of the operators, and thus the basic uncertainty relations, are given in terms of the linking number of the loops that bound the surfaces. Next, we consider the quantization of the Maxwell field based on self-dual connections in the loop representation. We show that the measure which determines the quantum inner product can be expressed in terms of the self linking number of thickened loops. Therefore, the linking number manifests itself at two key points of the theory: the Heisenberg uncertainty principle and the inner product. In the second part, we bring gravity into play. First we consider quantum test particles on certain stationary space-times. We demonstrate that a geometric phase exists for those space-times and focus on the example of a rotating cosmic string. The geometric phase can be explicitly computed, providing a fully relativistic gravitational Aharonov-Bohm effect. Finally, we consider 3-dimensional gravity with non-vanishing cosmological constant in the connection dynamics formulation. We restrict our attention to Lorentzian gravity with positive cosmological constant and Euclidean signature with negative cosmological constant. A complex transformation is performed in phase space that makes the constraints simple. The reduced phase space is characterized as the moduli space of flat complex connections. We construct the quantization of the theory when the initial hyper-surface is a torus. Two important issues relevant to full 3 + 1 gravity are clarified, namely, the incorporation of the 'reality conditions' in the quantum theory and the role played by the signature of the classical metric in the quantum theory.

Quantum Hurwitz numbers and Macdonald polynomials

NASA Astrophysics Data System (ADS)

Harnad, J.

2016-11-01

Parametric families in the center Z(C[Sn]) of the group algebra of the symmetric group are obtained by identifying the indeterminates in the generating function for Macdonald polynomials as commuting Jucys-Murphy elements. Their eigenvalues provide coefficients in the double Schur function expansion of 2D Toda τ-functions of hypergeometric type. Expressing these in the basis of products of power sum symmetric functions, the coefficients may be interpreted geometrically as parametric families of quantum Hurwitz numbers, enumerating weighted branched coverings of the Riemann sphere. Combinatorially, they give quantum weighted sums over paths in the Cayley graph of Sn generated by transpositions. Dual pairs of bases for the algebra of symmetric functions with respect to the scalar product in which the Macdonald polynomials are orthogonal provide both the geometrical and combinatorial significance of these quantum weighted enumerative invariants.

Loop Quantum Gravity.

PubMed

Rovelli, Carlo

2008-01-01

The problem of describing the quantum behavior of gravity, and thus understanding quantum spacetime , is still open. Loop quantum gravity is a well-developed approach to this problem. It is a mathematically well-defined background-independent quantization of general relativity, with its conventional matter couplings. Today research in loop quantum gravity forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained so far are: (i) The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planck-scale physics. (ii) A physical picture of the microstructure of quantum spacetime, characterized by Planck-scale discreteness. Discreteness emerges as a standard quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler's "spacetime foam" intuition. (iii) Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv) A derivation of the Bekenstein-Hawking black-hole entropy. (v) Low-energy calculations, yielding n -point functions well defined in a background-independent context. The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing background-independent quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.

The pentagon relation and incidence geometry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Doliwa, Adam, E-mail: doliwa@matman.uwm.edu.pl; Sergeev, Sergey M., E-mail: Sergey.Sergeev@canberra.edu.au

2014-06-01

We define a map S:D²×D²→D²×D², where D is an arbitrary division ring (skew field), associated with the Veblen configuration, and we show that such a map provides solutions to the functional dynamical pentagon equation. We explain that fact in elementary geometric terms using the symmetry of the Veblen and Desargues configurations. We introduce also another map of a geometric origin with the pentagon property. We show equivalence of these maps with recently introduced Desargues maps which provide geometric interpretation to a non-commutative version of Hirota's discrete Kadomtsev–Petviashvili equation. Finally, we demonstrate that in an appropriate gauge the (commutative version ofmore » the) maps preserves a natural Poisson structure—the quasiclassical limit of the Weyl commutation relations. The corresponding quantum reduction is then studied. In particular, we discuss uniqueness of the Weyl relations for the ultra-local reduction of the map. We give then the corresponding solution of the quantum pentagon equation in terms of the non-compact quantum dilogarithm function.« less

On the unification of nuclear-structure theory: A response to Bortignon and Broglia

NASA Astrophysics Data System (ADS)

Cook, Norman D.

2016-09-01

Nuclear-structure theory is unusual among the diverse fields of quantum physics. Although it provides a coherent description of all known isotopes on the basis of a quantum-mechanical understanding of nucleon states, nevertheless, in the absence of a fundamental theory of the nuclear force acting between nucleons, the prediction of all ground-state and excited-state nuclear binding energies is inherently semi-empirical. I suggest that progress can be made by returning to the foundational work of Eugene Wigner from 1937, where the mathematical symmetries of nucleon states were first defined. Those symmetries were later successfully exploited in the development of the independent-particle model ( IPM ˜ shell model , but the geometrical implications noted by Wigner were neglected. Here I review how the quantum-mechanical, but remarkably easy-to-understand geometrical interpretation of the IPM provides constraints on the parametrization of the nuclear force. The proposed "geometrical IPM" indicates a way forward toward the unification of nuclear-structure theory that Bortignon and Broglia have called for.

Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

DOE PAGES

Ruiz, D. E.; Dodin, I. Y.

2015-07-29

Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Here, both phenomena are governed by an effective gauge Hamiltonian vanishing in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the Stern-Gerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler-Lagrange equations can describe simultaneous interactions of N resonant modes, where N is arbitrary, and leadmore » to equations for the wave spin, which happens to be an (N 2 - 1)-dimensional spin vector. As a special case, classical equations for a Dirac particle (N = 2) are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangian with the Pauli term. The model reproduces the Bargmann-Michel-Telegdi equations with added Stern-Gerlach force.« less

Single particle nonlocality, geometric phases and time-dependent boundary conditions

NASA Astrophysics Data System (ADS)

Matzkin, A.

2018-03-01

We investigate the issue of single particle nonlocality in a quantum system subjected to time-dependent boundary conditions. We discuss earlier claims according to which the quantum state of a particle remaining localized at the center of an infinite well with moving walls would be specifically modified by the change in boundary conditions due to the wall’s motion. We first prove that the evolution of an initially localized Gaussian state is not affected nonlocally by a linearly moving wall: as long as the quantum state has negligible amplitude near the wall, the boundary motion has no effect. This result is further extended to related confined time-dependent oscillators in which the boundary’s motion is known to give rise to geometric phases: for a Gaussian state remaining localized far from the boundaries, the effect of the geometric phases is washed out and the particle dynamics shows no traces of a nonlocal influence that would be induced by the moving boundaries.

Advanced Concepts in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Esposito, Giampiero; Marmo, Giuseppe; Miele, Gennaro; Sudarshan, George

2014-11-01

Preface; 1. Introduction: the need for a quantum theory; 2. Experimental foundations of quantum theory; 3. Waves and particles; 4. Schrödinger picture, Heisenberg picture and probabilistic aspects; 5. Integrating the equations of motion; 6. Elementary applications: 1-dimensional problems; 7. Elementary applications: multidimensional problems; 8. Coherent states and related formalism; 9. Introduction to spin; 10. Symmetries in quantum mechanics; 11. Approximation methods; 12. Modern pictures of quantum mechanics; 13. Formulations of quantum mechanics and their physical implications; 14. Exam problems; Glossary of geometric concepts; References; Index.

Central charge from adiabatic transport of cusp singularities in the quantum Hall effect

NASA Astrophysics Data System (ADS)

Can, Tankut

2017-04-01

We study quantum Hall (QH) states on a punctured Riemann sphere. We compute the Berry curvature under adiabatic motion in the moduli space in the large N limit. The Berry curvature is shown to be finite in the large N limit and controlled by the conformal dimension of the cusp singularity, a local property of the mean density. Utilizing exact sum rules obtained from a Ward identity, we show that for the Laughlin wave function, the dimension of a cusp singularity is given by the central charge, a robust geometric response coefficient in the QHE. Thus, adiabatic transport of curvature singularities can be used to determine the central charge of QH states. We also consider the effects of threaded fluxes and spin-deformed wave functions. Finally, we give a closed expression for all moments of the mean density in the integer QH state on a punctured disk.

Effects of external magnetic field and magnetic anisotropy on chiral spin structures of square nanodisks investigated with a quantum simulation approach

NASA Astrophysics Data System (ADS)

Liu, Zhaosen; Ian, Hou

2016-04-01

We employed a quantum simulation approach to investigate the magnetic properties of monolayer square nanodisks with Dzyaloshinsky-Moriya (DM) interaction. The computational program converged very quickly, and generated chiral spin structures on the disk planes with good symmetry. When the DM interaction is sufficiently strong, multi-domain structures appears, their sizes or average distance between each pair of domains can be approximately described by a modified grid theory. We further found that the external magnetic field and uniaxial magnetic anisotropy both normal to the disk plane lead to reductions of the total free energy and total energy of the nanosystems, thus are able to stabilize and/or induce the vortical structures, however, the chirality of the vortex is still determined by the sign of the DM interaction parameter. Moreover, the geometric shape of the nanodisk affects the spin configuration on the disk plane as well.

Topologies on quantum topoi induced by quantization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nakayama, Kunji

2013-07-15

In the present paper, we consider effects of quantization in a topos approach of quantum theory. A quantum system is assumed to be coded in a quantum topos, by which we mean the topos of presheaves on the context category of commutative subalgebras of a von Neumann algebra of bounded operators on a Hilbert space. A classical system is modeled by a Lie algebra of classical observables. It is shown that a quantization map from the classical observables to self-adjoint operators on the Hilbert space naturally induces geometric morphisms from presheaf topoi related to the classical system to the quantummore » topos. By means of the geometric morphisms, we give Lawvere-Tierney topologies on the quantum topos (and their equivalent Grothendieck topologies on the context category). We show that, among them, there exists a canonical one which we call a quantization topology. We furthermore give an explicit expression of a sheafification functor associated with the quantization topology.« less

The Madelung Picture as a Foundation of Geometric Quantum Theory

NASA Astrophysics Data System (ADS)

Reddiger, Maik

2017-10-01

Despite its age, quantum theory still suffers from serious conceptual difficulties. To create clarity, mathematical physicists have been attempting to formulate quantum theory geometrically and to find a rigorous method of quantization, but this has not resolved the problem. In this article we argue that a quantum theory recursing to quantization algorithms is necessarily incomplete. To provide an alternative approach, we show that the Schrödinger equation is a consequence of three partial differential equations governing the time evolution of a given probability density. These equations, discovered by Madelung, naturally ground the Schrödinger theory in Newtonian mechanics and Kolmogorovian probability theory. A variety of far-reaching consequences for the projection postulate, the correspondence principle, the measurement problem, the uncertainty principle, and the modeling of particle creation and annihilation are immediate. We also give a speculative interpretation of the equations following Bohm, Vigier and Tsekov, by claiming that quantum mechanical behavior is possibly caused by gravitational background noise.

Nonadiabatic effect on the quantum heat flux control.

PubMed

Uchiyama, Chikako

2014-05-01

We provide a general formula of quantum transfer that includes the nonadiabatic effect under periodic environmental modulation by using full counting statistics in Hilbert-Schmidt space. Applying the formula to an anharmonic junction model that interacts with two bosonic environments within the Markovian approximation, we find that the quantum transfer is divided into the adiabatic (dynamical and geometrical phases) and nonadiabatic contributions. This extension shows the dependence of quantum transfer on the initial condition of the anharmonic junction just before the modulation, as well as the characteristic environmental parameters such as interaction strength and cut-off frequency of spectral density. We show that the nonadiabatic contribution represents the reminiscent effect of past modulation including the transition from the initial condition of the anharmonic junction to a steady state determined by the very beginning of the modulation. This enables us to tune the frequency range of modulation, whereby we can obtain the quantum flux corresponding to the geometrical phase by setting the initial condition of the anharmonic junction.

Elucidating the mass spectrum of the retronecine alkaloid using DFT calculations.

PubMed

Modesto-Costa, Lucas; Martinez, Sabrina T; Pinto, Angelo C; Vessecchi, Ricardo; Borges, Itamar

2018-06-23

Pyrrolizidine alkaloids are natural molecules playing important roles in different biochemical processes in nature and in humans. In this work, the electron ionization mass spectrum (EI-MS) of retronecine, an alkaloid molecule found in plants, is investigated computationally. Its mass spectrum can be characterized by three main fragment ions having the following m/z ratios: 111, 94 and 80. In order to rationalize the mass spectrum, minima and transition state geometries were computed using density functional theory (DFT). It was showed that the dissociation process includes an aromatization of the originally five-membered ring of retronecine converted into a six-membered ring compound. A fragmentation pathway mechanism involving dissociation activation barriers that are easily overcome by the initial ionization energy was found. From the computed quantum chemical geometric, atomic charges and energetic parameters, the abundance of each ion in the mass spectrum of retronecine was discussed. This article is protected by copyright. All rights reserved.

Infinite-mode squeezed coherent states and non-equilibrium statistical mechanics (phase-space-picture approach)

NASA Technical Reports Server (NTRS)

Yeh, Leehwa

1993-01-01

The phase-space-picture approach to quantum non-equilibrium statistical mechanics via the characteristic function of infinite-mode squeezed coherent states is introduced. We use quantum Brownian motion as an example to show how this approach provides an interesting geometrical interpretation of quantum non-equilibrium phenomena.

Conformational, structural, vibrational and quantum chemical analysis on 4-aminobenzohydrazide and 4-hydroxybenzohydrazide--a comparative study.

PubMed

Arjunan, V; Jayaprakash, A; Carthigayan, K; Periandy, S; Mohan, S

2013-05-01

Experimental and theoretical quantum chemical studies were carried out on 4-hydroxybenzohydrazide (4HBH) and 4-aminobenzohydrazide (4ABH) using FTIR and FT-Raman spectral data. The structural characteristics and vibrational spectroscopic analysis were carried performed by quantum chemical methods with the hybrid exchange-correlation functional B3LYP using 6-31G(**), 6-311++G(**) and aug-cc-pVDZ basis sets. The most stable conformer of the title compounds have been determined from the analysis of potential energy surface. The stable molecular geometries, electronic and thermodynamic parameters, IR intensities, harmonic vibrational frequencies, depolarisation ratio and Raman intensities have been computed. Molecular electrostatic potential and frontier molecular orbitals were constructed to understand the electronic properties. The potential energy distributions (PEDs) were calculated to explain the mixing of fundamental modes. The theoretical geometrical parameters and the fundamental frequencies were compared with the experimental. The interactions of hydroxy and amino group substitutions on the characteristic vibrations of the ring and hydrazide group have been analysed. Copyright © 2013 Elsevier B.V. All rights reserved.

Full-band quantum simulation of electron devices with the pseudopotential method: Theory, implementation, and applications

NASA Astrophysics Data System (ADS)

Pala, M. G.; Esseni, D.

2018-03-01

This paper presents the theory, implementation, and application of a quantum transport modeling approach based on the nonequilibrium Green's function formalism and a full-band empirical pseudopotential Hamiltonian. We here propose to employ a hybrid real-space/plane-wave basis that results in a significant reduction of the computational complexity compared to a full plane-wave basis. To this purpose, we provide a theoretical formulation in the hybrid basis of the quantum confinement, the self-energies of the leads, and the coupling between the device and the leads. After discussing the theory and the implementation of the new simulation methodology, we report results for complete, self-consistent simulations of different electron devices, including a silicon Esaki diode, a thin-body silicon field effect transistor (FET), and a germanium tunnel FET. The simulated transistors have technologically relevant geometrical features with a semiconductor film thickness of about 4 nm and a channel length ranging from 10 to 17 nm. We believe that the newly proposed formalism may find applications also in transport models based on ab initio Hamiltonians, as those employed in density functional theory methods.

The Influence of Geometrical Structure of AlInGaN Double Quantum Well (DQWs) UV Diode Laser on Its Performance and Operating Parameters

NASA Astrophysics Data System (ADS)

Ghazai, A. J.; Thahab, S. M.; Hassan, H. Abu; Hassan, Z.

2010-07-01

The development of efficient MQWs active regions of quaternary InAlGaN in the ultraviolet (UV) region is an engaging challenge by itself. Demonstrating lasers at such low wavelength will require resolving a number of materials, growth and device design issues. However, the quaternary AlInGaN represents a more versatile material since the bandgap and lattice constant can be independently varied. We report a quaternary AlInGaN double-quantum wells (DQWs) UV laser diode (LDs) study by using the simulation program of Integrated System Engineering-Technical Computer Aided Design (ISE TCAD). Advanced physical models of semiconductor properties were used. In this paper, the enhancement in the performance of AlInGaN laser diode can be achieved by optimizing the laser structure geometry design. The AlInGaN laser diodes operating parameters such as internal quantum efficiency ηi, internal loss αi and transparency threshold current density show effective improvements that contribute to a better performance.

Quantum mechanics of a constrained particle on an ellipsoid: Bein formalism and Geometric momentum

DOE Office of Scientific and Technical Information (OSTI.GOV)

Panahi, H., E-mail: t-panahi@guilan.ac.ir; Jahangiri, L., E-mail: laleh.jahangiry@yahoo.com

2016-09-15

In this work we apply the Dirac method in order to obtain the classical relations for a particle on an ellipsoid. We also determine the quantum mechanical form of these relations by using Dirac quantization. Then by considering the canonical commutation relations between the position and momentum operators in terms of curved coordinates, we try to propose the suitable representations for momentum operator that satisfy the obtained commutators between position and momentum in Euclidean space. We see that our representations for momentum operators are the same as geometric one.

Phase space localization for anti-de Sitter quantum mechanics and its zero curvature limit

NASA Technical Reports Server (NTRS)

Elgradechi, Amine M.

1993-01-01

Using techniques of geometric quantization and SO(sub 0)(3,2)-coherent states, a notion of optimal localization on phase space is defined for the quantum theory of a massive and spinning particle in anti-de Sitter space time. It is shown that this notion disappears in the zero curvature limit, providing one with a concrete example of the regularizing character of the constant (nonzero) curvature of the anti-de Sitter space time. As a byproduct a geometric characterization of masslessness is obtained.

Quantum-metric contribution to the pair mass in spin-orbit-coupled Fermi superfluids

NASA Astrophysics Data System (ADS)

Iskin, M.

2018-03-01

As a measure of the quantum distance between Bloch states in the Hilbert space, the quantum metric was introduced to solid-state physics through the real part of the so-called geometric Fubini-Study tensor, the imaginary part of which corresponds to the Berry curvature measuring the emergent gauge field in momentum space. Here, we first derive the Ginzburg-Landau theory near the critical superfluid transition temperature and then identify and analyze the geometric effects on the effective mass tensor of the Cooper pairs. By showing that the quantum-metric contribution accounts for a sizable fraction of the pair mass in a surprisingly large parameter regime throughout the BCS-Bose-Einstein condensate crossover, we not only reveal the physical origin of its governing role in the superfluid density tensor but also hint at its plausible roles in many other observables.

Thermal and magnetic properties of electron gas in toroidal quantum dot

NASA Astrophysics Data System (ADS)

Baghdasaryan, D. A.; Hayrapetyan, D. B.; Kazaryan, E. M.; Sarkisyan, H. A.

2018-07-01

One-electron states in a toroidal quantum dot in the presence of an external magnetic field have been considered. The magnetic field operator and the Schrodinger equation have been written in toroidal coordinates. The dependence of one-electron energy spectrum and wave function on the geometrical parameters of a toroidal quantum dot and magnetic field strength have been studied. The energy levels are employed to calculate the canonical partition function, which in its turn is used to obtain mean energy, heat capacity, entropy, magnetization, and susceptibility of noninteracting electron gas. The possibility to control the thermodynamic and magnetic properties of the noninteracting electron gas via changing the geometric parameters of the QD, magnetic field, and temperature, was demonstrated.

Efficient Numeric and Geometric Computations using Heterogeneous Shared Memory Architectures

DTIC Science & Technology

2017-10-04

Report: Efficient Numeric and Geometric Computations using Heterogeneous Shared Memory Architectures The views, opinions and/or findings contained in this...Chapel Hill Title: Efficient Numeric and Geometric Computations using Heterogeneous Shared Memory Architectures Report Term: 0-Other Email: dm...algorithms for scientific and geometric computing by exploiting the power and performance efficiency of heterogeneous shared memory architectures . These

Fisher metric, geometric entanglement, and spin networks

NASA Astrophysics Data System (ADS)

Chirco, Goffredo; Mele, Fabio M.; Oriti, Daniele; Vitale, Patrizia

2018-02-01

Starting from recent results on the geometric formulation of quantum mechanics, we propose a new information geometric characterization of entanglement for spin network states in the context of quantum gravity. For the simple case of a single-link fixed graph (Wilson line), we detail the construction of a Riemannian Fisher metric tensor and a symplectic structure on the graph Hilbert space, showing how these encode the whole information about separability and entanglement. In particular, the Fisher metric defines an entanglement monotone which provides a notion of distance among states in the Hilbert space. In the maximally entangled gauge-invariant case, the entanglement monotone is proportional to a power of the area of the surface dual to the link thus supporting a connection between entanglement and the (simplicial) geometric properties of spin network states. We further extend such analysis to the study of nonlocal correlations between two nonadjacent regions of a generic spin network graph characterized by the bipartite unfolding of an intertwiner state. Our analysis confirms the interpretation of spin network bonds as a result of entanglement and to regard the same spin network graph as an information graph, whose connectivity encodes, both at the local and nonlocal level, the quantum correlations among its parts. This gives a further connection between entanglement and geometry.

Blending Determinism with Evolutionary Computing: Applications to the Calculation of the Molecular Electronic Structure of Polythiophene.

PubMed

Sarkar, Kanchan; Sharma, Rahul; Bhattacharyya, S P

2010-03-09

A density matrix based soft-computing solution to the quantum mechanical problem of computing the molecular electronic structure of fairly long polythiophene (PT) chains is proposed. The soft-computing solution is based on a "random mutation hill climbing" scheme which is modified by blending it with a deterministic method based on a trial single-particle density matrix [P((0))(R)] for the guessed structural parameters (R), which is allowed to evolve under a unitary transformation generated by the Hamiltonian H(R). The Hamiltonian itself changes as the geometrical parameters (R) defining the polythiophene chain undergo mutation. The scale (λ) of the transformation is optimized by making the energy [E(λ)] stationary with respect to λ. The robustness and the performance levels of variants of the algorithm are analyzed and compared with those of other derivative free methods. The method is further tested successfully with optimization of the geometry of bipolaron-doped long PT chains.

A Synthetic Approach to the Transfer Matrix Method in Classical and Quantum Physics

ERIC Educational Resources Information Center

Pujol, O.; Perez, J. P.

2007-01-01

The aim of this paper is to propose a synthetic approach to the transfer matrix method in classical and quantum physics. This method is an efficient tool to deal with complicated physical systems of practical importance in geometrical light or charged particle optics, classical electronics, mechanics, electromagnetics and quantum physics. Teaching…

Interfacing External Quantum Devices to a Universal Quantum Computer

PubMed Central

Lagana, Antonio A.; Lohe, Max A.; von Smekal, Lorenz

2011-01-01

We present a scheme to use external quantum devices using the universal quantum computer previously constructed. We thereby show how the universal quantum computer can utilize networked quantum information resources to carry out local computations. Such information may come from specialized quantum devices or even from remote universal quantum computers. We show how to accomplish this by devising universal quantum computer programs that implement well known oracle based quantum algorithms, namely the Deutsch, Deutsch-Jozsa, and the Grover algorithms using external black-box quantum oracle devices. In the process, we demonstrate a method to map existing quantum algorithms onto the universal quantum computer. PMID:22216276

Interfacing external quantum devices to a universal quantum computer.

PubMed

Lagana, Antonio A; Lohe, Max A; von Smekal, Lorenz

2011-01-01

We present a scheme to use external quantum devices using the universal quantum computer previously constructed. We thereby show how the universal quantum computer can utilize networked quantum information resources to carry out local computations. Such information may come from specialized quantum devices or even from remote universal quantum computers. We show how to accomplish this by devising universal quantum computer programs that implement well known oracle based quantum algorithms, namely the Deutsch, Deutsch-Jozsa, and the Grover algorithms using external black-box quantum oracle devices. In the process, we demonstrate a method to map existing quantum algorithms onto the universal quantum computer. © 2011 Lagana et al.

Universal blind quantum computation for hybrid system

NASA Astrophysics Data System (ADS)

Huang, He-Liang; Bao, Wan-Su; Li, Tan; Li, Feng-Guang; Fu, Xiang-Qun; Zhang, Shuo; Zhang, Hai-Long; Wang, Xiang

2017-08-01

As progress on the development of building quantum computer continues to advance, first-generation practical quantum computers will be available for ordinary users in the cloud style similar to IBM's Quantum Experience nowadays. Clients can remotely access the quantum servers using some simple devices. In such a situation, it is of prime importance to keep the security of the client's information. Blind quantum computation protocols enable a client with limited quantum technology to delegate her quantum computation to a quantum server without leaking any privacy. To date, blind quantum computation has been considered only for an individual quantum system. However, practical universal quantum computer is likely to be a hybrid system. Here, we take the first step to construct a framework of blind quantum computation for the hybrid system, which provides a more feasible way for scalable blind quantum computation.

Modeling of the whispering gallery mode in microdisk and microgear resonators using a Toeplitz matrix formalism for single-photon source

NASA Astrophysics Data System (ADS)

Attia, Moez; Gueddana, Amor; Chatta, Rihab; Morand, Alain

2013-09-01

The work presented in this paper develops a new formalism to design microdisks and microgears structures. The main objective is to study the optics and geometrics parameters influence on the microdisks and microgears structures resonance behavior. This study is conducted to choice a resonance structure with height quality factor Q to be associated with Quantum dot to form a single photon source. This new method aims to design resonant structures that are simpler and requires less computing performances than FDTD and Floquet Block methods. This formalism is based on simplifying Fourier transformed and using toeplitz matrix writing. This new writing allows designing all kind of resonance structures with any defect and any modification. In other study we have design a quantum dot emitting a photon at 1550 nm of the fundamental mode, but the quantum dot emits other photons at other wavelengths. The focus of the resonant structure and the quantum dot association is the resonance of the photon at 1550 nm and the elimination of all other photons with others energies. The quantum dot studied in [1] is an InAs/GaAs quantum dot, we design an GaAS microdisk and microgear and we compare the quality factor Q of this two structures and we conclude that the microgear is more appropriated to be associate to the quantum dot and increase the probability P1 to obtain a single photon source at 1550 nm and promotes the obtaining of single photon. The performance improving of the resonant structure is able to increase the success of quantum applications such as quantum gates based on single photon source.

Transverse correlation in entangled photons and light-matter interaction

NASA Astrophysics Data System (ADS)

Wen, Jianming

In recent years, quantum entanglement has attracted much attention, because its unique properties provide potential applications, which could not be achieved using conventional techniques, such as quantum computing, quantum imaging and lithography. To realize these advancements, one has to obtain an entanglement-generation source, thoroughly master its physical properties, and fully understand the light-matter interaction. This dissertation is an attempt to address such issues as stated above. Conventionally, paired photons are created from spontaneous parametric down-conversion (SPDC). It is known that the transverse correlation in biphotons may improve the visibility and resolution in quantum imaging and lithography. In this thesis, we described an alternative biphoton source---Raman-EIT (electromagnetically induced transparency) generator, and emphasize on its geometrical and optical properties. We found that to utilize the transverse effects in paired Stokes-anti-Stokes, it is necessary to make the product of the EIT window times the group delay much greater than unity. To gain further insight into quantum imaging and lithography, we studied the transverse correlation in triphoton entanglement theoretically. We found that in the two-image process, the quality of images is determined by the optical path-lengths, even though the Gaussian thin lens equations are satisfied. The ghost interference-diffraction patterns of double slits show one more fold interference, which is essentially different from the biphoton case. Klyshko's advanced-wave model is still applicable, with some modifications. We also generalized the transverse correlation to the case of multi-photon entangled states. To implement quantum computing, one key element is quantum memory. In this thesis, we have theoretically explored the feasibility of such a memory by using nonclassical SPDC light in an EIT system at the single-photon level. We found that both the quantum coherence of SPDC and atomic coherence of EIT can survive after interacting within a vapor cell. Due to the inherent mismatch of magnitude between the spectral bandwidth of SPDC and the very narrow transmission width of EIT, the coincidence counts of the two-photon interference is reduced to one pair per second, which is barely doable in the current experimental situation.

The feasibility of coherent energy transfer in microtubules.

PubMed

Craddock, Travis John Adrian; Friesen, Douglas; Mane, Jonathan; Hameroff, Stuart; Tuszynski, Jack A

2014-11-06

It was once purported that biological systems were far too 'warm and wet' to support quantum phenomena mainly owing to thermal effects disrupting quantum coherence. However, recent experimental results and theoretical analyses have shown that thermal energy may assist, rather than disrupt, quantum coherent transport, especially in the 'dry' hydrophobic interiors of biomolecules. Specifically, evidence has been accumulating for the necessary involvement of quantum coherent energy transfer between uniquely arranged chromophores in light harvesting photosynthetic complexes. The 'tubulin' subunit proteins, which comprise microtubules, also possess a distinct architecture of chromophores, namely aromatic amino acids, including tryptophan. The geometry and dipolar properties of these aromatics are similar to those found in photosynthetic units indicating that tubulin may support coherent energy transfer. Tubulin aggregated into microtubule geometric lattices may support such energy transfer, which could be important for biological signalling and communication essential to living processes. Here, we perform a computational investigation of energy transfer between chromophoric amino acids in tubulin via dipole excitations coupled to the surrounding thermal environment. We present the spatial structure and energetic properties of the tryptophan residues in the microtubule constituent protein tubulin. Plausibility arguments for the conditions favouring a quantum mechanism of signal propagation along a microtubule are provided. Overall, we find that coherent energy transfer in tubulin and microtubules is biologically feasible. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Investigation of the spinfoam path integral with quantum cuboid intertwiners

NASA Astrophysics Data System (ADS)

Bahr, Benjamin; Steinhaus, Sebastian

2016-05-01

In this work, we investigate the 4d path integral for Euclidean quantum gravity on a hypercubic lattice, as given by the spinfoam model by Engle, Pereira, Rovelli, Livine, Freidel and Krasnov. To tackle the problem, we restrict to a set of quantum geometries that reflects the large amount of lattice symmetries. In particular, the sum over intertwiners is restricted to quantum cuboids, i.e. coherent intertwiners which describe a cuboidal geometry in the large-j limit. Using asymptotic expressions for the vertex amplitude, we find several interesting properties of the state sum. First of all, the value of coupling constants in the amplitude functions determines whether geometric or nongeometric configurations dominate the path integral. Secondly, there is a critical value of the coupling constant α , which separates two phases. In both phases, the diffeomorphism symmetry appears to be broken. In one, the dominant contribution comes from highly irregular, in the other from highly regular configurations, both describing flat Euclidean space with small quantum fluctuations around them, viewed in different coordinate systems. On the critical point diffeomorphism symmetry is nearly restored, however. Thirdly, we use the state sum to compute the physical norm of kinematical states, i.e. their norm in the physical Hilbert space. We find that states which describe boundary geometry with high torsion have an exponentially suppressed physical norm. We argue that this allows one to exclude them from the state sum in calculations.

Blind Quantum Signature with Blind Quantum Computation

NASA Astrophysics Data System (ADS)

Li, Wei; Shi, Ronghua; Guo, Ying

2017-04-01

Blind quantum computation allows a client without quantum abilities to interact with a quantum server to perform a unconditional secure computing protocol, while protecting client's privacy. Motivated by confidentiality of blind quantum computation, a blind quantum signature scheme is designed with laconic structure. Different from the traditional signature schemes, the signing and verifying operations are performed through measurement-based quantum computation. Inputs of blind quantum computation are securely controlled with multi-qubit entangled states. The unique signature of the transmitted message is generated by the signer without leaking information in imperfect channels. Whereas, the receiver can verify the validity of the signature using the quantum matching algorithm. The security is guaranteed by entanglement of quantum system for blind quantum computation. It provides a potential practical application for e-commerce in the cloud computing and first-generation quantum computation.

Open-system dynamics of entanglement:a key issues review

NASA Astrophysics Data System (ADS)

Aolita, Leandro; de Melo, Fernando; Davidovich, Luiz

2015-04-01

One of the greatest challenges in the fields of quantum information processing and quantum technologies is the detailed coherent control over each and every constituent of quantum systems with an ever increasing number of particles. Within this endeavor, harnessing of many-body entanglement against the detrimental effects of the environment is a major pressing issue. Besides being an important concept from a fundamental standpoint, entanglement has been recognized as a crucial resource for quantum speed-ups or performance enhancements over classical methods. Understanding and controlling many-body entanglement in open systems may have strong implications in quantum computing, quantum simulations of many-body systems, secure quantum communication or cryptography, quantum metrology, our understanding of the quantum-to-classical transition, and other important questions of quantum foundations. In this paper we present an overview of recent theoretical and experimental efforts to underpin the dynamics of entanglement under the influence of noise. Entanglement is thus taken as a dynamic quantity on its own, and we survey how it evolves due to the unavoidable interaction of the entangled system with its surroundings. We analyze several scenarios, corresponding to different families of states and environments, which render a very rich diversity of dynamical behaviors. In contrast to single-particle quantities, like populations and coherences, which typically vanish only asymptotically in time, entanglement may disappear at a finite time. In addition, important classes of entanglement display an exponential decay with the number of particles when subject to local noise, which poses yet another threat to the already-challenging scaling of quantum technologies. Other classes, however, turn out to be extremely robust against local noise. Theoretical results and recent experiments regarding the difference between local and global decoherence are summarized. Control and robustness-enhancement techniques, scaling laws, statistical and geometrical aspects of multipartite-entanglement decay are also reviewed; all in order to give a broad picture of entanglement dynamics in open quantum systems addressed to both theorists and experimentalists inside and outside the field of quantum information.

Open-system dynamics of entanglement: a key issues review.

PubMed

Aolita, Leandro; de Melo, Fernando; Davidovich, Luiz

2015-04-01

One of the greatest challenges in the fields of quantum information processing and quantum technologies is the detailed coherent control over each and every constituent of quantum systems with an ever increasing number of particles. Within this endeavor, harnessing of many-body entanglement against the detrimental effects of the environment is a major pressing issue. Besides being an important concept from a fundamental standpoint, entanglement has been recognized as a crucial resource for quantum speed-ups or performance enhancements over classical methods. Understanding and controlling many-body entanglement in open systems may have strong implications in quantum computing, quantum simulations of many-body systems, secure quantum communication or cryptography, quantum metrology, our understanding of the quantum-to-classical transition, and other important questions of quantum foundations.In this paper we present an overview of recent theoretical and experimental efforts to underpin the dynamics of entanglement under the influence of noise. Entanglement is thus taken as a dynamic quantity on its own, and we survey how it evolves due to the unavoidable interaction of the entangled system with its surroundings. We analyze several scenarios, corresponding to different families of states and environments, which render a very rich diversity of dynamical behaviors.In contrast to single-particle quantities, like populations and coherences, which typically vanish only asymptotically in time, entanglement may disappear at a finite time. In addition, important classes of entanglement display an exponential decay with the number of particles when subject to local noise, which poses yet another threat to the already-challenging scaling of quantum technologies. Other classes, however, turn out to be extremely robust against local noise. Theoretical results and recent experiments regarding the difference between local and global decoherence are summarized. Control and robustness-enhancement techniques, scaling laws, statistical and geometrical aspects of multipartite-entanglement decay are also reviewed; all in order to give a broad picture of entanglement dynamics in open quantum systems addressed to both theorists and experimentalists inside and outside the field of quantum information.

Measurement-only verifiable blind quantum computing with quantum input verification

NASA Astrophysics Data System (ADS)

Morimae, Tomoyuki

2016-10-01

Verifiable blind quantum computing is a secure delegated quantum computing where a client with a limited quantum technology delegates her quantum computing to a server who has a universal quantum computer. The client's privacy is protected (blindness), and the correctness of the computation is verifiable by the client despite her limited quantum technology (verifiability). There are mainly two types of protocols for verifiable blind quantum computing: the protocol where the client has only to generate single-qubit states and the protocol where the client needs only the ability of single-qubit measurements. The latter is called the measurement-only verifiable blind quantum computing. If the input of the client's quantum computing is a quantum state, whose classical efficient description is not known to the client, there was no way for the measurement-only client to verify the correctness of the input. Here we introduce a protocol of measurement-only verifiable blind quantum computing where the correctness of the quantum input is also verifiable.

Programmable Quantum Photonic Processor Using Silicon Photonics

DTIC Science & Technology

2017-04-01

quantum information processing and quantum sensing, ranging from linear optics quantum computing and quantum simulation to quantum ...transformers have driven experimental and theoretical advances in quantum simulation, cluster-state quantum computing , all-optical quantum repeaters...neuromorphic computing , and other applications. In addition, we developed new schemes for ballistic quantum computation , new methods for

Photodissociation of phenol via nonadiabatic tunneling: Comparison of two ab initio based potential energy surfaces

NASA Astrophysics Data System (ADS)

Xie, Changjian; Guo, Hua

2017-09-01

The nonadiabatic tunneling-facilitated photodissociation of phenol is investigated using a reduced-dimensional quantum model on two ab initio-based coupled potential energy surfaces (PESs). Although dynamics occurs largely on the lower adiabat, the proximity to a conical intersection between the S1 and S2 states requires the inclusion of both the geometric phase (GP) and diagonal Born-Oppenheimer correction (DBOC). The lifetime of the lowest-lying vibronic state is computed using the diabatic and various adiabatic models. The GP and DBOC terms are found to be essential on one set of PESs, but have a small impact on the other.

Vibrational properties of gold nanoparticles obtained by green synthesis

NASA Astrophysics Data System (ADS)

Alvarez, Ramón A. B.; Cortez-Valadez, M.; Bueno, L. Oscar Neira; Britto Hurtado, R.; Rocha-Rocha, O.; Delgado-Beleño, Y.; Martinez-Nuñez, C. E.; Serrano-Corrales, Luis Ivan; Arizpe-Chávez, H.; Flores-Acosta, M.

2016-10-01

This study reports the synthesis and characterization of gold nanoparticles through an ecological method to obtain nanostructures from the extract of the plant Opuntia ficus-indica. Colloidal nanoparticles show sizes that vary between 10-20 nm, and present various geometric morphologies. The samples were characterized through optical absorption, Raman Spectroscopy and Transmission Electron Microscopy (TEM). Additionally, low energy metallic clusters of Aun (n=2-20 atoms) were modeled by computational quantum chemistry. The theoretical results were obtained with Density Functional Theory (DFT). The predicted results of Au clusters show a tendency and are correlated with the experimental results concerning the optical absorption bands and Raman spectroscopy in gold nanoparticles.

MDO can help resolve the designer's dilemma. [multidisciplinary design optimization

NASA Technical Reports Server (NTRS)

Sobieszczanski-Sobieski, Jaroslaw; Tulinius, Jan R.

1991-01-01

Multidisciplinary design optimization (MDO) is presented as a rapidly growing body of methods, algorithms, and techniques that will provide a quantum jump in the effectiveness and efficiency of the quantitative side of design, and will turn that side into an environment in which the qualitative side can thrive. MDO borrows from CAD/CAM for graphic visualization of geometrical and numerical data, data base technology, and in computer software and hardware. Expected benefits from this methodology are a rational, mathematically consistent approach to hypersonic aircraft designs, designs pushed closer to the optimum, and a design process either shortened or leaving time available for different concepts to be explored.

Quantum analogue computing.

PubMed

Kendon, Vivien M; Nemoto, Kae; Munro, William J

2010-08-13

We briefly review what a quantum computer is, what it promises to do for us and why it is so hard to build one. Among the first applications anticipated to bear fruit is the quantum simulation of quantum systems. While most quantum computation is an extension of classical digital computation, quantum simulation differs fundamentally in how the data are encoded in the quantum computer. To perform a quantum simulation, the Hilbert space of the system to be simulated is mapped directly onto the Hilbert space of the (logical) qubits in the quantum computer. This type of direct correspondence is how data are encoded in a classical analogue computer. There is no binary encoding, and increasing precision becomes exponentially costly: an extra bit of precision doubles the size of the computer. This has important consequences for both the precision and error-correction requirements of quantum simulation, and significant open questions remain about its practicality. It also means that the quantum version of analogue computers, continuous-variable quantum computers, becomes an equally efficient architecture for quantum simulation. Lessons from past use of classical analogue computers can help us to build better quantum simulators in future.

Triple-server blind quantum computation using entanglement swapping

NASA Astrophysics Data System (ADS)

Li, Qin; Chan, Wai Hong; Wu, Chunhui; Wen, Zhonghua

2014-04-01

Blind quantum computation allows a client who does not have enough quantum resources or technologies to achieve quantum computation on a remote quantum server such that the client's input, output, and algorithm remain unknown to the server. Up to now, single- and double-server blind quantum computation have been considered. In this work, we propose a triple-server blind computation protocol where the client can delegate quantum computation to three quantum servers by the use of entanglement swapping. Furthermore, the three quantum servers can communicate with each other and the client is almost classical since one does not require any quantum computational power, quantum memory, and the ability to prepare any quantum states and only needs to be capable of getting access to quantum channels.

Background-independent condensed matter models for quantum gravity

NASA Astrophysics Data System (ADS)

Hamma, Alioscia; Markopoulou, Fotini

2011-09-01

A number of recent proposals on a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two fundamental challenges to any such approach. At the conceptual level, there is a clash between the 'timelessness' of general relativity and emergence. Secondly, the lack of a fundamental spacetime renders difficult the straightforward application of well-known methods of statistical physics to the problem. We recently initiated a study of such problems using spin systems based on the evolution of quantum networks with no a priori geometric notions as models for emergent geometry and gravity. In this paper, we review two such models. The first model is a model of emergent (flat) space and matter, and we show how to use methods from quantum information theory to derive features such as the speed of light from a non-geometric quantum system. The second model exhibits interacting matter and geometry, with the geometry defined by the behavior of matter. This model has primitive notions of gravitational attraction that we illustrate with a toy black hole, and exhibits entanglement between matter and geometry and thermalization of the quantum geometry.

Non-Abelian monopole in the parameter space of point-like interactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ohya, Satoshi, E-mail: ohyasato@fjfi.cvut.cz

2014-12-15

We study non-Abelian geometric phase in N=2 supersymmetric quantum mechanics for a free particle on a circle with two point-like interactions at antipodal points. We show that non-Abelian Berry’s connection is that of SU(2) magnetic monopole discovered by Moody, Shapere and Wilczek in the context of adiabatic decoupling limit of diatomic molecule. - Highlights: • Supersymmetric quantum mechanics is an ideal playground for studying geometric phase. • We determine the parameter space of supersymmetric point-like interactions. • Berry’s connection is given by a Wu–Yang-like magnetic monopole in SU(2) Yang–Mills.

Quantum Gravity and Cosmology: an intimate interplay

NASA Astrophysics Data System (ADS)

Sakellariadou, Mairi

2017-08-01

I will briefly discuss three cosmological models built upon three distinct quantum gravity proposals. I will first highlight the cosmological rôle of a vector field in the framework of a string/brane cosmological model. I will then present the resolution of the big bang singularity and the occurrence of an early era of accelerated expansion of a geometric origin, in the framework of group field theory condensate cosmology. I will then summarise results from an extended gravitational model based on non-commutative spectral geometry, a model that offers a purely geometric explanation for the standard model of particle physics.

Characterizing nonclassical correlations via local quantum Fisher information

NASA Astrophysics Data System (ADS)

Kim, Sunho; Li, Longsuo; Kumar, Asutosh; Wu, Junde

2018-03-01

We define two ways of quantifying the quantum correlations based on quantum Fisher information (QFI) in order to study the quantum correlations as a resource in quantum metrology. By investigating the hierarchy of measurement-induced Fisher information introduced in Lu et al. [X. M. Lu, S. Luo, and C. H. Oh, Phys. Rev. A 86, 022342 (2012), 10.1103/PhysRevA.86.022342], we show that the presence of quantum correlation can be confirmed by the difference of the Fisher information induced by the measurements of two hierarchies. In particular, the quantitative quantum correlations based on QFI coincide with the geometric discord for pure quantum states.

How to Build a Quantum Computer

NASA Astrophysics Data System (ADS)

Sanders, Barry C.

2017-11-01

Quantum computer technology is progressing rapidly with dozens of qubits and hundreds of quantum logic gates now possible. Although current quantum computer technology is distant from being able to solve computational problems beyond the reach of non-quantum computers, experiments have progressed well beyond simply demonstrating the requisite components. We can now operate small quantum logic processors with connected networks of qubits and quantum logic gates, which is a great stride towards functioning quantum computers. This book aims to be accessible to a broad audience with basic knowledge of computers, electronics and physics. The goal is to convey key notions relevant to building quantum computers and to present state-of-the-art quantum-computer research in various media such as trapped ions, superconducting circuits, photonics and beyond.

Blind topological measurement-based quantum computation.

PubMed

Morimae, Tomoyuki; Fujii, Keisuke

2012-01-01

Blind quantum computation is a novel secure quantum-computing protocol that enables Alice, who does not have sufficient quantum technology at her disposal, to delegate her quantum computation to Bob, who has a fully fledged quantum computer, in such a way that Bob cannot learn anything about Alice's input, output and algorithm. A recent proof-of-principle experiment demonstrating blind quantum computation in an optical system has raised new challenges regarding the scalability of blind quantum computation in realistic noisy conditions. Here we show that fault-tolerant blind quantum computation is possible in a topologically protected manner using the Raussendorf-Harrington-Goyal scheme. The error threshold of our scheme is 4.3 × 10(-3), which is comparable to that (7.5 × 10(-3)) of non-blind topological quantum computation. As the error per gate of the order 10(-3) was already achieved in some experimental systems, our result implies that secure cloud quantum computation is within reach.

Blind topological measurement-based quantum computation

NASA Astrophysics Data System (ADS)

Morimae, Tomoyuki; Fujii, Keisuke

2012-09-01

Blind quantum computation is a novel secure quantum-computing protocol that enables Alice, who does not have sufficient quantum technology at her disposal, to delegate her quantum computation to Bob, who has a fully fledged quantum computer, in such a way that Bob cannot learn anything about Alice's input, output and algorithm. A recent proof-of-principle experiment demonstrating blind quantum computation in an optical system has raised new challenges regarding the scalability of blind quantum computation in realistic noisy conditions. Here we show that fault-tolerant blind quantum computation is possible in a topologically protected manner using the Raussendorf-Harrington-Goyal scheme. The error threshold of our scheme is 4.3×10-3, which is comparable to that (7.5×10-3) of non-blind topological quantum computation. As the error per gate of the order 10-3 was already achieved in some experimental systems, our result implies that secure cloud quantum computation is within reach.

Metric dimensional reduction at singularities with implications to Quantum Gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stoica, Ovidiu Cristinel, E-mail: holotronix@gmail.com

2014-08-15

A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at high energy scales. But an identification of the deep mechanism causing this dimensional reduction would still be desirable. The main contribution of this article is to show that dimensional reduction effects are due to General Relativity at singularities, and do not need to be postulated ad-hoc. Recent advances in understanding the geometry of singularities do not require modification of General Relativity, being justmore » non-singular extensions of its mathematics to the limit cases. They turn out to work fine for some known types of cosmological singularities (black holes and FLRW Big-Bang), allowing a choice of the fundamental geometric invariants and physical quantities which remain regular. The resulting equations are equivalent to the standard ones outside the singularities. One consequence of this mathematical approach to the singularities in General Relativity is a special, (geo)metric type of dimensional reduction: at singularities, the metric tensor becomes degenerate in certain spacetime directions, and some properties of the fields become independent of those directions. Effectively, it is like one or more dimensions of spacetime just vanish at singularities. This suggests that it is worth exploring the possibility that the geometry of singularities leads naturally to the spontaneous dimensional reduction needed by Quantum Gravity. - Highlights: • The singularities we introduce are described by finite geometric/physical objects. • Our singularities are accompanied by dimensional reduction effects. • They affect the metric, the measure, the topology, the gravitational DOF (Weyl = 0). • Effects proposed in other approaches to Quantum Gravity are obtained naturally. • The geometric dimensional reduction obtained opens new ways for Quantum Gravity.« less

Demonstration of blind quantum computing.

PubMed

Barz, Stefanie; Kashefi, Elham; Broadbent, Anne; Fitzsimons, Joseph F; Zeilinger, Anton; Walther, Philip

2012-01-20

Quantum computers, besides offering substantial computational speedups, are also expected to preserve the privacy of a computation. We present an experimental demonstration of blind quantum computing in which the input, computation, and output all remain unknown to the computer. We exploit the conceptual framework of measurement-based quantum computation that enables a client to delegate a computation to a quantum server. Various blind delegated computations, including one- and two-qubit gates and the Deutsch and Grover quantum algorithms, are demonstrated. The client only needs to be able to prepare and transmit individual photonic qubits. Our demonstration is crucial for unconditionally secure quantum cloud computing and might become a key ingredient for real-life applications, especially when considering the challenges of making powerful quantum computers widely available.

Quantum Computation: Entangling with the Future

NASA Technical Reports Server (NTRS)

Jiang, Zhang

2017-01-01

Commercial applications of quantum computation have become viable due to the rapid progress of the field in the recent years. Efficient quantum algorithms are discovered to cope with the most challenging real-world problems that are too hard for classical computers. Manufactured quantum hardware has reached unprecedented precision and controllability, enabling fault-tolerant quantum computation. Here, I give a brief introduction on what principles in quantum mechanics promise its unparalleled computational power. I will discuss several important quantum algorithms that achieve exponential or polynomial speedup over any classical algorithm. Building a quantum computer is a daunting task, and I will talk about the criteria and various implementations of quantum computers. I conclude the talk with near-future commercial applications of a quantum computer.

A tale of two fractals: The Hofstadter butterfly and the integral Apollonian gaskets

NASA Astrophysics Data System (ADS)

Satija, Indubala I.

2016-11-01

This paper unveils a mapping between a quantum fractal that describes a physical phenomena, and an abstract geometrical fractal. The quantum fractal is the Hofstadter butterfly discovered in 1976 in an iconic condensed matter problem of electrons moving in a two-dimensional lattice in a transverse magnetic field. The geometric fractal is the integer Apollonian gasket characterized in terms of a 300 BC problem of mutually tangent circles. Both of these fractals are made up of integers. In the Hofstadter butterfly, these integers encode the topological quantum numbers of quantum Hall conductivity. In the Apollonian gaskets an infinite number of mutually tangent circles are nested inside each other, where each circle has integer curvature. The mapping between these two fractals reveals a hidden D3 symmetry embedded in the kaleidoscopic images that describe the asymptotic scaling properties of the butterfly. This paper also serves as a mini review of these fractals, emphasizing their hierarchical aspects in terms of Farey fractions.

Magnetic gaps in organic tri-radicals: From a simple model to accurate estimates.

PubMed

Barone, Vincenzo; Cacelli, Ivo; Ferretti, Alessandro; Prampolini, Giacomo

2017-03-14

The calculation of the energy gap between the magnetic states of organic poly-radicals still represents a challenging playground for quantum chemistry, and high-level techniques are required to obtain accurate estimates. On these grounds, the aim of the present study is twofold. From the one side, it shows that, thanks to recent algorithmic and technical improvements, we are able to compute reliable quantum mechanical results for the systems of current fundamental and technological interest. From the other side, proper parameterization of a simple Hubbard Hamiltonian allows for a sound rationalization of magnetic gaps in terms of basic physical effects, unraveling the role played by electron delocalization, Coulomb repulsion, and effective exchange in tuning the magnetic character of the ground state. As case studies, we have chosen three prototypical organic tri-radicals, namely, 1,3,5-trimethylenebenzene, 1,3,5-tridehydrobenzene, and 1,2,3-tridehydrobenzene, which differ either for geometric or electronic structure. After discussing the differences among the three species and their consequences on the magnetic properties in terms of the simple model mentioned above, accurate and reliable values for the energy gap between the lowest quartet and doublet states are computed by means of the so-called difference dedicated configuration interaction (DDCI) technique, and the final results are discussed and compared to both available experimental and computational estimates.

Undergraduate computational physics projects on quantum computing

NASA Astrophysics Data System (ADS)

Candela, D.

2015-08-01

Computational projects on quantum computing suitable for students in a junior-level quantum mechanics course are described. In these projects students write their own programs to simulate quantum computers. Knowledge is assumed of introductory quantum mechanics through the properties of spin 1/2. Initial, more easily programmed projects treat the basics of quantum computation, quantum gates, and Grover's quantum search algorithm. These are followed by more advanced projects to increase the number of qubits and implement Shor's quantum factoring algorithm. The projects can be run on a typical laptop or desktop computer, using most programming languages. Supplementing resources available elsewhere, the projects are presented here in a self-contained format especially suitable for a short computational module for physics students.

A comparative experimental and quantum chemical study on monomeric and dimeric structures of 3,5-dibromoanthranilic acid.

PubMed

Karabacak, Mehmet; Cinar, Mehmet

2012-10-01

This study presents the structural and spectroscopic characterization of 3,5-dibromoanthranilic acid with help of experimental techniques (FT-IR, FT-Raman, UV, NMR) and quantum chemical calculations. The vibrational spectra of title compound were recorded in solid state with FT-IR and FT-Raman in the range of 4000-400 and 4000-50 cm(-1), respectively. The vibrational frequencies were also computed using B3LYP method of DFT with 6-311++G(d,p) basis set. The fundamental assignments were done on the basis of the total energy distribution (TED) of the vibrational modes, calculated with scaled quantum mechanical (SQM) method. The (1)H, (13)C and DEPT NMR spectra were recorded in DMSO solution and calculated by gauge-invariant atomic orbitals (GIAO) method. The UV absorption spectra of the compound were recorded in the range of 200-400 nm in ethanol, water and DMSO solutions. Solvent effects were calculated using time-dependent density functional theory and CIS method. The ground state geometrical structure of compound was predicted by B3LYP method and compared with the crystallographic structure of similar compounds. All calculations were made for monomeric and dimeric structure of compound. Moreover, molecular electrostatic potential (MEP) and thermodynamic properties were performed. Mulliken atomic charges of neutral and anionic form of the molecule were computed and compared with anthranilic acid. Copyright © 2012 Elsevier B.V. All rights reserved.

General N=2 supersymmetric quantum mechanical model: Supervariable approach to its off-shell nilpotent symmetries

DOE Office of Scientific and Technical Information (OSTI.GOV)

Krishna, S., E-mail: skrishna.bhu@gmail.com; Shukla, A., E-mail: ashukla038@gmail.com; Malik, R.P., E-mail: rpmalik1995@gmail.com

2014-12-15

Using the supersymmetric (SUSY) invariant restrictions on the (anti-)chiral supervariables, we derive the off-shell nilpotent symmetries of the general one (0+1)-dimensional N=2 SUSY quantum mechanical (QM) model which is considered on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables θ and θ-bar with θ{sup 2}=(θ-bar){sup 2}=0,θ(θ-bar)+(θ-bar)θ=0). We provide the geometrical meanings to the two SUSY transformations of our present theory which are valid for any arbitrary type of superpotential. We express the conserved charges and Lagrangian of the theory in terms of the supervariables (that are obtained after the application of SUSYmore » invariant restrictions) and provide the geometrical interpretation for the nilpotency property and SUSY invariance of the Lagrangian for the general N=2 SUSY quantum theory. We also comment on the mathematical interpretation of the above symmetry transformations. - Highlights: • A novel method has been proposed for the derivation of N=2 SUSY transformations. • General N=2 SUSY quantum mechanical (QM) model with a general superpotential, is considered. • The above SUSY QM model is generalized onto a (1, 2)-dimensional supermanifold. • SUSY invariant restrictions are imposed on the (anti-)chiral supervariables. • Geometrical meaning of the nilpotency property is provided.« less

Quantum motion on a torus as a submanifold problem in a generalized Dirac's theory of second-class constraints

NASA Astrophysics Data System (ADS)

Xun, D. M.; Liu, Q. H.; Zhu, X. M.

2013-11-01

A generalization of Dirac's canonical quantization scheme for a system with second-class constraints is proposed, in which the fundamental commutation relations are constituted by all commutators between positions, momenta and Hamiltonian, so they are simultaneously quantized in a self-consistent manner, rather than by those between merely positions and momenta which leads to ambiguous forms of the Hamiltonian and the momenta. The application of the generalized scheme to the quantum motion on a torus leads to a remarkable result: the quantum theory is inconsistent if built up in an intrinsic geometric manner, whereas it becomes consistent within an extrinsic examination of the torus as a submanifold in three dimensional flat space with the use of the Cartesian coordinate system. The geometric momentum and potential are then reasonably reproduced.

Blind topological measurement-based quantum computation

PubMed Central

Morimae, Tomoyuki; Fujii, Keisuke

2012-01-01

Blind quantum computation is a novel secure quantum-computing protocol that enables Alice, who does not have sufficient quantum technology at her disposal, to delegate her quantum computation to Bob, who has a fully fledged quantum computer, in such a way that Bob cannot learn anything about Alice's input, output and algorithm. A recent proof-of-principle experiment demonstrating blind quantum computation in an optical system has raised new challenges regarding the scalability of blind quantum computation in realistic noisy conditions. Here we show that fault-tolerant blind quantum computation is possible in a topologically protected manner using the Raussendorf–Harrington–Goyal scheme. The error threshold of our scheme is 4.3×10−3, which is comparable to that (7.5×10−3) of non-blind topological quantum computation. As the error per gate of the order 10−3 was already achieved in some experimental systems, our result implies that secure cloud quantum computation is within reach. PMID:22948818

Quantum computation for solving linear systems

NASA Astrophysics Data System (ADS)

Cao, Yudong

Quantum computation is a subject born out of the combination between physics and computer science. It studies how the laws of quantum mechanics can be exploited to perform computations much more efficiently than current computers (termed classical computers as oppose to quantum computers). The thesis starts by introducing ideas from quantum physics and theoretical computer science and based on these ideas, introducing the basic concepts in quantum computing. These introductory discussions are intended for non-specialists to obtain the essential knowledge needed for understanding the new results presented in the subsequent chapters. After introducing the basics of quantum computing, we focus on the recently proposed quantum algorithm for linear systems. The new results include i) special instances of quantum circuits that can be implemented using current experimental resources; ii) detailed quantum algorithms that are suitable for a broader class of linear systems. We show that for some particular problems the quantum algorithm is able to achieve exponential speedup over their classical counterparts.

Abstract quantum computing machines and quantum computational logics

NASA Astrophysics Data System (ADS)

Chiara, Maria Luisa Dalla; Giuntini, Roberto; Sergioli, Giuseppe; Leporini, Roberto

2016-06-01

Classical and quantum parallelism are deeply different, although it is sometimes claimed that quantum Turing machines are nothing but special examples of classical probabilistic machines. We introduce the concepts of deterministic state machine, classical probabilistic state machine and quantum state machine. On this basis, we discuss the question: To what extent can quantum state machines be simulated by classical probabilistic state machines? Each state machine is devoted to a single task determined by its program. Real computers, however, behave differently, being able to solve different kinds of problems. This capacity can be modeled, in the quantum case, by the mathematical notion of abstract quantum computing machine, whose different programs determine different quantum state machines. The computations of abstract quantum computing machines can be linguistically described by the formulas of a particular form of quantum logic, termed quantum computational logic.

Some foundational aspects of quantum computers and quantum robots.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Benioff, P.; Physics

1998-01-01

This paper addresses foundational issues related to quantum computing. The need for a universally valid theory such as quantum mechanics to describe to some extent its own validation is noted. This includes quantum mechanical descriptions of systems that do theoretical calculations (i.e. quantum computers) and systems that perform experiments. Quantum robots interacting with an environment are a small first step in this direction. Quantum robots are described here as mobile quantum systems with on-board quantum computers that interact with environments. Included are discussions on the carrying out of tasks and the division of tasks into computation and action phases. Specificmore » models based on quantum Turing machines are described. Differences and similarities between quantum robots plus environments and quantum computers are discussed.« less

Quantum computers: Definition and implementations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perez-Delgado, Carlos A.; Kok, Pieter

The DiVincenzo criteria for implementing a quantum computer have been seminal in focusing both experimental and theoretical research in quantum-information processing. These criteria were formulated specifically for the circuit model of quantum computing. However, several new models for quantum computing (paradigms) have been proposed that do not seem to fit the criteria well. Therefore, the question is what are the general criteria for implementing quantum computers. To this end, a formal operational definition of a quantum computer is introduced. It is then shown that, according to this definition, a device is a quantum computer if it obeys the following criteria:more » Any quantum computer must consist of a quantum memory, with an additional structure that (1) facilitates a controlled quantum evolution of the quantum memory; (2) includes a method for information theoretic cooling of the memory; and (3) provides a readout mechanism for subsets of the quantum memory. The criteria are met when the device is scalable and operates fault tolerantly. We discuss various existing quantum computing paradigms and how they fit within this framework. Finally, we present a decision tree for selecting an avenue toward building a quantum computer. This is intended to help experimentalists determine the most natural paradigm given a particular physical implementation.« less

Quantum simulator review

NASA Astrophysics Data System (ADS)

Bednar, Earl; Drager, Steven L.

2007-04-01

Quantum information processing's objective is to utilize revolutionary computing capability based on harnessing the paradigm shift offered by quantum computing to solve classically hard and computationally challenging problems. Some of our computationally challenging problems of interest include: the capability for rapid image processing, rapid optimization of logistics, protecting information, secure distributed simulation, and massively parallel computation. Currently, one important problem with quantum information processing is that the implementation of quantum computers is difficult to realize due to poor scalability and great presence of errors. Therefore, we have supported the development of Quantum eXpress and QuIDD Pro, two quantum computer simulators running on classical computers for the development and testing of new quantum algorithms and processes. This paper examines the different methods used by these two quantum computing simulators. It reviews both simulators, highlighting each simulators background, interface, and special features. It also demonstrates the implementation of current quantum algorithms on each simulator. It concludes with summary comments on both simulators.

Quantum walk computation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kendon, Viv

2014-12-04

Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. Recent results showing quantum walks are “universal for quantum computation” relate to algorithms, to be run on quantum computers. We consider whether an experimental implementation of a quantum walk could provide useful computation before we have a universal quantum computer.

Geometrical Description of fractional quantum Hall quasiparticles

NASA Astrophysics Data System (ADS)

Park, Yeje; Yang, Bo; Haldane, F. D. M.

2012-02-01

We examine a description of fractional quantum Hall quasiparticles and quasiholes suggested by a recent geometrical approach (F. D. M. Haldane, Phys. Rev. Lett. 108, 116801 (2011)) to FQH systems, where the local excess electric charge density in the incompressible state is given by a topologically-quantized ``guiding-center spin'' times the Gaussian curvature of a ``guiding-center metric tensor'' that characterizes the local shape of the correlation hole around electrons in the fluid. We use a phenomenological energy function with two ingredients: the shear distortion energy of area-preserving distortions of the fluid, and a local (short-range) approximation to the Coulomb energy of the fluctuation of charge density associated with the Gaussian curvature. Quasiparticles and quasiholes of the 1/3 Laughlin state are modeled as ``punctures'' in the incompressible fluid which then relax by geometric distortion which generates Gaussian curvature, giving rise to the charge-density profile around the topological excitation.

Quantum simulations with noisy quantum computers

NASA Astrophysics Data System (ADS)

Gambetta, Jay

Quantum computing is a new computational paradigm that is expected to lie beyond the standard model of computation. This implies a quantum computer can solve problems that can't be solved by a conventional computer with tractable overhead. To fully harness this power we need a universal fault-tolerant quantum computer. However the overhead in building such a machine is high and a full solution appears to be many years away. Nevertheless, we believe that we can build machines in the near term that cannot be emulated by a conventional computer. It is then interesting to ask what these can be used for. In this talk we will present our advances in simulating complex quantum systems with noisy quantum computers. We will show experimental implementations of this on some small quantum computers.

Geometric rectification for nanoscale vibrational energy harvesting

NASA Astrophysics Data System (ADS)

Bustos-Marún, Raúl A.

2018-02-01

In this work, we present a mechanism that, based on quantum-mechanical principles, allows one to recover kinetic energy at the nanoscale. Our premise is that very small mechanical excitations, such as those arising from sound waves propagating through a nanoscale system or similar phenomena, can be quite generally converted into useful electrical work by applying the same principles behind conventional adiabatic quantum pumping. The proposal is potentially useful for nanoscale vibrational energy harvesting where it can have several advantages. The most important one is that it avoids the use of classical rectification mechanisms as it is based on what we call geometric rectification. We show that this geometric rectification results from applying appropriate but quite general initial conditions to damped harmonic systems coupled to electronic reservoirs. We analyze an analytically solvable example consisting of a wire suspended over permanent charges where we find the condition for maximizing the pumped charge. We also studied the effects of coupling the system to a capacitor including the effect of current-induced forces and analyzing the steady-state voltage of operation. Finally, we show how quantum effects can be used to boost the performance of the proposed device.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berrada, K., E-mail: kberrada@ictp.it; The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, Miramare-Trieste; Ooi, C. H. Raymond

Robustness of the geometric phase (GP) with respect to different noise effects is a basic condition for an effective quantum computation. Here, we propose a useful quantum system with real physical parameters by studying the GP of a pair of Stokes and anti-Stokes photons, involving Raman emission processes with and without photonic band gap (PBG) effect. We show that the properties of GP are very sensitive to the change of the Rabi frequency and time, exhibiting collapse phenomenon as the time becomes significantly large. The system allows us to obtain a state which remains with zero GP for longer times.more » This result plays a significant role to enhance the stabilization and control of the system dynamics. Finally, we investigate the nonlocal correlation (entanglement) between the pair photons by taking into account the effect of different parameters. An interesting correlation between the GP and entanglement is observed showing that the PBG stabilizes the fluctuations in the system and makes the entanglement more robust against the change of time and frequency.« less

Quantization of Poisson Manifolds from the Integrability of the Modular Function

NASA Astrophysics Data System (ADS)

Bonechi, F.; Ciccoli, N.; Qiu, J.; Tarlini, M.

2014-10-01

We discuss a framework for quantizing a Poisson manifold via the quantization of its symplectic groupoid, combining the tools of geometric quantization with the results of Renault's theory of groupoid C*-algebras. This setting allows very singular polarizations. In particular, we consider the case when the modular function is multiplicatively integrable, i.e., when the space of leaves of the polarization inherits a groupoid structure. If suitable regularity conditions are satisfied, then one can define the quantum algebra as the convolution algebra of the subgroupoid of leaves satisfying the Bohr-Sommerfeld conditions. We apply this procedure to the case of a family of Poisson structures on , seen as Poisson homogeneous spaces of the standard Poisson-Lie group SU( n + 1). We show that a bihamiltonian system on defines a multiplicative integrable model on the symplectic groupoid; we compute the Bohr-Sommerfeld groupoid and show that it satisfies the needed properties for applying Renault theory. We recover and extend Sheu's description of quantum homogeneous spaces as groupoid C*-algebras.

Geometric phase effects in ultracold chemistry

NASA Astrophysics Data System (ADS)

Hazra, Jisha; Naduvalath, Balakrishnan; Kendrick, Brian K.

2016-05-01

In molecules, the geometric phase, also known as Berry's phase, originates from the adiabatic transport of the electronic wavefunction when the nuclei follow a closed path encircling a conical intersection between two electronic potential energy surfaces. It is demonstrated that the inclusion of the geometric phase has an important effect on ultracold chemical reaction rates. The effect appears in rotationally and vibrationally resolved integral cross sections as well as cross sections summed over all product quantum states. It arises from interference between scattering amplitudes of two reaction pathways: a direct path and a looping path that encircle the conical intersection between the two lowest adiabatic electronic potential energy surfaces. Illustrative results are presented for the O+ OH --> H+ O2 reaction and for hydrogen exchange in H+ H2 and D+HD reactions. It is also qualitatively demonstrated that the geometric phase effect can be modulated by applying an external electric field allowing the possibility of quantum control of chemical reactions in the ultracold regime. This work was supported in part by NSF Grant PHY-1505557 (N.B.) and ARO MURI Grant No. W911NF-12-1-0476 (N.B.).

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.

PubMed

Goto, Hayato

2016-02-22

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

NASA Astrophysics Data System (ADS)

Goto, Hayato

2016-02-01

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

Computation and Dynamics: Classical and Quantum

NASA Astrophysics Data System (ADS)

Kisil, Vladimir V.

2010-05-01

We discuss classical and quantum computations in terms of corresponding Hamiltonian dynamics. This allows us to introduce quantum computations which involve parallel processing of both: the data and programme instructions. Using mixed quantum-classical dynamics we look for a full cost of computations on quantum computers with classical terminals.

Quantum chemistry simulation on quantum computers: theories and experiments.

PubMed

Lu, Dawei; Xu, Boruo; Xu, Nanyang; Li, Zhaokai; Chen, Hongwei; Peng, Xinhua; Xu, Ruixue; Du, Jiangfeng

2012-07-14

It has been claimed that quantum computers can mimic quantum systems efficiently in the polynomial scale. Traditionally, those simulations are carried out numerically on classical computers, which are inevitably confronted with the exponential growth of required resources, with the increasing size of quantum systems. Quantum computers avoid this problem, and thus provide a possible solution for large quantum systems. In this paper, we first discuss the ideas of quantum simulation, the background of quantum simulators, their categories, and the development in both theories and experiments. We then present a brief introduction to quantum chemistry evaluated via classical computers followed by typical procedures of quantum simulation towards quantum chemistry. Reviewed are not only theoretical proposals but also proof-of-principle experimental implementations, via a small quantum computer, which include the evaluation of the static molecular eigenenergy and the simulation of chemical reaction dynamics. Although the experimental development is still behind the theory, we give prospects and suggestions for future experiments. We anticipate that in the near future quantum simulation will become a powerful tool for quantum chemistry over classical computations.

Algorithmes et architectures pour ordinateurs quantiques supraconducteurs

NASA Astrophysics Data System (ADS)

Blais, A.

2003-09-01

Algorithms and architectures for superconducting quantum computers Since its formulation, information theory was based, implicitly, on the laws of classical physics. Such a formulation is however incomplete because it does not take into account quantum reality. During the last twenty years, expansion of theory information to include quantum effects has known growing interest. The practical realization of a system for quantum data processing system, a quantum computer, presents however many challenges. In this book, we are interested in various aspects of these challenges. We start by presenting algorithmic concepts like optimization of quantum computations and geometric quantum computation. We then consider various designs and aspects of qubits based on Josephson junctions. In particular, an original approach to the interaction between superconducting qubits is presented. This approach is very general since it can be applied to various designs of qubits. Finally, we are interested in read-out of the superconductic flux qubits. The detector suggested here has the advantage that it is possible to uncouple it from the qubit when no measurement is in progress. Depuis sa formulation, la théorie de l'information a été basée, implicitement, sur les lois de la physique classique. Une telle formulation est toutefois incomplète puisqu'elle ne tient pas compte de la réalité quantique. Au cours des vingt dernières années, l'expansion de la théorie de l'information, de façon à englober les effets purement quantiques, a connu un intérêt grandissant. La réalisation d'un système de traitement de l'information quantique, un ordinateur quantique, présente toutefois de nombreux défis. Dans cet ouvrage, on s'intéresse à différents aspects concernant ces défis. On commence par présenter des concepts algorithmiques comme l'optimisation de calculs quantiques et le calcul quantique géométrique. Par la suite, on s'intéresse à différents designs et aspects de l'utilisation de qubits basés sur les jonctions Josephson. On présente entre autres une approche originale pour l'interaction entre qubits. Cette approche est très générale puisqu'elle peut être appliquée à différents designs de qubits. Finalement, on s'intéresse à la lecture des qubits supraconducteurs de flux. Le détecteur suggéré ici a l'avantage de pouvoir être découplé du qubit lorsqu'il n'y a pas de mesure en cours.

ASCR Workshop on Quantum Computing for Science

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aspuru-Guzik, Alan; Van Dam, Wim; Farhi, Edward

This report details the findings of the DOE ASCR Workshop on Quantum Computing for Science that was organized to assess the viability of quantum computing technologies to meet the computational requirements of the DOE’s science and energy mission, and to identify the potential impact of quantum technologies. The workshop was held on February 17-18, 2015, in Bethesda, MD, to solicit input from members of the quantum computing community. The workshop considered models of quantum computation and programming environments, physical science applications relevant to DOE's science mission as well as quantum simulation, and applied mathematics topics including potential quantum algorithms formore » linear algebra, graph theory, and machine learning. This report summarizes these perspectives into an outlook on the opportunities for quantum computing to impact problems relevant to the DOE’s mission as well as the additional research required to bring quantum computing to the point where it can have such impact.« less

Flow Ambiguity: A Path Towards Classically Driven Blind Quantum Computation

NASA Astrophysics Data System (ADS)

Mantri, Atul; Demarie, Tommaso F.; Menicucci, Nicolas C.; Fitzsimons, Joseph F.

2017-07-01

Blind quantum computation protocols allow a user to delegate a computation to a remote quantum computer in such a way that the privacy of their computation is preserved, even from the device implementing the computation. To date, such protocols are only known for settings involving at least two quantum devices: either a user with some quantum capabilities and a remote quantum server or two or more entangled but noncommunicating servers. In this work, we take the first step towards the construction of a blind quantum computing protocol with a completely classical client and single quantum server. Specifically, we show how a classical client can exploit the ambiguity in the flow of information in measurement-based quantum computing to construct a protocol for hiding critical aspects of a computation delegated to a remote quantum computer. This ambiguity arises due to the fact that, for a fixed graph, there exist multiple choices of the input and output vertex sets that result in deterministic measurement patterns consistent with the same fixed total ordering of vertices. This allows a classical user, computing only measurement angles, to drive a measurement-based computation performed on a remote device while hiding critical aspects of the computation.

One-way quantum computing in superconducting circuits

NASA Astrophysics Data System (ADS)

Albarrán-Arriagada, F.; Alvarado Barrios, G.; Sanz, M.; Romero, G.; Lamata, L.; Retamal, J. C.; Solano, E.

2018-03-01

We propose a method for the implementation of one-way quantum computing in superconducting circuits. Measurement-based quantum computing is a universal quantum computation paradigm in which an initial cluster state provides the quantum resource, while the iteration of sequential measurements and local rotations encodes the quantum algorithm. Up to now, technical constraints have limited a scalable approach to this quantum computing alternative. The initial cluster state can be generated with available controlled-phase gates, while the quantum algorithm makes use of high-fidelity readout and coherent feedforward. With current technology, we estimate that quantum algorithms with above 20 qubits may be implemented in the path toward quantum supremacy. Moreover, we propose an alternative initial state with properties of maximal persistence and maximal connectedness, reducing the required resources of one-way quantum computing protocols.

Einstein-Podolsky-Rosen steering: Its geometric quantification and witness

NASA Astrophysics Data System (ADS)

Ku, Huan-Yu; Chen, Shin-Liang; Budroni, Costantino; Miranowicz, Adam; Chen, Yueh-Nan; Nori, Franco

2018-02-01

We propose a measure of quantum steerability, namely, a convex steering monotone, based on the trace distance between a given assemblage and its corresponding closest assemblage admitting a local-hidden-state (LHS) model. We provide methods to estimate such a quantity, via lower and upper bounds, based on semidefinite programming. One of these upper bounds has a clear geometrical interpretation as a linear function of rescaled Euclidean distances in the Bloch sphere between the normalized quantum states of (i) a given assemblage and (ii) an LHS assemblage. For a qubit-qubit quantum state, these ideas also allow us to visualize various steerability properties of the state in the Bloch sphere via the so-called LHS surface. In particular, some steerability properties can be obtained by comparing such an LHS surface with a corresponding quantum steering ellipsoid. Thus, we propose a witness of steerability corresponding to the difference of the volumes enclosed by these two surfaces. This witness (which reveals the steerability of a quantum state) enables one to find an optimal measurement basis, which can then be used to determine the proposed steering monotone (which describes the steerability of an assemblage) optimized over all mutually unbiased bases.

Quantum Spin Glasses, Annealing and Computation

NASA Astrophysics Data System (ADS)

Chakrabarti, Bikas K.; Inoue, Jun-ichi; Tamura, Ryo; Tanaka, Shu

2017-05-01

List of tables; List of figures, Preface; 1. Introduction; Part I. Quantum Spin Glass, Annealing and Computation: 2. Classical spin models from ferromagnetic spin systems to spin glasses; 3. Simulated annealing; 4. Quantum spin glass; 5. Quantum dynamics; 6. Quantum annealing; Part II. Additional Notes: 7. Notes on adiabatic quantum computers; 8. Quantum information and quenching dynamics; 9. A brief historical note on the studies of quantum glass, annealing and computation.

Quantum-Enhanced Cyber Security: Experimental Computation on Quantum-Encrypted Data

DTIC Science & Technology

2017-03-02

AFRL-AFOSR-UK-TR-2017-0020 Quantum-Enhanced Cyber Security: Experimental Computation on Quantum-Encrypted Data Philip Walther UNIVERSITT WIEN Final...REPORT TYPE Final 3. DATES COVERED (From - To) 15 Oct 2015 to 31 Dec 2016 4. TITLE AND SUBTITLE Quantum-Enhanced Cyber Security: Experimental Computation...FORM SF 298 Final Report for FA9550-1-6-1-0004 Quantum-enhanced cyber security: Experimental quantum computation with quantum-encrypted data

Computing quantum discord is NP-complete

NASA Astrophysics Data System (ADS)

Huang, Yichen

2014-03-01

We study the computational complexity of quantum discord (a measure of quantum correlation beyond entanglement), and prove that computing quantum discord is NP-complete. Therefore, quantum discord is computationally intractable: the running time of any algorithm for computing quantum discord is believed to grow exponentially with the dimension of the Hilbert space so that computing quantum discord in a quantum system of moderate size is not possible in practice. As by-products, some entanglement measures (namely entanglement cost, entanglement of formation, relative entropy of entanglement, squashed entanglement, classical squashed entanglement, conditional entanglement of mutual information, and broadcast regularization of mutual information) and constrained Holevo capacity are NP-hard/NP-complete to compute. These complexity-theoretic results are directly applicable in common randomness distillation, quantum state merging, entanglement distillation, superdense coding, and quantum teleportation; they may offer significant insights into quantum information processing. Moreover, we prove the NP-completeness of two typical problems: linear optimization over classical states and detecting classical states in a convex set, providing evidence that working with classical states is generically computationally intractable.

Quantum Computation

NASA Astrophysics Data System (ADS)

Aharonov, Dorit

In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically powerful computational tool, capable of performing tasks which seem intractable for classical computers. This review is about to tell the story of theoretical quantum computation. I l out the developing topic of experimental realizations of the model, and neglected other closely related topics which are quantum information and quantum communication. As a result of narrowing the scope of this paper, I hope it has gained the benefit of being an almost self contained introduction to the exciting field of quantum computation. The review begins with background on theoretical computer science, Turing machines and Boolean circuits. In light of these models, I define quantum computers, and discuss the issue of universal quantum gates. Quantum algorithms, including Shor's factorization algorithm and Grover's algorithm for searching databases, are explained. I will devote much attention to understanding what the origins of the quantum computational power are, and what the limits of this power are. Finally, I describe the recent theoretical results which show that quantum computers maintain their complexity power even in the presence of noise, inaccuracies and finite precision. This question cannot be separated from that of quantum complexity because any realistic model will inevitably be subjected to such inaccuracies. I tried to put all results in their context, asking what the implications to other issues in computer science and physics are. In the end of this review, I make these connections explicit by discussing the possible implications of quantum computation on fundamental physical questions such as the transition from quantum to classical physics.

Silicon superlattices: Theory and application to semiconductor devices

NASA Technical Reports Server (NTRS)

Moriarty, J. A.

1981-01-01

Silicon superlattices and their applicability to improved semiconductor devices were studied. The device application potential of the atomic like dimension of III-V semiconductor superlattices fabricated in the form of ultrathin periodically layered heterostructures was examined. Whether this leads to quantum size effects and creates the possibility to alter familiar transport and optical properties over broad physical ranges was studied. Applications to improved semiconductor lasers and electrondevices were achieved. Possible application of silicon sperlattices to faster high speed computing devices was examined. It was found that the silicon lattices show features of smaller fundamental energyband gaps and reduced effective masses. The effects correlate strongly with both the chemical and geometrical nature of the superlattice.

Notes on wall crossing and instanton in compactified gauge theory with matter

NASA Astrophysics Data System (ADS)

Chen, Heng-Yu; Petunin, Kirill

2010-10-01

We study the quantum effects on the Coulomb branch of mathcal{N} = 2 SU(2) super-symmetric Yang-Mills with fundamental matters compactified on {mathbb{R}^3} × {S^1} , and extract the explicit perturbative and leading non-perturbative corrections to the moduli space metric predicted from the recent work of Gaiotto, Moore and Neitzke on wall-crossing [1]. We verify the predicted metric by computing the leading weak coupling instanton contribution to the four fermion correlation using standard field theory techniques, and demonstrate perfect agreement. We also demonstrate how previously known three dimensional quantities can be recovered in appropriate small radius limit, and provide a simple geometric picture from brane construction.

Quantum correlations and Bell’s inequality violation in a Heisenberg spin dimer via neutron scattering

NASA Astrophysics Data System (ADS)

Cruz, C.

The characterization of quantum information quantifiers has attracted a considerable attention of the scientific community, since they are a useful tool to verify the presence of quantum correlations in a quantum system. In this context, in the present work we show a theoretical study of some quantifiers, such as entanglement witness, entanglement of formation, Bell’s inequality violation and geometric quantum discord as a function of the diffractive properties of neutron scattering. We provide one path toward identifying the presence of quantum correlations and quantum nonlocality in a molecular magnet as a Heisenberg spin-1/2 dimer, by diffractive properties typically obtained via neutron scattering experiments.

Ultrafast optical control of individual quantum dot spin qubits.

PubMed

De Greve, Kristiaan; Press, David; McMahon, Peter L; Yamamoto, Yoshihisa

2013-09-01

Single spins in semiconductor quantum dots form a promising platform for solid-state quantum information processing. The spin-up and spin-down states of a single electron or hole, trapped inside a quantum dot, can represent a single qubit with a reasonably long decoherence time. The spin qubit can be optically coupled to excited (charged exciton) states that are also trapped in the quantum dot, which provides a mechanism to quickly initialize, manipulate and measure the spin state with optical pulses, and to interface between a stationary matter qubit and a 'flying' photonic qubit for quantum communication and distributed quantum information processing. The interaction of the spin qubit with light may be enhanced by placing the quantum dot inside a monolithic microcavity. An entire system, consisting of a two-dimensional array of quantum dots and a planar microcavity, may plausibly be constructed by modern semiconductor nano-fabrication technology and could offer a path toward chip-sized scalable quantum repeaters and quantum computers. This article reviews the recent experimental developments in optical control of single quantum dot spins for quantum information processing. We highlight demonstrations of a complete set of all-optical single-qubit operations on a single quantum dot spin: initialization, an arbitrary SU(2) gate, and measurement. We review the decoherence and dephasing mechanisms due to hyperfine interaction with the nuclear-spin bath, and show how the single-qubit operations can be combined to perform spin echo sequences that extend the qubit decoherence from a few nanoseconds to several microseconds, more than 5 orders of magnitude longer than the single-qubit gate time. Two-qubit coupling is discussed, both within a single chip by means of exchange coupling of nearby spins and optically induced geometric phases, as well as over longer-distances. Long-distance spin-spin entanglement can be generated if each spin can emit a photon that is entangled with the spin, and these photons are then interfered. We review recent work demonstrating entanglement between a stationary spin qubit and a flying photonic qubit. These experiments utilize the polarization- and frequency-dependent spontaneous emission from the lowest charged exciton state to single spin Zeeman sublevels.

Quantum Computing: Selected Internet Resources for Librarians, Researchers, and the Casually Curious

ERIC Educational Resources Information Center

Cirasella, Jill

2009-01-01

This article presents an annotated selection of the most important and informative Internet resources for learning about quantum computing, finding quantum computing literature, and tracking quantum computing news. All of the quantum computing resources described in this article are freely available, English-language web sites that fall into one…

Contextuality as a Resource for Models of Quantum Computation with Qubits

NASA Astrophysics Data System (ADS)

Bermejo-Vega, Juan; Delfosse, Nicolas; Browne, Dan E.; Okay, Cihan; Raussendorf, Robert

2017-09-01

A central question in quantum computation is to identify the resources that are responsible for quantum speed-up. Quantum contextuality has been recently shown to be a resource for quantum computation with magic states for odd-prime dimensional qudits and two-dimensional systems with real wave functions. The phenomenon of state-independent contextuality poses a priori an obstruction to characterizing the case of regular qubits, the fundamental building block of quantum computation. Here, we establish contextuality of magic states as a necessary resource for a large class of quantum computation schemes on qubits. We illustrate our result with a concrete scheme related to measurement-based quantum computation.

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

PubMed Central

Goto, Hayato

2016-01-01

The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence. PMID:26899997

Computer Code for Nanostructure Simulation

NASA Technical Reports Server (NTRS)

Filikhin, Igor; Vlahovic, Branislav

2009-01-01

Due to their small size, nanostructures can have stress and thermal gradients that are larger than any macroscopic analogue. These gradients can lead to specific regions that are susceptible to failure via processes such as plastic deformation by dislocation emission, chemical debonding, and interfacial alloying. A program has been developed that rigorously simulates and predicts optoelectronic properties of nanostructures of virtually any geometrical complexity and material composition. It can be used in simulations of energy level structure, wave functions, density of states of spatially configured phonon-coupled electrons, excitons in quantum dots, quantum rings, quantum ring complexes, and more. The code can be used to calculate stress distributions and thermal transport properties for a variety of nanostructures and interfaces, transport and scattering at nanoscale interfaces and surfaces under various stress states, and alloy compositional gradients. The code allows users to perform modeling of charge transport processes through quantum-dot (QD) arrays as functions of inter-dot distance, array order versus disorder, QD orientation, shape, size, and chemical composition for applications in photovoltaics and physical properties of QD-based biochemical sensors. The code can be used to study the hot exciton formation/relation dynamics in arrays of QDs of different shapes and sizes at different temperatures. It also can be used to understand the relation among the deposition parameters and inherent stresses, strain deformation, heat flow, and failure of nanostructures.

Architectures and Applications for Scalable Quantum Information Systems

DTIC Science & Technology

2007-01-01

quantum computation models, such as adiabatic quantum computing , can be converted to quantum circuits. Therefore, in our design flow’s first phase...vol. 26, no. 5, pp. 1484–1509, 1997. [19] A. Childs, E. Farhi, and J. Preskill, “Robustness of adiabatic quantum computation ,” Phys. Rev. A, vol. 65...magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm. Adiabatic

Hybrid quantum computing with ancillas

NASA Astrophysics Data System (ADS)

Proctor, Timothy J.; Kendon, Viv

2016-10-01

In the quest to build a practical quantum computer, it is important to use efficient schemes for enacting the elementary quantum operations from which quantum computer programs are constructed. The opposing requirements of well-protected quantum data and fast quantum operations must be balanced to maintain the integrity of the quantum information throughout the computation. One important approach to quantum operations is to use an extra quantum system - an ancilla - to interact with the quantum data register. Ancillas can mediate interactions between separated quantum registers, and by using fresh ancillas for each quantum operation, data integrity can be preserved for longer. This review provides an overview of the basic concepts of the gate model quantum computer architecture, including the different possible forms of information encodings - from base two up to continuous variables - and a more detailed description of how the main types of ancilla-mediated quantum operations provide efficient quantum gates.

QCE: A Simulator for Quantum Computer Hardware

NASA Astrophysics Data System (ADS)

Michielsen, Kristel; de Raedt, Hans

2003-09-01

The Quantum Computer Emulator (QCE) described in this paper consists of a simulator of a generic, general purpose quantum computer and a graphical user interface. The latter is used to control the simulator, to define the hardware of the quantum computer and to debug and execute quantum algorithms. QCE runs in a Windows 98/NT/2000/ME/XP environment. It can be used to validate designs of physically realizable quantum processors and as an interactive educational tool to learn about quantum computers and quantum algorithms. A detailed exposition is given of the implementation of the CNOT and the Toffoli gate, the quantum Fourier transform, Grover's database search algorithm, an order finding algorithm, Shor's algorithm, a three-input adder and a number partitioning algorithm. We also review the results of simulations of an NMR-like quantum computer.

Verification for measurement-only blind quantum computing

NASA Astrophysics Data System (ADS)

Morimae, Tomoyuki

2014-06-01

Blind quantum computing is a new secure quantum computing protocol where a client who does not have any sophisticated quantum technology can delegate her quantum computing to a server without leaking any privacy. It is known that a client who has only a measurement device can perform blind quantum computing [T. Morimae and K. Fujii, Phys. Rev. A 87, 050301(R) (2013), 10.1103/PhysRevA.87.050301]. It has been an open problem whether the protocol can enjoy the verification, i.e., the ability of the client to check the correctness of the computing. In this paper, we propose a protocol of verification for the measurement-only blind quantum computing.

Experimental demonstration of blind quantum computing

NASA Astrophysics Data System (ADS)

Barz, Stefanie; Kashefi, Elham; Broadbent, Anne; Fitzsimons, Joe; Zeilinger, Anton; Walther, Philip

2012-02-01

Quantum computers are among the most promising applications of quantum-enhanced technologies. Quantum effects such as superposition and entanglement enable computational speed-ups that are unattainable using classical computers. The challenges in realising quantum computers suggest that in the near future, only a few facilities worldwide will be capable of operating such devices. In order to exploit these computers, users would seemingly have to give up their privacy. It was recently shown that this is not the case and that, via the universal blind quantum computation protocol, quantum mechanics provides a way to guarantee that the user's data remain private. Here, we demonstrate the first experimental version of this protocol using polarisation-entangled photonic qubits. We demonstrate various blind one- and two-qubit gate operations as well as blind versions of the Deutsch's and Grover's algorithms. When the technology to build quantum computers becomes available, this will become an important privacy-preserving feature of quantum information processing.

Single-server blind quantum computation with quantum circuit model

NASA Astrophysics Data System (ADS)

Zhang, Xiaoqian; Weng, Jian; Li, Xiaochun; Luo, Weiqi; Tan, Xiaoqing; Song, Tingting

2018-06-01

Blind quantum computation (BQC) enables the client, who has few quantum technologies, to delegate her quantum computation to a server, who has strong quantum computabilities and learns nothing about the client's quantum inputs, outputs and algorithms. In this article, we propose a single-server BQC protocol with quantum circuit model by replacing any quantum gate with the combination of rotation operators. The trap quantum circuits are introduced, together with the combination of rotation operators, such that the server is unknown about quantum algorithms. The client only needs to perform operations X and Z, while the server honestly performs rotation operators.

Accurate calculation of the geometric measure of entanglement for multipartite quantum states

NASA Astrophysics Data System (ADS)

Teng, Peiyuan

2017-07-01

This article proposes an efficient way of calculating the geometric measure of entanglement using tensor decomposition methods. The connection between these two concepts is explored using the tensor representation of the wavefunction. Numerical examples are benchmarked and compared. Furthermore, we search for highly entangled qubit states to show the applicability of this method.

Contextuality supplies the 'magic' for quantum computation.

PubMed

Howard, Mark; Wallman, Joel; Veitch, Victor; Emerson, Joseph

2014-06-19

Quantum computers promise dramatic advantages over their classical counterparts, but the source of the power in quantum computing has remained elusive. Here we prove a remarkable equivalence between the onset of contextuality and the possibility of universal quantum computation via 'magic state' distillation, which is the leading model for experimentally realizing a fault-tolerant quantum computer. This is a conceptually satisfying link, because contextuality, which precludes a simple 'hidden variable' model of quantum mechanics, provides one of the fundamental characterizations of uniquely quantum phenomena. Furthermore, this connection suggests a unifying paradigm for the resources of quantum information: the non-locality of quantum theory is a particular kind of contextuality, and non-locality is already known to be a critical resource for achieving advantages with quantum communication. In addition to clarifying these fundamental issues, this work advances the resource framework for quantum computation, which has a number of practical applications, such as characterizing the efficiency and trade-offs between distinct theoretical and experimental schemes for achieving robust quantum computation, and putting bounds on the overhead cost for the classical simulation of quantum algorithms.

Exploiting Locality in Quantum Computation for Quantum Chemistry.

PubMed

McClean, Jarrod R; Babbush, Ryan; Love, Peter J; Aspuru-Guzik, Alán

2014-12-18

Accurate prediction of chemical and material properties from first-principles quantum chemistry is a challenging task on traditional computers. Recent developments in quantum computation offer a route toward highly accurate solutions with polynomial cost; however, this solution still carries a large overhead. In this Perspective, we aim to bring together known results about the locality of physical interactions from quantum chemistry with ideas from quantum computation. We show that the utilization of spatial locality combined with the Bravyi-Kitaev transformation offers an improvement in the scaling of known quantum algorithms for quantum chemistry and provides numerical examples to help illustrate this point. We combine these developments to improve the outlook for the future of quantum chemistry on quantum computers.

Computational Multiqubit Tunnelling in Programmable Quantum Annealers

DTIC Science & Technology

2016-08-25

ARTICLE Received 3 Jun 2015 | Accepted 26 Nov 2015 | Published 7 Jan 2016 Computational multiqubit tunnelling in programmable quantum annealers...state itself. Quantum tunnelling has been hypothesized as an advantageous physical resource for optimization in quantum annealing. However, computational ...qubit tunnelling plays a computational role in a currently available programmable quantum annealer. We devise a probe for tunnelling, a computational

Complexity Bounds for Quantum Computation

DTIC Science & Technology

2007-06-22

Programs Trustees of Boston University Boston, MA 02215 - Complexity Bounds for Quantum Computation REPORT DOCUMENTATION PAGE 18. SECURITY CLASSIFICATION...Complexity Bounds for Quantum Comp[utation Report Title ABSTRACT This project focused on upper and lower bounds for quantum computability using constant...classical computation models, particularly emphasizing new examples of where quantum circuits are more powerful than their classical counterparts. A second

Application of Blind Quantum Computation to Two-Party Quantum Computation

NASA Astrophysics Data System (ADS)

Sun, Zhiyuan; Li, Qin; Yu, Fang; Chan, Wai Hong

2018-06-01

Blind quantum computation (BQC) allows a client who has only limited quantum power to achieve quantum computation with the help of a remote quantum server and still keep the client's input, output, and algorithm private. Recently, Kashefi and Wallden extended BQC to achieve two-party quantum computation which allows two parties Alice and Bob to perform a joint unitary transform upon their inputs. However, in their protocol Alice has to prepare rotated single qubits and perform Pauli operations, and Bob needs to have a powerful quantum computer. In this work, we also utilize the idea of BQC to put forward an improved two-party quantum computation protocol in which the operations of both Alice and Bob are simplified since Alice only needs to apply Pauli operations and Bob is just required to prepare and encrypt his input qubits.

Application of Blind Quantum Computation to Two-Party Quantum Computation

NASA Astrophysics Data System (ADS)

Sun, Zhiyuan; Li, Qin; Yu, Fang; Chan, Wai Hong

2018-03-01

Blind quantum computation (BQC) allows a client who has only limited quantum power to achieve quantum computation with the help of a remote quantum server and still keep the client's input, output, and algorithm private. Recently, Kashefi and Wallden extended BQC to achieve two-party quantum computation which allows two parties Alice and Bob to perform a joint unitary transform upon their inputs. However, in their protocol Alice has to prepare rotated single qubits and perform Pauli operations, and Bob needs to have a powerful quantum computer. In this work, we also utilize the idea of BQC to put forward an improved two-party quantum computation protocol in which the operations of both Alice and Bob are simplified since Alice only needs to apply Pauli operations and Bob is just required to prepare and encrypt his input qubits.

Decoherence in adiabatic quantum computation

NASA Astrophysics Data System (ADS)

Albash, Tameem; Lidar, Daniel A.

2015-06-01

Recent experiments with increasingly larger numbers of qubits have sparked renewed interest in adiabatic quantum computation, and in particular quantum annealing. A central question that is repeatedly asked is whether quantum features of the evolution can survive over the long time scales used for quantum annealing relative to standard measures of the decoherence time. We reconsider the role of decoherence in adiabatic quantum computation and quantum annealing using the adiabatic quantum master-equation formalism. We restrict ourselves to the weak-coupling and singular-coupling limits, which correspond to decoherence in the energy eigenbasis and in the computational basis, respectively. We demonstrate that decoherence in the instantaneous energy eigenbasis does not necessarily detrimentally affect adiabatic quantum computation, and in particular that a short single-qubit T2 time need not imply adverse consequences for the success of the quantum adiabatic algorithm. We further demonstrate that boundary cancellation methods, designed to improve the fidelity of adiabatic quantum computing in the closed-system setting, remain beneficial in the open-system setting. To address the high computational cost of master-equation simulations, we also demonstrate that a quantum Monte Carlo algorithm that explicitly accounts for a thermal bosonic bath can be used to interpolate between classical and quantum annealing. Our study highlights and clarifies the significantly different role played by decoherence in the adiabatic and circuit models of quantum computing.

Description of quantum states using in free space optic communication

NASA Astrophysics Data System (ADS)

Kučera, Petr

2017-11-01

In the article we concentrate our attention on the quantum description of states which are prepared by light sources. The main goal of the article is the determination of density matrix of background radiation source. It is shown that these matrix elements satisfy Geometric distribution in the number state representation.

Dirac electrons in quantum rings

NASA Astrophysics Data System (ADS)

Gioia, L.; Zülicke, U.; Governale, M.; Winkler, R.

2018-05-01

We consider quantum rings realized in materials where the dynamics of charge carriers mimics that of two-dimensional (2D) Dirac electrons. A general theoretical description of the ring-subband structure is developed that applies to a range of currently available 2D systems, including graphene, transition-metal dichalcogenides, and narrow-gap semiconductor quantum wells. We employ the scattering-matrix approach to calculate the electronic two-terminal conductance through the ring and investigate how it is affected by Dirac-electron interference. The interplay of pseudospin chirality and hard-wall confinement is found to distinctly affect the geometric phase that is experimentally accessible in mesoscopic-conductance measurements. We derive an effective Hamiltonian for the azimuthal motion of charge carriers in the ring that yields deeper insight into the physical origin of the observed transport effects, including the unique behavior exhibited by the lowest ring subband in the normal and topological (i.e., band-inverted) regimes. Our paper provides a unified approach to characterizing confined Dirac electrons, which can be used to explore the design of valley- and spintronic devices based on quantum interference and the confinement-tunable geometric phase.

Spin-based quantum computation in multielectron quantum dots

NASA Astrophysics Data System (ADS)

Hu, Xuedong; Das Sarma, S.

2001-10-01

In a quantum computer the hardware and software are intrinsically connected because the quantum Hamiltonian (or more precisely its time development) is the code that runs the computer. We demonstrate this subtle and crucial relationship by considering the example of electron-spin-based solid-state quantum computer in semiconductor quantum dots. We show that multielectron quantum dots with one valence electron in the outermost shell do not behave simply as an effective single-spin system unless special conditions are satisfied. Our work compellingly demonstrates that a delicate synergy between theory and experiment (between software and hardware) is essential for constructing a quantum computer.

Connection between optimal control theory and adiabatic-passage techniques in quantum systems

NASA Astrophysics Data System (ADS)

Assémat, E.; Sugny, D.

2012-08-01

This work explores the relationship between optimal control theory and adiabatic passage techniques in quantum systems. The study is based on a geometric analysis of the Hamiltonian dynamics constructed from Pontryagin's maximum principle. In a three-level quantum system, we show that the stimulated Raman adiabatic passage technique can be associated to a peculiar Hamiltonian singularity. One deduces that the adiabatic pulse is solution of the optimal control problem only for a specific cost functional. This analysis is extended to the case of a four-level quantum system.

Impact of heavy hole-light hole coupling on optical selection rules in GaAs quantum dots

DOE Office of Scientific and Technical Information (OSTI.GOV)

Belhadj, T.; Amand, T.; Kunz, S.

2010-08-02

We report strong heavy hole-light hole mixing in GaAs quantum dots grown by droplet epitaxy. Using the neutral and charged exciton emission as a monitor we observe the direct consequence of quantum dot symmetry reduction in this strain free system. By fitting the polar diagram of the emission with simple analytical expressions obtained from k{center_dot}p theory we are able to extract the mixing that arises from the heavy-light hole coupling due to the geometrical asymmetry of the quantum dot.

Elucidating reaction mechanisms on quantum computers.

PubMed

Reiher, Markus; Wiebe, Nathan; Svore, Krysta M; Wecker, Dave; Troyer, Matthias

2017-07-18

With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.

Elucidating reaction mechanisms on quantum computers

PubMed Central

Reiher, Markus; Wiebe, Nathan; Svore, Krysta M.; Wecker, Dave; Troyer, Matthias

2017-01-01

With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources. PMID:28674011

Elucidating reaction mechanisms on quantum computers

NASA Astrophysics Data System (ADS)

Reiher, Markus; Wiebe, Nathan; Svore, Krysta M.; Wecker, Dave; Troyer, Matthias

2017-07-01

With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.

Software Systems for High-performance Quantum Computing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Humble, Travis S; Britt, Keith A

Quantum computing promises new opportunities for solving hard computational problems, but harnessing this novelty requires breakthrough concepts in the design, operation, and application of computing systems. We define some of the challenges facing the development of quantum computing systems as well as software-based approaches that can be used to overcome these challenges. Following a brief overview of the state of the art, we present models for the quantum programming and execution models, the development of architectures for hybrid high-performance computing systems, and the realization of software stacks for quantum networking. This leads to a discussion of the role that conventionalmore » computing plays in the quantum paradigm and how some of the current challenges for exascale computing overlap with those facing quantum computing.« less

Homomorphic encryption experiments on IBM's cloud quantum computing platform

NASA Astrophysics Data System (ADS)

Huang, He-Liang; Zhao, You-Wei; Li, Tan; Li, Feng-Guang; Du, Yu-Tao; Fu, Xiang-Qun; Zhang, Shuo; Wang, Xiang; Bao, Wan-Su

2017-02-01

Quantum computing has undergone rapid development in recent years. Owing to limitations on scalability, personal quantum computers still seem slightly unrealistic in the near future. The first practical quantum computer for ordinary users is likely to be on the cloud. However, the adoption of cloud computing is possible only if security is ensured. Homomorphic encryption is a cryptographic protocol that allows computation to be performed on encrypted data without decrypting them, so it is well suited to cloud computing. Here, we first applied homomorphic encryption on IBM's cloud quantum computer platform. In our experiments, we successfully implemented a quantum algorithm for linear equations while protecting our privacy. This demonstration opens a feasible path to the next stage of development of cloud quantum information technology.

A cross-disciplinary introduction to quantum annealing-based algorithms

NASA Astrophysics Data System (ADS)

Venegas-Andraca, Salvador E.; Cruz-Santos, William; McGeoch, Catherine; Lanzagorta, Marco

2018-04-01

A central goal in quantum computing is the development of quantum hardware and quantum algorithms in order to analyse challenging scientific and engineering problems. Research in quantum computation involves contributions from both physics and computer science; hence this article presents a concise introduction to basic concepts from both fields that are used in annealing-based quantum computation, an alternative to the more familiar quantum gate model. We introduce some concepts from computer science required to define difficult computational problems and to realise the potential relevance of quantum algorithms to find novel solutions to those problems. We introduce the structure of quantum annealing-based algorithms as well as two examples of this kind of algorithms for solving instances of the max-SAT and Minimum Multicut problems. An overview of the quantum annealing systems manufactured by D-Wave Systems is also presented.

Experimental contextuality in classical light

NASA Astrophysics Data System (ADS)

Li, Tao; Zeng, Qiang; Song, Xinbing; Zhang, Xiangdong

2017-03-01

The Klyachko, Can, Binicioglu, and Shumovsky (KCBS) inequality is an important contextuality inequality in three-level system, which has been demonstrated experimentally by using quantum states. Using the path and polarization degrees of freedom of classical optics fields, we have constructed the classical trit (cetrit), tested the KCBS inequality and its geometrical form (Wright’s inequality) in this work. The projection measurement has been implemented, the clear violations of the KCBS inequality and its geometrical form have been observed. This means that the contextuality inequality, which is commonly used in test of the conflict between quantum theory and noncontextual realism, may be used as a quantitative tool in classical optical coherence to describe correlation characteristics of the classical fields.

Some Thoughts Regarding Practical Quantum Computing

NASA Astrophysics Data System (ADS)

Ghoshal, Debabrata; Gomez, Richard; Lanzagorta, Marco; Uhlmann, Jeffrey

2006-03-01

Quantum computing has become an important area of research in computer science because of its potential to provide more efficient algorithmic solutions to certain problems than are possible with classical computing. The ability of performing parallel operations over an exponentially large computational space has proved to be the main advantage of the quantum computing model. In this regard, we are particularly interested in the potential applications of quantum computers to enhance real software systems of interest to the defense, industrial, scientific and financial communities. However, while much has been written in popular and scientific literature about the benefits of the quantum computational model, several of the problems associated to the practical implementation of real-life complex software systems in quantum computers are often ignored. In this presentation we will argue that practical quantum computation is not as straightforward as commonly advertised, even if the technological problems associated to the manufacturing and engineering of large-scale quantum registers were solved overnight. We will discuss some of the frequently overlooked difficulties that plague quantum computing in the areas of memories, I/O, addressing schemes, compilers, oracles, approximate information copying, logical debugging, error correction and fault-tolerant computing protocols.

Biphoton optics

NASA Astrophysics Data System (ADS)

Strekalov, Dmitry Vladimirovich

1997-10-01

The subject of this dissertation is the study of the two- photon entanglement. This phenomenon has been paid a great deal of attention since 1935, when A. Einstein, B. Podolsky and N. Rosen asked their famous question, 'Can quantum-mechanical description of physical reality be considered complete?' An entangled system behavior is inconsistent with many classical concepts. Therefore, the understanding of two-photon entanglement is important for the foundations of quantum theory. A two-photon entangled sate represents a two-photon, or a biphoton, rather than two photons. The concept of biphoton as a single nonlocal quantum object is fundamentally different from the concept of a photon pair, as has been experimentally demonstrated in the present dissertation. Two-photon entanglement gives rise to unusual 'ghost' interference and diffraction, nonlocal geometrical phase, and other quantum phenomena originally studied in the present dissertation. The variety of available results calls for bringing them into a general system which we call Biphoton Optics. This is the main goal of this dissertation. Biphoton optics operate with two-photon wave packets, or with an equivalent concept of advanced wave. We show that in the framework of the advanced wave concept two-photon phenomena can be effectively described in terms of classical optics. Therefore the biphoton optics has the same structure as the classical optics. It includes two- photon geometrical optics, dispersion and frequency beating, polarization effects, interference, diffraction, and geometrical phase. All these two-photon effects are represented by experiments included in this dissertation. Our approach does not make two-photon quantum effects 'classical', however. It should be understood that the advanced wave model operates with counter-propagation in time which does not correspond to any real physical process. Therefore it is just a model, but it is clearly a great advantage to have such a model that is both simple and powerful, in terms of its ability to describe the known results and accurately predict the new ones. Therefore an important step is made in understanding and describing of the quantum phenomena of two-photon entanglement.

Non-unitary probabilistic quantum computing circuit and method

NASA Technical Reports Server (NTRS)

Williams, Colin P. (Inventor); Gingrich, Robert M. (Inventor)

2009-01-01

A quantum circuit performing quantum computation in a quantum computer. A chosen transformation of an initial n-qubit state is probabilistically obtained. The circuit comprises a unitary quantum operator obtained from a non-unitary quantum operator, operating on an n-qubit state and an ancilla state. When operation on the ancilla state provides a success condition, computation is stopped. When operation on the ancilla state provides a failure condition, computation is performed again on the ancilla state and the n-qubit state obtained in the previous computation, until a success condition is obtained.

The dynamics of local quantum uncertainty and trace distance discord for two-qubit X states under decoherence: a comparative study

NASA Astrophysics Data System (ADS)

Slaoui, A.; Daoud, M.; Laamara, R. Ahl

2018-07-01

We employ the concepts of local quantum uncertainty and geometric quantum discord based on the trace norm to investigate the environmental effects on quantum correlations of two bipartite quantum systems. The first one concerns a two-qubit system coupled with two independent bosonic reservoirs. We show that the trace discord exhibits frozen phenomenon contrarily to local quantum uncertainty. The second scenario deals with a two-level system, initially prepared in a separable state, interacting with a quantized electromagnetic radiation. Our results show that there exists an exchange of quantum correlations between the two-level system and its surrounding which is responsible for the revival phenomenon of non-classical correlations.

Vibrational frequency analysis, FT-IR, DFT and M06-2X studies on tert-Butyl N-(thiophen-2yl)carbamate

NASA Astrophysics Data System (ADS)

Sert, Yusuf; Singer, L. M.; Findlater, M.; Doğan, Hatice; Çırak, Ç.

2014-07-01

In this study, the experimental and theoretical vibrational frequencies of a newly synthesized tert-Butyl N-(thiophen-2yl)carbamate have been investigated. The experimental FT-IR (4000-400 cm-1) spectrum of the molecule in the solid phase have been recorded. The theoretical vibrational frequencies and optimized geometric parameters (bond lengths and bond angles) have been calculated by using density functional theory (DFT/B3LYP: Becke, 3-parameter, Lee-Yang-Parr) and DFT/M06-2X (the highly parametrized, empirical exchange correlation function) quantum chemical methods with the 6-311++G(d,p) basis set by Gaussian 09W software, for the first time. The vibrational frequencies have been assigned using potential energy distribution (PED) analysis by using VEDA 4 software. The computational optimized geometric parameters and vibrational frequencies have been found to be in good agreement with the corresponding experimental data, and with related literature results. In addition, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energies and the other related molecular energy values have been calculated and are depicted.

Programming languages and compiler design for realistic quantum hardware.

PubMed

Chong, Frederic T; Franklin, Diana; Martonosi, Margaret

2017-09-13

Quantum computing sits at an important inflection point. For years, high-level algorithms for quantum computers have shown considerable promise, and recent advances in quantum device fabrication offer hope of utility. A gap still exists, however, between the hardware size and reliability requirements of quantum computing algorithms and the physical machines foreseen within the next ten years. To bridge this gap, quantum computers require appropriate software to translate and optimize applications (toolflows) and abstraction layers. Given the stringent resource constraints in quantum computing, information passed between layers of software and implementations will differ markedly from in classical computing. Quantum toolflows must expose more physical details between layers, so the challenge is to find abstractions that expose key details while hiding enough complexity.

Programming languages and compiler design for realistic quantum hardware

NASA Astrophysics Data System (ADS)

Chong, Frederic T.; Franklin, Diana; Martonosi, Margaret

2017-09-01

Quantum computing sits at an important inflection point. For years, high-level algorithms for quantum computers have shown considerable promise, and recent advances in quantum device fabrication offer hope of utility. A gap still exists, however, between the hardware size and reliability requirements of quantum computing algorithms and the physical machines foreseen within the next ten years. To bridge this gap, quantum computers require appropriate software to translate and optimize applications (toolflows) and abstraction layers. Given the stringent resource constraints in quantum computing, information passed between layers of software and implementations will differ markedly from in classical computing. Quantum toolflows must expose more physical details between layers, so the challenge is to find abstractions that expose key details while hiding enough complexity.

Building an adiabatic quantum computer simulation in the classroom

NASA Astrophysics Data System (ADS)

Rodríguez-Laguna, Javier; Santalla, Silvia N.

2018-05-01

We present a didactic introduction to adiabatic quantum computation (AQC) via the explicit construction of a classical simulator of quantum computers. This constitutes a suitable route to introduce several important concepts for advanced undergraduates in physics: quantum many-body systems, quantum phase transitions, disordered systems, spin-glasses, and computational complexity theory.

Universal Behavior of Quantum Spin Liquid and Optical Conductivity in the Insulator Herbertsmithite

NASA Astrophysics Data System (ADS)

Shaginyan, V. R.; Msezane, A. Z.; Stephanovich, V. A.; Popov, K. G.; Japaridze, G. S.

2018-04-01

We analyze optical conductivity with the goal to demonstrate experimental manifestation of a new state of matter, the so-called fermion condensate. Fermion condensates are realized in quantum spin liquids, exhibiting typical behavior of heavy-fermion metals. Measurements of the low-frequency optical conductivity collected on the geometrically frustrated insulator herbertsmithite provide important experimental evidence of the nature of its quantum spin liquid composed of spinons. To analyze recent measurements of the herbertsmithite optical conductivity at different temperatures, we employ a model of strongly correlated quantum spin liquid located near the fermion condensation phase transition. Our theoretical analysis of the optical conductivity allows us to expose the physical mechanism of its temperature dependence. We also predict a dependence of the optical conductivity on a magnetic field. We consider an experimental manifestation (optical conductivity) of a new state of matter (so-called fermion condensate) realized in quantum spin liquids, for, in many ways, they exhibit typical behavior of heavy-fermion metals. Measurements of the low-frequency optical conductivity collected on the geometrically frustrated insulator herbertsmithite produce important experimental evidence of the nature of its quantum spin liquid composed of spinons. To analyze recent measurements of the herbertsmithite optical conductivity at different temperatures, we employ a model of a strongly correlated quantum spin liquid located near the fermion condensation phase transition. Our theoretical analysis of the optical conductivity allows us to reveal the physical mechanism of its temperature dependence. We also predict a dependence of the optical conductivity on a magnetic field.

On the geometry of inhomogeneous quantum groups

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aschieri, Paolo

1998-01-01

The author gives a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case. He further analyzes the relation between differential calculus and quantum Lie algebra of left (right) invariant vectorfields. Equivalent definitions of bicovariant differential calculus are studied and their geometrical interpretation is explained. From these data he constructs and analyzes the space of vectorfields, and naturally introduces a contraction operator and a Lie derivative. Their properties are discussed.

Nontrivial Quantum Effects in Biology: A Skeptical Physicists' View

NASA Astrophysics Data System (ADS)

Wiseman, Howard; Eisert, Jens

The following sections are included: * Introduction * A Quantum Life Principle * A quantum chemistry principle? * The anthropic principle * Quantum Computing in the Brain * Nature did everything first? * Decoherence as the make or break issue * Quantum error correction * Uselessness of quantum algorithms for organisms * Quantum Computing in Genetics * Quantum search * Teleological aspects and the fast-track to life * Quantum Consciousness * Computability and free will * Time scales * Quantum Free Will * Predictability and free will * Determinism and free will * Acknowledgements * References

Algorithmic complexity of quantum capacity

NASA Astrophysics Data System (ADS)

Oskouei, Samad Khabbazi; Mancini, Stefano

2018-04-01

We analyze the notion of quantum capacity from the perspective of algorithmic (descriptive) complexity. To this end, we resort to the concept of semi-computability in order to describe quantum states and quantum channel maps. We introduce algorithmic entropies (like algorithmic quantum coherent information) and derive relevant properties for them. Then we show that quantum capacity based on semi-computable concept equals the entropy rate of algorithmic coherent information, which in turn equals the standard quantum capacity. Thanks to this, we finally prove that the quantum capacity, for a given semi-computable channel, is limit computable.

Computing quantum hashing in the model of quantum branching programs

NASA Astrophysics Data System (ADS)

Ablayev, Farid; Ablayev, Marat; Vasiliev, Alexander

2018-02-01

We investigate the branching program complexity of quantum hashing. We consider a quantum hash function that maps elements of a finite field into quantum states. We require that this function is preimage-resistant and collision-resistant. We consider two complexity measures for Quantum Branching Programs (QBP): a number of qubits and a number of compu-tational steps. We show that the quantum hash function can be computed efficiently. Moreover, we prove that such QBP construction is optimal. That is, we prove lower bounds that match the constructed quantum hash function computation.

Symmetrically private information retrieval based on blind quantum computing

NASA Astrophysics Data System (ADS)

Sun, Zhiwei; Yu, Jianping; Wang, Ping; Xu, Lingling

2015-05-01

Universal blind quantum computation (UBQC) is a new secure quantum computing protocol which allows a user Alice who does not have any sophisticated quantum technology to delegate her computing to a server Bob without leaking any privacy. Using the features of UBQC, we propose a protocol to achieve symmetrically private information retrieval, which allows a quantum limited Alice to query an item from Bob with a fully fledged quantum computer; meanwhile, the privacy of both parties is preserved. The security of our protocol is based on the assumption that malicious Alice has no quantum computer, which avoids the impossibility proof of Lo. For the honest Alice, she is almost classical and only requires minimal quantum resources to carry out the proposed protocol. Therefore, she does not need any expensive laboratory which can maintain the coherence of complicated quantum experimental setups.

Hybrid Quantum-Classical Approach to Quantum Optimal Control.

PubMed

Li, Jun; Yang, Xiaodong; Peng, Xinhua; Sun, Chang-Pu

2017-04-14

A central challenge in quantum computing is to identify more computational problems for which utilization of quantum resources can offer significant speedup. Here, we propose a hybrid quantum-classical scheme to tackle the quantum optimal control problem. We show that the most computationally demanding part of gradient-based algorithms, namely, computing the fitness function and its gradient for a control input, can be accomplished by the process of evolution and measurement on a quantum simulator. By posing queries to and receiving answers from the quantum simulator, classical computing devices update the control parameters until an optimal control solution is found. To demonstrate the quantum-classical scheme in experiment, we use a seven-qubit nuclear magnetic resonance system, on which we have succeeded in optimizing state preparation without involving classical computation of the large Hilbert space evolution.

Private quantum computation: an introduction to blind quantum computing and related protocols

NASA Astrophysics Data System (ADS)

Fitzsimons, Joseph F.

2017-06-01

Quantum technologies hold the promise of not only faster algorithmic processing of data, via quantum computation, but also of more secure communications, in the form of quantum cryptography. In recent years, a number of protocols have emerged which seek to marry these concepts for the purpose of securing computation rather than communication. These protocols address the task of securely delegating quantum computation to an untrusted device while maintaining the privacy, and in some instances the integrity, of the computation. We present a review of the progress to date in this emerging area.

Vibrational spectroscopy (FT-IR and Laser-Raman) investigation, and computational (M06-2X and B3LYP) analysis on the structure of 4-(3-fluorophenyl)-1-(propan-2-ylidene)-thiosemicarbazone.

PubMed

Sert, Yusuf; Miroslaw, Barbara; Çırak, Çağrı; Doğan, Hatice; Szulczyk, Daniel; Struga, Marta

2014-07-15

In this study, the experimental and theoretical vibrational spectral analysis of 4-(3-fluorophenyl)-1-(propan-2-ylidene)-thiosemicarbazone have been carried out. The experimental FT-IR (4000-400 cm(-1)) and Laser-Raman spectra (4000-100 cm(-1)) have been recorded for the solid state samples. The theoretical vibrational frequencies and the optimized geometric parameters (bond lengths and angles) have been calculated for gas phase using density functional theory (DFT/B3LYP: Becke, 3-parameter, Lee-Yang-Parr) and M06-2X (the highly parametrized, empirical exchange correlation function) quantum chemical methods with 6-311++G(d,p) basis set. The diversity in molecular geometry of fluorophenyl substituted thiosemicarbazones has been discussed based on the X-ray crystal structure reports and theoretical calculation results from the literature. The assignments of the vibrational frequencies have been done on the basis of potential energy distribution (PED) analysis by using VEDA4 software. A good correlation was found between the computed and experimental geometric and vibrational data. In addition, the highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbital energy levels and other related molecular energy values of the compound have been determined using the same level of theoretical calculations. Copyright © 2014 Elsevier B.V. All rights reserved.

OpenFlow Extensions for Programmable Quantum Networks

DTIC Science & Technology

2017-06-19

Extensions for Programmable Quantum Networks by Venkat Dasari, Nikolai Snow, and Billy Geerhart Computational and Information Sciences Directorate...distribution is unlimited. 1 1. Introduction Quantum networks and quantum computing have been receiving a surge of interest recently.1–3 However, there has...communicate using entangled particles and perform calculations using quantum logic gates. Additionally, quantum computing uses a quantum bit (qubit

Disciplines, models, and computers: the path to computational quantum chemistry.

PubMed

Lenhard, Johannes

2014-12-01

Many disciplines and scientific fields have undergone a computational turn in the past several decades. This paper analyzes this sort of turn by investigating the case of computational quantum chemistry. The main claim is that the transformation from quantum to computational quantum chemistry involved changes in three dimensions. First, on the side of instrumentation, small computers and a networked infrastructure took over the lead from centralized mainframe architecture. Second, a new conception of computational modeling became feasible and assumed a crucial role. And third, the field of computa- tional quantum chemistry became organized in a market-like fashion and this market is much bigger than the number of quantum theory experts. These claims will be substantiated by an investigation of the so-called density functional theory (DFT), the arguably pivotal theory in the turn to computational quantum chemistry around 1990.

Recent progress of quantum annealing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suzuki, Sei

2015-03-10

We review the recent progress of quantum annealing. Quantum annealing was proposed as a method to solve generic optimization problems. Recently a Canadian company has drawn a great deal of attention, as it has commercialized a quantum computer based on quantum annealing. Although the performance of quantum annealing is not sufficiently understood, it is likely that quantum annealing will be a practical method both on a conventional computer and on a quantum computer.

DOE pushes for useful quantum computing

NASA Astrophysics Data System (ADS)

Cho, Adrian

2018-01-01

The U.S. Department of Energy (DOE) is joining the quest to develop quantum computers, devices that would exploit quantum mechanics to crack problems that overwhelm conventional computers. The initiative comes as Google and other companies race to build a quantum computer that can demonstrate "quantum supremacy" by beating classical computers on a test problem. But reaching that milestone will not mean practical uses are at hand, and the new $40 million DOE effort is intended to spur the development of useful quantum computing algorithms for its work in chemistry, materials science, nuclear physics, and particle physics. With the resources at its 17 national laboratories, DOE could play a key role in developing the machines, researchers say, although finding problems with which quantum computers can help isn't so easy.

Cooling the Collective Motion of Trapped Ions to Initialize a Quantum Register

DTIC Science & Technology

2016-09-13

computation [1] provides a gen- eral framework for fundamental investigations into sub- jects such as entanglement, quantum measurement, and quantum ...information theory. Since quantum computation relies on entanglement between qubits, any implementa- tion of a quantum computer must offer isolation from the...for realiz- ing a quantum computer , which is scalable to an arbitrary number of qubits. Their scheme is based on a collection of trapped atomic ions

Quantum computing on encrypted data

NASA Astrophysics Data System (ADS)

Fisher, K. A. G.; Broadbent, A.; Shalm, L. K.; Yan, Z.; Lavoie, J.; Prevedel, R.; Jennewein, T.; Resch, K. J.

2014-01-01

The ability to perform computations on encrypted data is a powerful tool for protecting privacy. Recently, protocols to achieve this on classical computing systems have been found. Here, we present an efficient solution to the quantum analogue of this problem that enables arbitrary quantum computations to be carried out on encrypted quantum data. We prove that an untrusted server can implement a universal set of quantum gates on encrypted quantum bits (qubits) without learning any information about the inputs, while the client, knowing the decryption key, can easily decrypt the results of the computation. We experimentally demonstrate, using single photons and linear optics, the encryption and decryption scheme on a set of gates sufficient for arbitrary quantum computations. As our protocol requires few extra resources compared with other schemes it can be easily incorporated into the design of future quantum servers. These results will play a key role in enabling the development of secure distributed quantum systems.

Quantum computing on encrypted data.

PubMed

Fisher, K A G; Broadbent, A; Shalm, L K; Yan, Z; Lavoie, J; Prevedel, R; Jennewein, T; Resch, K J

2014-01-01

The ability to perform computations on encrypted data is a powerful tool for protecting privacy. Recently, protocols to achieve this on classical computing systems have been found. Here, we present an efficient solution to the quantum analogue of this problem that enables arbitrary quantum computations to be carried out on encrypted quantum data. We prove that an untrusted server can implement a universal set of quantum gates on encrypted quantum bits (qubits) without learning any information about the inputs, while the client, knowing the decryption key, can easily decrypt the results of the computation. We experimentally demonstrate, using single photons and linear optics, the encryption and decryption scheme on a set of gates sufficient for arbitrary quantum computations. As our protocol requires few extra resources compared with other schemes it can be easily incorporated into the design of future quantum servers. These results will play a key role in enabling the development of secure distributed quantum systems.

Research progress on quantum informatics and quantum computation

NASA Astrophysics Data System (ADS)

Zhao, Yusheng

2018-03-01

Quantum informatics is an emerging interdisciplinary subject developed by the combination of quantum mechanics, information science, and computer science in the 1980s. The birth and development of quantum information science has far-reaching significance in science and technology. At present, the application of quantum information technology has become the direction of people’s efforts. The preparation, storage, purification and regulation, transmission, quantum coding and decoding of quantum state have become the hotspot of scientists and technicians, which have a profound impact on the national economy and the people’s livelihood, technology and defense technology. This paper first summarizes the background of quantum information science and quantum computer and the current situation of domestic and foreign research, and then introduces the basic knowledge and basic concepts of quantum computing. Finally, several quantum algorithms are introduced in detail, including Quantum Fourier transform, Deutsch-Jozsa algorithm, Shor’s quantum algorithm, quantum phase estimation.

The formation of quantum images and their transformation and super-resolution reading

NASA Astrophysics Data System (ADS)

Balakin, D. A.; Belinsky, A. V.

2016-05-01

Images formed by light with suppressed photon fluctuations are interesting objects for studies with the aim of increasing their limiting information capacity and quality. This light in the sub-Poisson state can be prepared in a resonator filled with a medium with Kerr nonlinearity, in which self-phase modulation takes place. Spatially and temporally multimode light beams are studied and the production of spatial frequency spectra of suppressed photon fluctuations is described. The efficient operation regimes of the system are found. A particular schematic solution is described, which allows one to realize the potential possibilities laid in the formation of the squeezed states of light to a maximum degree during self-phase modulation in a resonator for the maximal suppression of amplitude quantum noises upon two-dimensional imaging. The efficiency of using light with suppressed quantum fluctuations for computer image processing is studied. An algorithm is described for interpreting measurements for increasing the resolution with respect to the geometrical resolution. A mathematical model that characterizes the measurement scheme is constructed and the problem of the image reconstruction is solved. The algorithm for the interpretation of images is verified. Conditions are found for the efficient application of sub-Poisson light for super-resolution imaging. It is found that the image should have a low contrast and be maximally transparent.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ballesteros, Ángel, E-mail: angelb@ubu.es; Enciso, Alberto, E-mail: aenciso@icmat.es; Herranz, Francisco J., E-mail: fjherranz@ubu.es

In this paper we quantize the N-dimensional classical Hamiltonian system H=(|q|)/(2(η+|q|)) p{sup 2}−k/(η+|q|) , that can be regarded as a deformation of the Coulomb problem with coupling constant k, that it is smoothly recovered in the limit η→0. Moreover, the kinetic energy term in H is just the one corresponding to an N-dimensional Taub–NUT space, a fact that makes this system relevant from a geometric viewpoint. Since the Hamiltonian H is known to be maximally superintegrable, we propose a quantization prescription that preserves such superintegrability in the quantum mechanical setting. We show that, to this end, one must choose asmore » the kinetic part of the Hamiltonian the conformal Laplacian of the underlying Riemannian manifold, which combines the usual Laplace–Beltrami operator on the Taub–NUT manifold and a multiple of its scalar curvature. As a consequence, we obtain a novel exactly solvable deformation of the quantum Coulomb problem, whose spectrum is computed in closed form for positive values of η and k, and showing that the well-known maximal degeneracy of the flat system is preserved in the deformed case. Several interesting algebraic and physical features of this new exactly solvable quantum system are analyzed, and the quantization problem for negative values of η and/or k is also sketched.« less

Elucidating Reaction Mechanisms on Quantum Computers

NASA Astrophysics Data System (ADS)

Wiebe, Nathan; Reiher, Markus; Svore, Krysta; Wecker, Dave; Troyer, Matthias

We show how a quantum computer can be employed to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical-computer simulations for such problems, to significantly increase their accuracy and enable hitherto intractable simulations. Detailed resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. This demonstrates that quantum computers will realistically be able to tackle important problems in chemistry that are both scientifically and economically significant.

Blueprint for a microwave trapped ion quantum computer.

PubMed

Lekitsch, Bjoern; Weidt, Sebastian; Fowler, Austin G; Mølmer, Klaus; Devitt, Simon J; Wunderlich, Christof; Hensinger, Winfried K

2017-02-01

The availability of a universal quantum computer may have a fundamental impact on a vast number of research fields and on society as a whole. An increasingly large scientific and industrial community is working toward the realization of such a device. An arbitrarily large quantum computer may best be constructed using a modular approach. We present a blueprint for a trapped ion-based scalable quantum computer module, making it possible to create a scalable quantum computer architecture based on long-wavelength radiation quantum gates. The modules control all operations as stand-alone units, are constructed using silicon microfabrication techniques, and are within reach of current technology. To perform the required quantum computations, the modules make use of long-wavelength radiation-based quantum gate technology. To scale this microwave quantum computer architecture to a large size, we present a fully scalable design that makes use of ion transport between different modules, thereby allowing arbitrarily many modules to be connected to construct a large-scale device. A high error-threshold surface error correction code can be implemented in the proposed architecture to execute fault-tolerant operations. With appropriate adjustments, the proposed modules are also suitable for alternative trapped ion quantum computer architectures, such as schemes using photonic interconnects.

A scalable quantum computer with ions in an array of microtraps

PubMed

Cirac; Zoller

2000-04-06

Quantum computers require the storage of quantum information in a set of two-level systems (called qubits), the processing of this information using quantum gates and a means of final readout. So far, only a few systems have been identified as potentially viable quantum computer models--accurate quantum control of the coherent evolution is required in order to realize gate operations, while at the same time decoherence must be avoided. Examples include quantum optical systems (such as those utilizing trapped ions or neutral atoms, cavity quantum electrodynamics and nuclear magnetic resonance) and solid state systems (using nuclear spins, quantum dots and Josephson junctions). The most advanced candidates are the quantum optical and nuclear magnetic resonance systems, and we expect that they will allow quantum computing with about ten qubits within the next few years. This is still far from the numbers required for useful applications: for example, the factorization of a 200-digit number requires about 3,500 qubits, rising to 100,000 if error correction is implemented. Scalability of proposed quantum computer architectures to many qubits is thus of central importance. Here we propose a model for an ion trap quantum computer that combines scalability (a feature usually associated with solid state proposals) with the advantages of quantum optical systems (in particular, quantum control and long decoherence times).

Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy

DTIC Science & Technology

2016-08-25

life quantum computers are inevitably affected by intrinsic noise resulting in dissipative nonunitary dynamics realized by these devices. We consider an... quantum computer . DOI: 10.1103/PhysRevX.6.021028 Subject Areas: Condensed Matter Physics, Quantum Physics, Quantum Information I. INTRODUCTION Quantum ... computing hardware is affected by a substantial level of intrinsic noise and therefore naturally realizes dis- sipative quantum dynamics [1,2

Geometric phase effects in the ultracold D + HD $$ \\rightarrow $$ D + HD and D + HD $$\\leftrightarrow $$ H + D 2 reactions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kendrick, Brian Kent; Hazra, Jisha; Balakrishnan, Naduvaluth

The results of accurate quantum reactive scattering calculations for the D + HD(v = 4, j = 0)more » $$\\to $$ D + HD($$v^{\\prime} $$, $$j^{\\prime} $$), D + HD(v = 4, j = 0) $$\\to $$ H + D2($$v^{\\prime} $$, $$j^{\\prime} $$) and H + D2(v = 4, j = 0) $$\\to $$ D + HD($$v^{\\prime} $$, $$j^{\\prime} $$) reactions are presented for collision energies between $$1\\,\\mu {\\rm{K}}$$ and $$100\\,{\\rm{K}}$$. The ab initio BKMP2 PES for the ground electronic state of H3 is used and all values of total angular momentum between $J=0-4$ are included. The general vector potential approach is used to include the geometric phase. The rotationally resolved, vibrationally resolved, and total reaction rate coefficients are reported as a function of collision energy. Rotationally resolved differential cross sections are also reported as a function of collision energy and scattering angle. Large geometric phase effects appear in the ultracold reaction rate coefficients which result in a significant enhancement or suppression of the rate coefficient (up to 3 orders of magnitude) relative to calculations which ignore the geometric phase. The results are interpreted using a new quantum interference mechanism which is unique to ultracold collisions. Significant effects of the geometric phase also appear in the rotationally resolved differential cross sections which lead to a very different oscillatory structure in both energy and scattering angle. Several shape resonances occur in the 1–$$10\\,{\\rm{K}}$$ energy range and the geometric phase is shown to significantly alter the predicted resonance spectrum. The geometric phase effects and ultracold rate coefficients depend sensitively on the nuclear spin. Furthermore, experimentalists may be able to control the reaction by the selection of a particular nuclear spin state.« less

Geometric phase effects in the ultracold D + HD $$ \\rightarrow $$ D + HD and D + HD $$\\leftrightarrow $$ H + D 2 reactions

DOE PAGES

Kendrick, Brian Kent; Hazra, Jisha; Balakrishnan, Naduvaluth

2016-12-15

The results of accurate quantum reactive scattering calculations for the D + HD(v = 4, j = 0)more » $$\\to $$ D + HD($$v^{\\prime} $$, $$j^{\\prime} $$), D + HD(v = 4, j = 0) $$\\to $$ H + D2($$v^{\\prime} $$, $$j^{\\prime} $$) and H + D2(v = 4, j = 0) $$\\to $$ D + HD($$v^{\\prime} $$, $$j^{\\prime} $$) reactions are presented for collision energies between $$1\\,\\mu {\\rm{K}}$$ and $$100\\,{\\rm{K}}$$. The ab initio BKMP2 PES for the ground electronic state of H3 is used and all values of total angular momentum between $J=0-4$ are included. The general vector potential approach is used to include the geometric phase. The rotationally resolved, vibrationally resolved, and total reaction rate coefficients are reported as a function of collision energy. Rotationally resolved differential cross sections are also reported as a function of collision energy and scattering angle. Large geometric phase effects appear in the ultracold reaction rate coefficients which result in a significant enhancement or suppression of the rate coefficient (up to 3 orders of magnitude) relative to calculations which ignore the geometric phase. The results are interpreted using a new quantum interference mechanism which is unique to ultracold collisions. Significant effects of the geometric phase also appear in the rotationally resolved differential cross sections which lead to a very different oscillatory structure in both energy and scattering angle. Several shape resonances occur in the 1–$$10\\,{\\rm{K}}$$ energy range and the geometric phase is shown to significantly alter the predicted resonance spectrum. The geometric phase effects and ultracold rate coefficients depend sensitively on the nuclear spin. Furthermore, experimentalists may be able to control the reaction by the selection of a particular nuclear spin state.« less

Vibrational spectroscopic and quantum chemical calculations of (E)-N-Carbamimidoyl-4-((naphthalen-1-yl-methylene)amino)benzene sulfonamide.

PubMed

Chandran, Asha; Varghese, Hema Tresa; Mary, Y Sheena; Panicker, C Yohannan; Manojkumar, T K; Van Alsenoy, Christian; Rajendran, G

2012-02-15

FT-IR and FT-Raman spectra of (E)-N-Carbamimidoyl-4-((naphthalen-1-yl-methylene)amino)benzene sulfonamide were recorded and analyzed. The vibrational wavenumbers were computing at various levels of theory. The data obtained from theoretical calculations are used to assign vibrational bands obtained experimentally. The results indicate that B3LYP method is able to provide satisfactory results for predicting vibrational frequencies and structural parameters. The calculated first hyperpolarizability is comparable with reported values of similar derivatives and is an attractive object for future studies of non-linear optics. The geometrical parameters of the title compound are in agreement with that of similar derivatives. Copyright © 2011 Elsevier B.V. All rights reserved.

Disjointness of Stabilizer Codes and Limitations on Fault-Tolerant Logical Gates

NASA Astrophysics Data System (ADS)

Jochym-O'Connor, Tomas; Kubica, Aleksander; Yoder, Theodore J.

2018-04-01

Stabilizer codes are among the most successful quantum error-correcting codes, yet they have important limitations on their ability to fault tolerantly compute. Here, we introduce a new quantity, the disjointness of the stabilizer code, which, roughly speaking, is the number of mostly nonoverlapping representations of any given nontrivial logical Pauli operator. The notion of disjointness proves useful in limiting transversal gates on any error-detecting stabilizer code to a finite level of the Clifford hierarchy. For code families, we can similarly restrict logical operators implemented by constant-depth circuits. For instance, we show that it is impossible, with a constant-depth but possibly geometrically nonlocal circuit, to implement a logical non-Clifford gate on the standard two-dimensional surface code.

Fictitious spin-12 operators and correlations in quadrupole nuclear spin system

NASA Astrophysics Data System (ADS)

Furman, G. B.; Goren, S. D.; Meerovich, V. M.; Sokolovsky, V. L.

The Hamiltonian and the spin operators for a spin 3/2 are represented in the basis formed by the Kronecker productions of the 2×2 Pauli matrices. This reformulation allows us to represent a spin 3/2 as a system of two coupled fictitious spins 1/2. Correlations between these fictitious spins are studied using well-developed methods. We investigate the temperature and field dependences of correlations, such as mutual information, classical correlations, entanglement, and geometric and quantum discords in the fictitious spin-1/2 system describing a nuclear spin 3/2 which is placed in magnetic and inhomogeneous electric fields. It is shown that the correlations between the fictitious spins demonstrate properties which differ from those of real two-spin systems. In contrast to real systems all the correlations between the fictitious spins do not vanish with increasing external magnetic field; at a high magnetic field the correlations tend to their limiting values. Classical correlations, quantum and geometric discords reveal a pronounced asymmetry relative to the measurements on subsystems (fictitious spins) even in a uniform magnetic field and at symmetrical EFG, η=0. The correlations depend also on the distribution of external charges, on the parameter of symmetry η. At η≠0 quantum and geometric discords have finite values in a zero magnetic field. The proposed approach may be useful in analysis of properties of particles with larger angular momentum, can provide the way to discover new physical phenomenon of quantum correlations, and can be a useful tool for similar definitions of other physical quantities of complex systems.

Quantum nonunital dynamics of spin-bath-assisted Fisher information

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hao, Xiang, E-mail: haoxiang-edu198126@163.com; Wu, Yinzhong

2016-04-15

The nonunital non-Markovian dynamics of qubits immersed in a spin bath is studied without any Markovian approximation. The environmental effects on the precisions of quantum parameter estimation are taken into account. The time-dependent transfer matrix and inhomogeneity vector are obtained for the description of the open dynamical process. The dynamical behaviour of one qubit coupled to a spin bath is geometrically described by the Bloch vector. It is found out that the nonunital non-Markovian effects can engender the improvement of the precision of quantum parameter estimation. This result contributes to the environment-assisted quantum information theory.

Quantum Accelerators for High-performance Computing Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Humble, Travis S.; Britt, Keith A.; Mohiyaddin, Fahd A.

We define some of the programming and system-level challenges facing the application of quantum processing to high-performance computing. Alongside barriers to physical integration, prominent differences in the execution of quantum and conventional programs challenges the intersection of these computational models. Following a brief overview of the state of the art, we discuss recent advances in programming and execution models for hybrid quantum-classical computing. We discuss a novel quantum-accelerator framework that uses specialized kernels to offload select workloads while integrating with existing computing infrastructure. We elaborate on the role of the host operating system to manage these unique accelerator resources, themore » prospects for deploying quantum modules, and the requirements placed on the language hierarchy connecting these different system components. We draw on recent advances in the modeling and simulation of quantum computing systems with the development of architectures for hybrid high-performance computing systems and the realization of software stacks for controlling quantum devices. Finally, we present simulation results that describe the expected system-level behavior of high-performance computing systems composed from compute nodes with quantum processing units. We describe performance for these hybrid systems in terms of time-to-solution, accuracy, and energy consumption, and we use simple application examples to estimate the performance advantage of quantum acceleration.« less

Static holes in the geometrically frustrated bow-tie ladder

NASA Astrophysics Data System (ADS)

Martins, George B.; Brenig, Wolfram

2008-10-01

We investigate the doping of a geometrically frustrated spin ladder with static holes by a complementary approach using exact diagonalization and quantum dimers. Results for thermodynamic properties, the singlet density of states, the hole-binding energy and the spin correlations will be presented. For the undoped systems the ground state is non-degenerate, with translationally invariant nearest-neighbor spin correlations. For the doped case, we find that static holes polarize their vicinity through a localization of singlets, reducing the frustration. This polarization induces short range repulsive forces between two holes and an oscillatory behavior of the long range two-hole energy. For most quantities investigated, we find very good agreement between the quantum dimer approach and the results from exact diagonalization.

Geometric model of topological insulators from the Maxwell algebra

NASA Astrophysics Data System (ADS)

Palumbo, Giandomenico

2017-11-01

We propose a novel geometric model of time-reversal-invariant topological insulators in three dimensions in presence of an external electromagnetic field. Their gapped boundary supports relativistic quantum Hall states and is described by a Chern-Simons theory, where the gauge connection takes values in the Maxwell algebra. This represents a non-central extension of the Poincaré algebra and takes into account both the Lorentz and magnetic-translation symmetries of the surface states. In this way, we derive a relativistic version of the Wen-Zee term and we show that the non-minimal coupling between the background geometry and the electromagnetic field in the model is in agreement with the main properties of the relativistic quantum Hall states in the flat space.

Generating spin squeezing states and Greenberger-Horne-Zeilinger entanglement using a hybrid phonon-spin ensemble in diamond

NASA Astrophysics Data System (ADS)

Xia, Keyu; Twamley, Jason

2016-11-01

Quantum squeezing and entanglement of spins can be used to improve the sensitivity in quantum metrology. Here we propose a scheme to create collective coupling of an ensemble of spins to a mechanical vibrational mode actuated by an external magnetic field. We find an evolution time where the mechanical motion decouples from the spins, and the accumulated geometric phase yields a squeezing of 5.9 dB for 20 spins. We also show the creation of a Greenberger-Horne-Zeilinger spin state for 20 spins with a fidelity of ˜0.62 at cryogenic temperature. The numerical simulations show that the geometric-phase-based scheme is mostly immune to thermal mechanical noise.

Efficient 3D geometric and Zernike moments computation from unstructured surface meshes.

PubMed

Pozo, José María; Villa-Uriol, Maria-Cruz; Frangi, Alejandro F

2011-03-01

This paper introduces and evaluates a fast exact algorithm and a series of faster approximate algorithms for the computation of 3D geometric moments from an unstructured surface mesh of triangles. Being based on the object surface reduces the computational complexity of these algorithms with respect to volumetric grid-based algorithms. In contrast, it can only be applied for the computation of geometric moments of homogeneous objects. This advantage and restriction is shared with other proposed algorithms based on the object boundary. The proposed exact algorithm reduces the computational complexity for computing geometric moments up to order N with respect to previously proposed exact algorithms, from N(9) to N(6). The approximate series algorithm appears as a power series on the rate between triangle size and object size, which can be truncated at any desired degree. The higher the number and quality of the triangles, the better the approximation. This approximate algorithm reduces the computational complexity to N(3). In addition, the paper introduces a fast algorithm for the computation of 3D Zernike moments from the computed geometric moments, with a computational complexity N(4), while the previously proposed algorithm is of order N(6). The error introduced by the proposed approximate algorithms is evaluated in different shapes and the cost-benefit ratio in terms of error, and computational time is analyzed for different moment orders.

Adiabatic topological quantum computing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cesare, Chris; Landahl, Andrew J.; Bacon, Dave

Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic excitations will be created that will disorder the encoded quantum information. Here, we explore this question in detail by studying adiabatic code deformations on Hamiltonians based on topological codes, notably Kitaev’s surface codes and the more recently discovered color codes. We develop protocols that enable universal quantum computing by adiabatic evolution in a way that keeps the energy gap of the system constant with respect to the computationmore » size and introduces only simple local Hamiltonian interactions. This allows one to perform holonomic quantum computing with these topological quantum computing systems. The tools we develop allow one to go beyond numerical simulations and understand these processes analytically.« less

Adiabatic topological quantum computing

DOE PAGES

Cesare, Chris; Landahl, Andrew J.; Bacon, Dave; ...

2015-07-31

Topological quantum computing promises error-resistant quantum computation without active error correction. However, there is a worry that during the process of executing quantum gates by braiding anyons around each other, extra anyonic excitations will be created that will disorder the encoded quantum information. Here, we explore this question in detail by studying adiabatic code deformations on Hamiltonians based on topological codes, notably Kitaev’s surface codes and the more recently discovered color codes. We develop protocols that enable universal quantum computing by adiabatic evolution in a way that keeps the energy gap of the system constant with respect to the computationmore » size and introduces only simple local Hamiltonian interactions. This allows one to perform holonomic quantum computing with these topological quantum computing systems. The tools we develop allow one to go beyond numerical simulations and understand these processes analytically.« less

Carboxylate-based molecular magnet: One path toward achieving stable quantum correlations at room temperature

DOE PAGES

Cruz, C.; Soares-Pinto, D. O.; Brandão, P.; ...

2016-03-07

The control of quantum correlations in solid-state systems by means of material engineering is a broad avenue to be explored, since it makes possible steps toward the limits of quantum mechanics and the design of novel materials with applications on emerging quantum technologies. This letter explores the potential of molecular magnets to be prototypes of materials for quantum information technology in this context. More precisely, we engineered a material and from its geometric quantum discord we found significant quantum correlations up to 9540 K (even without entanglement); and, a pure singlet state occupied up to around 80 K (above liquidmore » nitrogen temperature), additionally. Our results could only be achieved due to the carboxylate group promoting a metal-to-metal huge magnetic interaction.« less

Geometric phase effects in ultracold collisions of H/D with rotationally excited HD

NASA Astrophysics Data System (ADS)

Kendrick, Brian K.; Croft, James F. E.; Hazra, Jisha; Balakrishnan, N.

2017-04-01

Quantum reactive scattering calculations for the H/D + HD(v = 4 , j = 1 , 2) -> H/D + HD(v', j') and H + H2(v = 4 , j = 1 , 2) -> H + H2(v', j') exchange reactions are presented for the ground electronic state of H3. A numerically exact three-dimensional time-independent scattering method based on hyperspherical coordinates is used to compute rotationally resolved reaction cross sections and non-thermal rate coefficients for collision energies between 1 μK and 100 K . The geometric (Berry) phase associated with the D3h conical intersection in H3 is included using a U(1) vector (gauge) potential approach. It is shown that the geometric phase leads to a significant (up to three orders of magnitude) enhancement or suppression of the ultracold reaction rate coefficients depending upon whether the interference between the reaction pathways encircling the conical intersection is constructive or destructive. The nature of the interference is governed by a newly discovered mechanism which leads to an effective quantization of the ultracold scattering phase shifts. Interesting behavior due to rotational excitation of the HD and H2 is observed which might be exploited by experimentalists to control the reaction outcome. This work was supported in part by NSF Grant PHY-1505557 (N.B.) and ARO MURI Grant No. W911NF-12-1-0476 (N.B.), and DOE LDRD Grant No. 20170221ER (B.K.).

Geometric phase effects in ultracold hydrogen exchange reaction

DOE PAGES

Hazra, Jisha; Kendrick, Brian K.; Balakrishnan, Naduvalath

2016-10-14

The role of the geometric phase effect on chemical reaction dynamics is explored by examining the hydrogen exchange process in the fundamental H+HD reaction. Results are presented for vibrationally excited HD molecules in the v = 4 vibrational level and for collision energies ranging from 1 μK to 100 K. It is found that, for collision energies below 3 K, inclusion of the geometric phase leads to dramatic enhancement or suppression of the reaction rates depending on the final quantum state of the HD molecule. The effect was found to be the most prominent for rotationally resolved integral and differential cross sections but it persists to a lesser extent in the vibrationally resolved and total reaction rate coefficients. However, no significant GP effect is present in the reactive channel leading to the D+H 2 product or in the D+H 2more » $$(v=4,j=0)\\,\\to $$ HD+H reaction. A simple interference mechanism involving inelastic (nonreactive) and exchange scattering amplitudes is invoked to account for the observed GP effects. The computed results also reveal a shape resonance in the H+HD reaction near 1 K and the GP effect is found to influence the magnitude of the resonant part of the cross section. In conclusion, experimental detection of the resonance may allow a sensitive probe of the GP effect in the H+HD reaction.« less

Quantum computing and probability.

PubMed

Ferry, David K

2009-11-25

Over the past two decades, quantum computing has become a popular and promising approach to trying to solve computationally difficult problems. Missing in many descriptions of quantum computing is just how probability enters into the process. Here, we discuss some simple examples of how uncertainty and probability enter, and how this and the ideas of quantum computing challenge our interpretations of quantum mechanics. It is found that this uncertainty can lead to intrinsic decoherence, and this raises challenges for error correction.

Superposing pure quantum states with partial prior information

NASA Astrophysics Data System (ADS)

Dogra, Shruti; Thomas, George; Ghosh, Sibasish; Suter, Dieter

2018-05-01

The principle of superposition is an intriguing feature of quantum mechanics, which is regularly exploited in many different circumstances. A recent work [M. Oszmaniec et al., Phys. Rev. Lett. 116, 110403 (2016), 10.1103/PhysRevLett.116.110403] shows that the fundamentals of quantum mechanics restrict the process of superimposing two unknown pure states, even though it is possible to superimpose two quantum states with partial prior knowledge. The prior knowledge imposes geometrical constraints on the choice of input states. We discuss an experimentally feasible protocol to superimpose multiple pure states of a d -dimensional quantum system and carry out an explicit experimental realization for two single-qubit pure states with partial prior information on a two-qubit NMR quantum information processor.

Verifiable fault tolerance in measurement-based quantum computation

NASA Astrophysics Data System (ADS)

Fujii, Keisuke; Hayashi, Masahito

2017-09-01

Quantum systems, in general, cannot be simulated efficiently by a classical computer, and hence are useful for solving certain mathematical problems and simulating quantum many-body systems. This also implies, unfortunately, that verification of the output of the quantum systems is not so trivial, since predicting the output is exponentially hard. As another problem, the quantum system is very delicate for noise and thus needs an error correction. Here, we propose a framework for verification of the output of fault-tolerant quantum computation in a measurement-based model. In contrast to existing analyses on fault tolerance, we do not assume any noise model on the resource state, but an arbitrary resource state is tested by using only single-qubit measurements to verify whether or not the output of measurement-based quantum computation on it is correct. Verifiability is equipped by a constant time repetition of the original measurement-based quantum computation in appropriate measurement bases. Since full characterization of quantum noise is exponentially hard for large-scale quantum computing systems, our framework provides an efficient way to practically verify the experimental quantum error correction.

Spin interferometry in anisotropic spin-orbit fields

NASA Astrophysics Data System (ADS)

Saarikoski, Henri; Reynoso, Andres A.; Baltanás, José Pablo; Frustaglia, Diego; Nitta, Junsaku

2018-03-01

Electron spins in a two-dimensional electron gas can be manipulated by spin-orbit (SO) fields originating from either Rashba or Dresselhaus interactions with independent isotropic characteristics. Together, though, they produce anisotropic SO fields with consequences on quantum transport through spin interference. Here we study the transport properties of modeled mesoscopic rings subject to Rashba and Dresselhaus [001] SO couplings in the presence of an additional in-plane Zeeman field acting as a probe. By means of one- and two-dimensional quantum transport simulations we show that this setting presents anisotropies in the quantum resistance as a function of the Zeeman field direction. Moreover, the anisotropic resistance can be tuned by the Rashba strength up to the point to invert its response to the Zeeman field. We also find that a topological transition in the field texture that is associated with a geometric phase switching is imprinted in the anisotropy pattern. We conclude that resistance anisotropy measurements can reveal signatures of SO textures and geometric phases in spin carriers.

Probing the Topology of Density Matrices

NASA Astrophysics Data System (ADS)

Bardyn, Charles-Edouard; Wawer, Lukas; Altland, Alexander; Fleischhauer, Michael; Diehl, Sebastian

2018-01-01

The mixedness of a quantum state is usually seen as an adversary to topological quantization of observables. For example, exact quantization of the charge transported in a so-called Thouless adiabatic pump is lifted at any finite temperature in symmetry-protected topological insulators. Here, we show that certain directly observable many-body correlators preserve the integrity of topological invariants for mixed Gaussian quantum states in one dimension. Our approach relies on the expectation value of the many-body momentum-translation operator and leads to a physical observable—the "ensemble geometric phase" (EGP)—which represents a bona fide geometric phase for mixed quantum states, in the thermodynamic limit. In cyclic protocols, the EGP provides a topologically quantized observable that detects encircled spectral singularities ("purity-gap" closing points) of density matrices. While we identify the many-body nature of the EGP as a key ingredient, we propose a conceptually simple, interferometric setup to directly measure the latter in experiments with mesoscopic ensembles of ultracold atoms.

Unifying quantum heat transfer in a nonequilibrium spin-boson model with full counting statistics

NASA Astrophysics Data System (ADS)

Wang, Chen; Ren, Jie; Cao, Jianshu

2017-02-01

To study the full counting statistics of quantum heat transfer in a driven nonequilibrium spin-boson model, we develop a generalized nonequilibrium polaron-transformed Redfield equation with an auxiliary counting field. This enables us to study the impact of qubit-bath coupling ranging from weak to strong regimes. Without external modulations, we observe maximal values of both steady-state heat flux and noise power in moderate coupling regimes, below which we find that these two transport quantities are enhanced by the finite-qubit-energy bias. With external modulations, the geometric-phase-induced heat flux shows a monotonic decrease upon increasing the qubit-bath coupling at zero qubit energy bias (without bias). While under the finite-qubit-energy bias (with bias), the geometric-phase-induced heat flux exhibits an interesting reversal behavior in the strong coupling regime. Our results unify the seemingly contradictory results in weak and strong qubit-bath coupling regimes and provide detailed dissections for the quantum fluctuation of nonequilibrium heat transfer.

Dye-sensitization of CdS nano-cage - A density functional theory approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jain, Kalpna; Singh, Kh. S.; Kishor, Shyam

2016-05-23

Quantum dots a few nanometer in size exhibit unique properties in comparison to bulk due to quantum confinement. Their properties can be tuned according to their sizes. Dye sensitized quantum dot (DSQD) solar cells are based on the same principle with surface dangling bonds as a challenge. Researches have shown the existence and stability of nano-cages which are assembled such as to minimize the surface dangling bonds and hence maximize stability. Here, we report a first principles DFT study of optical and electronic properties of CdS-cage (Cd{sub 34}S{sub 34}) sensitized with nkx-2388 dye in three different geometric configurations of dyemore » attachment. A significant distortion is found to occur in the geometric structure of the cage when it interacts strongly with the dye. The relative positioning of dye and cage energy levels is found to be different in different configurations. The absorption spectrum has been analyzed with the help of natural transition orbitals (NTO).« less

Manipulating the Geometric Computer-aided Design of the Operational Requirements-based Casualty Assessment Model within BRL-CAD

DTIC Science & Technology

2018-03-30

ARL-TR-8336 ● MAR 2018 US Army Research Laboratory Manipulating the Geometric Computer-aided Design of the Operational...so designated by other authorized documents. Citation of manufacturer’s or trade names does not constitute an official endorsement or approval of...Army Research Laboratory Manipulating the Geometric Computer-aided Design of the Operational Requirements-based Casualty Assessment Model within

Embracing the quantum limit in silicon computing.

PubMed

Morton, John J L; McCamey, Dane R; Eriksson, Mark A; Lyon, Stephen A

2011-11-16

Quantum computers hold the promise of massive performance enhancements across a range of applications, from cryptography and databases to revolutionary scientific simulation tools. Such computers would make use of the same quantum mechanical phenomena that pose limitations on the continued shrinking of conventional information processing devices. Many of the key requirements for quantum computing differ markedly from those of conventional computers. However, silicon, which plays a central part in conventional information processing, has many properties that make it a superb platform around which to build a quantum computer. © 2011 Macmillan Publishers Limited. All rights reserved

Compiling Planning into Quantum Optimization Problems: A Comparative Study

DTIC Science & Technology

2015-06-07

and Sipser, M. 2000. Quantum computation by adiabatic evolution. arXiv:quant- ph/0001106. Fikes, R. E., and Nilsson, N. J. 1972. STRIPS: A new...become available: quantum annealing. Quantum annealing is one of the most accessible quantum algorithms for a computer sci- ence audience not versed...in quantum computing because of its close ties to classical optimization algorithms such as simulated annealing. While large-scale universal quantum

Quantum Computer Science

NASA Astrophysics Data System (ADS)

Mermin, N. David

2007-08-01

Preface; 1. Cbits and Qbits; 2. General features and some simple examples; 3. Breaking RSA encryption with a quantum computer; 4. Searching with a quantum computer; 5. Quantum error correction; 6. Protocols that use just a few Qbits; Appendices; Index.

Visualizing a silicon quantum computer

NASA Astrophysics Data System (ADS)

Sanders, Barry C.; Hollenberg, Lloyd C. L.; Edmundson, Darran; Edmundson, Andrew

2008-12-01

Quantum computation is a fast-growing, multi-disciplinary research field. The purpose of a quantum computer is to execute quantum algorithms that efficiently solve computational problems intractable within the existing paradigm of 'classical' computing built on bits and Boolean gates. While collaboration between computer scientists, physicists, chemists, engineers, mathematicians and others is essential to the project's success, traditional disciplinary boundaries can hinder progress and make communicating the aims of quantum computing and future technologies difficult. We have developed a four minute animation as a tool for representing, understanding and communicating a silicon-based solid-state quantum computer to a variety of audiences, either as a stand-alone animation to be used by expert presenters or embedded into a longer movie as short animated sequences. The paper includes a generally applicable recipe for successful scientific animation production.

Quantum Statistical Mechanics on a Quantum Computer

NASA Astrophysics Data System (ADS)

Raedt, H. D.; Hams, A. H.; Michielsen, K.; Miyashita, S.; Saito, K.

We describe a quantum algorithm to compute the density of states and thermal equilibrium properties of quantum many-body systems. We present results obtained by running this algorithm on a software implementation of a 21-qubit quantum computer for the case of an antiferromagnetic Heisenberg model on triangular lattices of different size.

An approach to quantum-computational hydrologic inverse analysis

DOE PAGES

O'Malley, Daniel

2018-05-02

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealermore » to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.« less

An approach to quantum-computational hydrologic inverse analysis.

PubMed

O'Malley, Daniel

2018-05-02

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealer to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.

An approach to quantum-computational hydrologic inverse analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

O'Malley, Daniel

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealermore » to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.« less

Calculated hyperfine coupling constants for 5,5-dimethyl-1-pyrroline N-oxide radical products in water and benzene

NASA Astrophysics Data System (ADS)

Nardali, Ş.; Ucun, F.; Karakaya, M.

2017-11-01

The optimized structures of some radical adducts of 5,5-dimethyl-1-pyrroline N-oxide were computed by different methods on ESR spectra. As trapped radicals, H, N3, NH2, CH3, CCl3, OOH in water and F, OH, CF3, CH2OH, OC2H5 in benzene solutions were used. The calculated isotropic hyperfine coupling constants of all the trapped radicals were compared with the corresponding experimental data. The hyperfine coupling constant due to the β proton of the nitroxide radical was seen to be consist with the McConnel's relation αβ = B 0 + B 1cos2θ and, to be effected with the opposite spin density of oxygen nucleus bonded to the nitrogen. It was concluded that in hyperfine calculations the DFT(B3PW91)/LanL2DZ level is superior computational quantum model relative to the used other level. Also, the study has been enriched by the computational of the optimized geometrical parameters, the hyper conjugative interaction energies, the atomic charges and spin densities for all the radical adducts.

Geometrically Constructed Markov Chain Monte Carlo Study of Quantum Spin-phonon Complex Systems

NASA Astrophysics Data System (ADS)

Suwa, Hidemaro

2013-03-01

We have developed novel Monte Carlo methods for precisely calculating quantum spin-boson models and investigated the critical phenomena of the spin-Peierls systems. Three significant methods are presented. The first is a new optimization algorithm of the Markov chain transition kernel based on the geometric weight allocation. This algorithm, for the first time, satisfies the total balance generally without imposing the detailed balance and always minimizes the average rejection rate, being better than the Metropolis algorithm. The second is the extension of the worm (directed-loop) algorithm to non-conserved particles, which cannot be treated efficiently by the conventional methods. The third is the combination with the level spectroscopy. Proposing a new gap estimator, we are successful in eliminating the systematic error of the conventional moment method. Then we have elucidated the phase diagram and the universality class of the one-dimensional XXZ spin-Peierls system. The criticality is totally consistent with the J1 -J2 model, an effective model in the antiadiabatic limit. Through this research, we have succeeded in investigating the critical phenomena of the effectively frustrated quantum spin system by the quantum Monte Carlo method without the negative sign. JSPS Postdoctoral Fellow for Research Abroad

Relativistic harmonic oscillator revisited

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bars, Itzhak

2009-02-15

The familiar Fock space commonly used to describe the relativistic harmonic oscillator, for example, as part of string theory, is insufficient to describe all the states of the relativistic oscillator. We find that there are three different vacua leading to three disconnected Fock sectors, all constructed with the same creation-annihilation operators. These have different spacetime geometric properties as well as different algebraic symmetry properties or different quantum numbers. Two of these Fock spaces include negative norm ghosts (as in string theory), while the third one is completely free of ghosts. We discuss a gauge symmetry in a worldline theory approachmore » that supplies appropriate constraints to remove all the ghosts from all Fock sectors of the single oscillator. The resulting ghost-free quantum spectrum in d+1 dimensions is then classified in unitary representations of the Lorentz group SO(d,1). Moreover, all states of the single oscillator put together make up a single infinite dimensional unitary representation of a hidden global symmetry SU(d,1), whose Casimir eigenvalues are computed. Possible applications of these new results in string theory and other areas of physics and mathematics are briefly mentioned.« less

High-Threshold Fault-Tolerant Quantum Computation with Analog Quantum Error Correction

NASA Astrophysics Data System (ADS)

Fukui, Kosuke; Tomita, Akihisa; Okamoto, Atsushi; Fujii, Keisuke

2018-04-01

To implement fault-tolerant quantum computation with continuous variables, the Gottesman-Kitaev-Preskill (GKP) qubit has been recognized as an important technological element. However, it is still challenging to experimentally generate the GKP qubit with the required squeezing level, 14.8 dB, of the existing fault-tolerant quantum computation. To reduce this requirement, we propose a high-threshold fault-tolerant quantum computation with GKP qubits using topologically protected measurement-based quantum computation with the surface code. By harnessing analog information contained in the GKP qubits, we apply analog quantum error correction to the surface code. Furthermore, we develop a method to prevent the squeezing level from decreasing during the construction of the large-scale cluster states for the topologically protected, measurement-based, quantum computation. We numerically show that the required squeezing level can be relaxed to less than 10 dB, which is within the reach of the current experimental technology. Hence, this work can considerably alleviate this experimental requirement and take a step closer to the realization of large-scale quantum computation.

Quantum Gauss-Jordan Elimination and Simulation of Accounting Principles on Quantum Computers

NASA Astrophysics Data System (ADS)

Diep, Do Ngoc; Giang, Do Hoang; Van Minh, Nguyen

2017-06-01

The paper is devoted to a version of Quantum Gauss-Jordan Elimination and its applications. In the first part, we construct the Quantum Gauss-Jordan Elimination (QGJE) Algorithm and estimate the complexity of computation of Reduced Row Echelon Form (RREF) of N × N matrices. The main result asserts that QGJE has computation time is of order 2 N/2. The second part is devoted to a new idea of simulation of accounting by quantum computing. We first expose the actual accounting principles in a pure mathematics language. Then, we simulate the accounting principles on quantum computers. We show that, all accounting actions are exhousted by the described basic actions. The main problems of accounting are reduced to some system of linear equations in the economic model of Leontief. In this simulation, we use our constructed Quantum Gauss-Jordan Elimination to solve the problems and the complexity of quantum computing is a square root order faster than the complexity in classical computing.

Blueprint for a microwave trapped ion quantum computer

PubMed Central

Lekitsch, Bjoern; Weidt, Sebastian; Fowler, Austin G.; Mølmer, Klaus; Devitt, Simon J.; Wunderlich, Christof; Hensinger, Winfried K.

2017-01-01

The availability of a universal quantum computer may have a fundamental impact on a vast number of research fields and on society as a whole. An increasingly large scientific and industrial community is working toward the realization of such a device. An arbitrarily large quantum computer may best be constructed using a modular approach. We present a blueprint for a trapped ion–based scalable quantum computer module, making it possible to create a scalable quantum computer architecture based on long-wavelength radiation quantum gates. The modules control all operations as stand-alone units, are constructed using silicon microfabrication techniques, and are within reach of current technology. To perform the required quantum computations, the modules make use of long-wavelength radiation–based quantum gate technology. To scale this microwave quantum computer architecture to a large size, we present a fully scalable design that makes use of ion transport between different modules, thereby allowing arbitrarily many modules to be connected to construct a large-scale device. A high error–threshold surface error correction code can be implemented in the proposed architecture to execute fault-tolerant operations. With appropriate adjustments, the proposed modules are also suitable for alternative trapped ion quantum computer architectures, such as schemes using photonic interconnects. PMID:28164154

Silicon CMOS architecture for a spin-based quantum computer.

PubMed

Veldhorst, M; Eenink, H G J; Yang, C H; Dzurak, A S

2017-12-15

Recent advances in quantum error correction codes for fault-tolerant quantum computing and physical realizations of high-fidelity qubits in multiple platforms give promise for the construction of a quantum computer based on millions of interacting qubits. However, the classical-quantum interface remains a nascent field of exploration. Here, we propose an architecture for a silicon-based quantum computer processor based on complementary metal-oxide-semiconductor (CMOS) technology. We show how a transistor-based control circuit together with charge-storage electrodes can be used to operate a dense and scalable two-dimensional qubit system. The qubits are defined by the spin state of a single electron confined in quantum dots, coupled via exchange interactions, controlled using a microwave cavity, and measured via gate-based dispersive readout. We implement a spin qubit surface code, showing the prospects for universal quantum computation. We discuss the challenges and focus areas that need to be addressed, providing a path for large-scale quantum computing.

Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator.

PubMed

Li, Keren; Wan, Yidun; Hung, Ling-Yan; Lan, Tian; Long, Guilu; Lu, Dawei; Zeng, Bei; Laflamme, Raymond

2017-02-24

Topological orders can be used as media for topological quantum computing-a promising quantum computation model due to its invulnerability against local errors. Conversely, a quantum simulator, often regarded as a quantum computing device for special purposes, also offers a way of characterizing topological orders. Here, we show how to identify distinct topological orders via measuring their modular S and T matrices. In particular, we employ a nuclear magnetic resonance quantum simulator to study the properties of three topologically ordered matter phases described by the string-net model with two string types, including the Z_{2} toric code, doubled semion, and doubled Fibonacci. The third one, non-Abelian Fibonacci order is notably expected to be the simplest candidate for universal topological quantum computing. Our experiment serves as the basic module, built on which one can simulate braiding of non-Abelian anyons and ultimately, topological quantum computation via the braiding, and thus provides a new approach of investigating topological orders using quantum computers.

Noise Threshold and Resource Cost of Fault-Tolerant Quantum Computing with Majorana Fermions in Hybrid Systems.

PubMed

Li, Ying

2016-09-16

Fault-tolerant quantum computing in systems composed of both Majorana fermions and topologically unprotected quantum systems, e.g., superconducting circuits or quantum dots, is studied in this Letter. Errors caused by topologically unprotected quantum systems need to be corrected with error-correction schemes, for instance, the surface code. We find that the error-correction performance of such a hybrid topological quantum computer is not superior to a normal quantum computer unless the topological charge of Majorana fermions is insusceptible to noise. If errors changing the topological charge are rare, the fault-tolerance threshold is much higher than the threshold of a normal quantum computer and a surface-code logical qubit could be encoded in only tens of topological qubits instead of about 1,000 normal qubits.

Demonstration of a small programmable quantum computer with atomic qubits.

PubMed

Debnath, S; Linke, N M; Figgatt, C; Landsman, K A; Wright, K; Monroe, C

2016-08-04

Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully connected set of gate operations that are native to the hardware and have a mean fidelity of 98 per cent. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa and Bernstein-Vazirani algorithms with average success rates of 95 and 90 per cent, respectively. We also perform a coherent quantum Fourier transform on five trapped-ion qubits for phase estimation and period finding with average fidelities of 62 and 84 per cent, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels.

Demonstration of a small programmable quantum computer with atomic qubits

NASA Astrophysics Data System (ADS)

Debnath, S.; Linke, N. M.; Figgatt, C.; Landsman, K. A.; Wright, K.; Monroe, C.

2016-08-01

Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully connected set of gate operations that are native to the hardware and have a mean fidelity of 98 per cent. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa and Bernstein-Vazirani algorithms with average success rates of 95 and 90 per cent, respectively. We also perform a coherent quantum Fourier transform on five trapped-ion qubits for phase estimation and period finding with average fidelities of 62 and 84 per cent, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels.

Two-spectral Yang-Baxter operators in topological quantum computation

NASA Astrophysics Data System (ADS)

Sanchez, William F.

2011-05-01

One of the current trends in quantum computing is the application of algebraic topological methods in the design of new algorithms and quantum computers, giving rise to topological quantum computing. One of the tools used in it is the Yang-Baxter equation whose solutions are interpreted as universal quantum gates. Lately, more general Yang-Baxter equations have been investigated, making progress as two-spectral equations and Yang-Baxter systems. This paper intends to apply these new findings to the field of topological quantum computation, more specifically, the proposition of the two-spectral Yang-Baxter operators as universal quantum gates for 2 qubits and 2 qutrits systems, obtaining 4x4 and 9x9 matrices respectively, and further elaboration of the corresponding Hamiltonian by the use of computer algebra software Mathematica® and its Qucalc package. In addition, possible physical systems to which the Yang-Baxter operators obtained can be applied are considered. In the present work it is demonstrated the utility of the Yang-Baxter equation to generate universal quantum gates and the power of computer algebra to design them; it is expected that these mathematical studies contribute to the further development of quantum computers

Universal non-adiabatic holonomic quantum computation in decoherence-free subspaces with quantum dots inside a cavity

NASA Astrophysics Data System (ADS)

Liu, Jun; Dong, Ping; Zhou, Jian; Cao, Zhuo-Liang

2017-05-01

A scheme for implementing the non-adiabatic holonomic quantum computation in decoherence-free subspaces is proposed with the interactions between a microcavity and quantum dots. A universal set of quantum gates can be constructed on the encoded logical qubits with high fidelities. The current scheme can suppress both local and collective noises, which is very important for achieving universal quantum computation. Discussions about the gate fidelities with the experimental parameters show that our schemes can be implemented in current experimental technology. Therefore, our scenario offers a method for universal and robust solid-state quantum computation.

A new software-based architecture for quantum computer

NASA Astrophysics Data System (ADS)

Wu, Nan; Song, FangMin; Li, Xiangdong

2010-04-01

In this paper, we study a reliable architecture of a quantum computer and a new instruction set and machine language for the architecture, which can improve the performance and reduce the cost of the quantum computing. We also try to address some key issues in detail in the software-driven universal quantum computers.

Efficient quantum walk on a quantum processor

PubMed Central

Qiang, Xiaogang; Loke, Thomas; Montanaro, Ashley; Aungskunsiri, Kanin; Zhou, Xiaoqi; O'Brien, Jeremy L.; Wang, Jingbo B.; Matthews, Jonathan C. F.

2016-01-01

The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks that could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle, we experimentally implement the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor. PMID:27146471

Estimating the Resources for Quantum Computation with the QuRE Toolbox

DTIC Science & Technology

2013-05-31

quantum computing. Quantum Info. Comput., 9(7):666–682, July 2009. [13] M. Saffman, T. G. Walker, and K. Mølmer. Quantum information with rydberg atoms...109(5):735–750, 2011. [24] Aram Harrow , Avinatan Hassidim, and Seth Lloyd. Quantum algorithm for solving linear systems of equations. Phys. Rev

Entanglement in a Quantum Annealing Processor

DTIC Science & Technology

2016-09-07

that QA is a viable technology for large- scale quantum computing . DOI: 10.1103/PhysRevX.4.021041 Subject Areas: Quantum Physics, Quantum Information...Superconductivity I. INTRODUCTION The past decade has been exciting for the field of quantum computation . A wide range of physical imple- mentations...measurements used in studying prototype universal quantum computers [9–14]. These constraints make it challenging to experimentally determine whether a scalable

Quantum Optical Implementations of Current Quantum Computing Paradigms

DTIC Science & Technology

2005-05-01

Conferences and Proceedings: The results were presented at several conferences. These include: 1. M. O. Scully, " Foundations of Quantum Mechanics ", in...applications have revealed a strong connection between the fundamental aspects of quantum mechanics that governs physical systems and the informational...could be solved in polynomial time using quantum computers. Another set of problems where quantum mechanics can carry out computations substantially

Experimental Adiabatic Quantum Factorization under Ambient Conditions Based on a Solid-State Single Spin System.

PubMed

Xu, Kebiao; Xie, Tianyu; Li, Zhaokai; Xu, Xiangkun; Wang, Mengqi; Ye, Xiangyu; Kong, Fei; Geng, Jianpei; Duan, Changkui; Shi, Fazhan; Du, Jiangfeng

2017-03-31

The adiabatic quantum computation is a universal and robust method of quantum computing. In this architecture, the problem can be solved by adiabatically evolving the quantum processor from the ground state of a simple initial Hamiltonian to that of a final one, which encodes the solution of the problem. Adiabatic quantum computation has been proved to be a compatible candidate for scalable quantum computation. In this Letter, we report on the experimental realization of an adiabatic quantum algorithm on a single solid spin system under ambient conditions. All elements of adiabatic quantum computation, including initial state preparation, adiabatic evolution (simulated by optimal control), and final state read-out, are realized experimentally. As an example, we found the ground state of the problem Hamiltonian S_{z}I_{z} on our adiabatic quantum processor, which can be mapped to the factorization of 35 into its prime factors 5 and 7.

Experimental Adiabatic Quantum Factorization under Ambient Conditions Based on a Solid-State Single Spin System

NASA Astrophysics Data System (ADS)

Xu, Kebiao; Xie, Tianyu; Li, Zhaokai; Xu, Xiangkun; Wang, Mengqi; Ye, Xiangyu; Kong, Fei; Geng, Jianpei; Duan, Changkui; Shi, Fazhan; Du, Jiangfeng

2017-03-01

The adiabatic quantum computation is a universal and robust method of quantum computing. In this architecture, the problem can be solved by adiabatically evolving the quantum processor from the ground state of a simple initial Hamiltonian to that of a final one, which encodes the solution of the problem. Adiabatic quantum computation has been proved to be a compatible candidate for scalable quantum computation. In this Letter, we report on the experimental realization of an adiabatic quantum algorithm on a single solid spin system under ambient conditions. All elements of adiabatic quantum computation, including initial state preparation, adiabatic evolution (simulated by optimal control), and final state read-out, are realized experimentally. As an example, we found the ground state of the problem Hamiltonian SzIz on our adiabatic quantum processor, which can be mapped to the factorization of 35 into its prime factors 5 and 7.

Compressed quantum computation using a remote five-qubit quantum computer

NASA Astrophysics Data System (ADS)

Hebenstreit, M.; Alsina, D.; Latorre, J. I.; Kraus, B.

2017-05-01

The notion of compressed quantum computation is employed to simulate the Ising interaction of a one-dimensional chain consisting of n qubits using the universal IBM cloud quantum computer running on log2(n ) qubits. The external field parameter that controls the quantum phase transition of this model translates into particular settings of the quantum gates that generate the circuit. We measure the magnetization, which displays the quantum phase transition, on a two-qubit system, which simulates a four-qubit Ising chain, and show its agreement with the theoretical prediction within a certain error. We also discuss the relevant point of how to assess errors when using a cloud quantum computer with a limited amount of runs. As a solution, we propose to use validating circuits, that is, to run independent controlled quantum circuits of similar complexity to the circuit of interest.

Experimental comparison of two quantum computing architectures.

PubMed

Linke, Norbert M; Maslov, Dmitri; Roetteler, Martin; Debnath, Shantanu; Figgatt, Caroline; Landsman, Kevin A; Wright, Kenneth; Monroe, Christopher

2017-03-28

We run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device (www. ibm.com/ibm-q) with limited connectivity, and the other is a fully connected trapped-ion system. Even though the two systems have different native quantum interactions, both can be programed in a way that is blind to the underlying hardware, thus allowing a comparison of identical quantum algorithms between different physical systems. We show that quantum algorithms and circuits that use more connectivity clearly benefit from a better-connected system of qubits. Although the quantum systems here are not yet large enough to eclipse classical computers, this experiment exposes critical factors of scaling quantum computers, such as qubit connectivity and gate expressivity. In addition, the results suggest that codesigning particular quantum applications with the hardware itself will be paramount in successfully using quantum computers in the future.

Continuous-variable quantum Gaussian process regression and quantum singular value decomposition of nonsparse low-rank matrices

NASA Astrophysics Data System (ADS)

Das, Siddhartha; Siopsis, George; Weedbrook, Christian

2018-02-01

With the significant advancement in quantum computation during the past couple of decades, the exploration of machine-learning subroutines using quantum strategies has become increasingly popular. Gaussian process regression is a widely used technique in supervised classical machine learning. Here we introduce an algorithm for Gaussian process regression using continuous-variable quantum systems that can be realized with technology based on photonic quantum computers under certain assumptions regarding distribution of data and availability of efficient quantum access. Our algorithm shows that by using a continuous-variable quantum computer a dramatic speedup in computing Gaussian process regression can be achieved, i.e., the possibility of exponentially reducing the time to compute. Furthermore, our results also include a continuous-variable quantum-assisted singular value decomposition method of nonsparse low rank matrices and forms an important subroutine in our Gaussian process regression algorithm.

Scalable quantum computer architecture with coupled donor-quantum dot qubits

DOEpatents

Schenkel, Thomas; Lo, Cheuk Chi; Weis, Christoph; Lyon, Stephen; Tyryshkin, Alexei; Bokor, Jeffrey

2014-08-26

A quantum bit computing architecture includes a plurality of single spin memory donor atoms embedded in a semiconductor layer, a plurality of quantum dots arranged with the semiconductor layer and aligned with the donor atoms, wherein a first voltage applied across at least one pair of the aligned quantum dot and donor atom controls a donor-quantum dot coupling. A method of performing quantum computing in a scalable architecture quantum computing apparatus includes arranging a pattern of single spin memory donor atoms in a semiconductor layer, forming a plurality of quantum dots arranged with the semiconductor layer and aligned with the donor atoms, applying a first voltage across at least one aligned pair of a quantum dot and donor atom to control a donor-quantum dot coupling, and applying a second voltage between one or more quantum dots to control a Heisenberg exchange J coupling between quantum dots and to cause transport of a single spin polarized electron between quantum dots.

Universal quantum gates for Single Cooper Pair Box based quantum computing

NASA Technical Reports Server (NTRS)

Echternach, P.; Williams, C. P.; Dultz, S. C.; Braunstein, S.; Dowling, J. P.

2000-01-01

We describe a method for achieving arbitrary 1-qubit gates and controlled-NOT gates within the context of the Single Cooper Pair Box (SCB) approach to quantum computing. Such gates are sufficient to support universal quantum computation.

Dissipative quantum computing with open quantum walks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sinayskiy, Ilya; Petruccione, Francesco

An open quantum walk approach to the implementation of a dissipative quantum computing scheme is presented. The formalism is demonstrated for the example of an open quantum walk implementation of a 3 qubit quantum circuit consisting of 10 gates.

Hybrid architecture for encoded measurement-based quantum computation

PubMed Central

Zwerger, M.; Briegel, H. J.; Dür, W.

2014-01-01

We present a hybrid scheme for quantum computation that combines the modular structure of elementary building blocks used in the circuit model with the advantages of a measurement-based approach to quantum computation. We show how to construct optimal resource states of minimal size to implement elementary building blocks for encoded quantum computation in a measurement-based way, including states for error correction and encoded gates. The performance of the scheme is determined by the quality of the resource states, where within the considered error model a threshold of the order of 10% local noise per particle for fault-tolerant quantum computation and quantum communication. PMID:24946906

Simulating chemistry using quantum computers.

PubMed

Kassal, Ivan; Whitfield, James D; Perdomo-Ortiz, Alejandro; Yung, Man-Hong; Aspuru-Guzik, Alán

2011-01-01

The difficulty of simulating quantum systems, well known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on conventional computers, by mapping the quantum system to another, more controllable one. In this review, we discuss to what extent the ideas in quantum computation, now a well-established field, have been applied to chemical problems. We describe algorithms that achieve significant advantages for the electronic-structure problem, the simulation of chemical dynamics, protein folding, and other tasks. Although theory is still ahead of experiment, we outline recent advances that have led to the first chemical calculations on small quantum information processors.

A software methodology for compiling quantum programs

NASA Astrophysics Data System (ADS)

Häner, Thomas; Steiger, Damian S.; Svore, Krysta; Troyer, Matthias

2018-04-01

Quantum computers promise to transform our notions of computation by offering a completely new paradigm. To achieve scalable quantum computation, optimizing compilers and a corresponding software design flow will be essential. We present a software architecture for compiling quantum programs from a high-level language program to hardware-specific instructions. We describe the necessary layers of abstraction and their differences and similarities to classical layers of a computer-aided design flow. For each layer of the stack, we discuss the underlying methods for compilation and optimization. Our software methodology facilitates more rapid innovation among quantum algorithm designers, quantum hardware engineers, and experimentalists. It enables scalable compilation of complex quantum algorithms and can be targeted to any specific quantum hardware implementation.

Resonant transition-based quantum computation

NASA Astrophysics Data System (ADS)

Chiang, Chen-Fu; Hsieh, Chang-Yu

2017-05-01

In this article we assess a novel quantum computation paradigm based on the resonant transition (RT) phenomenon commonly associated with atomic and molecular systems. We thoroughly analyze the intimate connections between the RT-based quantum computation and the well-established adiabatic quantum computation (AQC). Both quantum computing frameworks encode solutions to computational problems in the spectral properties of a Hamiltonian and rely on the quantum dynamics to obtain the desired output state. We discuss how one can adapt any adiabatic quantum algorithm to a corresponding RT version and the two approaches are limited by different aspects of Hamiltonians' spectra. The RT approach provides a compelling alternative to the AQC under various circumstances. To better illustrate the usefulness of the novel framework, we analyze the time complexity of an algorithm for 3-SAT problems and discuss straightforward methods to fine tune its efficiency.

Quantum computing without wavefunctions: time-dependent density functional theory for universal quantum computation.

PubMed

Tempel, David G; Aspuru-Guzik, Alán

2012-01-01

We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, we also demonstrate that TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions. This establishes the foundations of TDDFT for quantum computation and opens the possibility of developing density functionals for use in quantum algorithms.

Quantum Computing: Solving Complex Problems

ScienceCinema

DiVincenzo, David

2018-05-22

One of the motivating ideas of quantum computation was that there could be a new kind of machine that would solve hard problems in quantum mechanics. There has been significant progress towards the experimental realization of these machines (which I will review), but there are still many questions about how such a machine could solve computational problems of interest in quantum physics. New categorizations of the complexity of computational problems have now been invented to describe quantum simulation. The bad news is that some of these problems are believed to be intractable even on a quantum computer, falling into a quantum analog of the NP class. The good news is that there are many other new classifications of tractability that may apply to several situations of physical interest.

Cloud Quantum Computing of an Atomic Nucleus

NASA Astrophysics Data System (ADS)

Dumitrescu, E. F.; McCaskey, A. J.; Hagen, G.; Jansen, G. R.; Morris, T. D.; Papenbrock, T.; Pooser, R. C.; Dean, D. J.; Lougovski, P.

2018-05-01

We report a quantum simulation of the deuteron binding energy on quantum processors accessed via cloud servers. We use a Hamiltonian from pionless effective field theory at leading order. We design a low-depth version of the unitary coupled-cluster ansatz, use the variational quantum eigensolver algorithm, and compute the binding energy to within a few percent. Our work is the first step towards scalable nuclear structure computations on a quantum processor via the cloud, and it sheds light on how to map scientific computing applications onto nascent quantum devices.

Cloud Quantum Computing of an Atomic Nucleus

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dumitrescu, Eugene F.; McCaskey, Alex J.; Hagen, Gaute

Here, we report a quantum simulation of the deuteron binding energy on quantum processors accessed via cloud servers. We use a Hamiltonian from pionless effective field theory at leading order. We design a low-depth version of the unitary coupled-cluster ansatz, use the variational quantum eigensolver algorithm, and compute the binding energy to within a few percent. Our work is the first step towards scalable nuclear structure computations on a quantum processor via the cloud, and it sheds light on how to map scientific computing applications onto nascent quantum devices.

Cloud Quantum Computing of an Atomic Nucleus.

PubMed

Dumitrescu, E F; McCaskey, A J; Hagen, G; Jansen, G R; Morris, T D; Papenbrock, T; Pooser, R C; Dean, D J; Lougovski, P

2018-05-25

We report a quantum simulation of the deuteron binding energy on quantum processors accessed via cloud servers. We use a Hamiltonian from pionless effective field theory at leading order. We design a low-depth version of the unitary coupled-cluster ansatz, use the variational quantum eigensolver algorithm, and compute the binding energy to within a few percent. Our work is the first step towards scalable nuclear structure computations on a quantum processor via the cloud, and it sheds light on how to map scientific computing applications onto nascent quantum devices.

Cloud Quantum Computing of an Atomic Nucleus

DOE PAGES

Dumitrescu, Eugene F.; McCaskey, Alex J.; Hagen, Gaute; ...

2018-05-23

Here, we report a quantum simulation of the deuteron binding energy on quantum processors accessed via cloud servers. We use a Hamiltonian from pionless effective field theory at leading order. We design a low-depth version of the unitary coupled-cluster ansatz, use the variational quantum eigensolver algorithm, and compute the binding energy to within a few percent. Our work is the first step towards scalable nuclear structure computations on a quantum processor via the cloud, and it sheds light on how to map scientific computing applications onto nascent quantum devices.

The sudden death and sudden birth of quantum discord.

PubMed

Xia, Wei; Hou, Jin-Xing; Wang, Xiao-Hui; Liu, Si-Yuan

2018-03-28

The interaction of quantum system and its environment brings out abundant quantum phenomenons. The sudden death of quantum resources, including entanglement, quantum discord and coherence, have been studied from the perspective of quantum breaking channels (QBC). QBC of quantum resources reveal the common features of quantum resources. The definition of QBC implies the relationship between quantum resources. However, sudden death of quantum resources can also appear under some other quantum channels. We consider the dynamics of Bell-diagonal states under a stochastic dephasing noise along the z-direction, and the sudden death and sudden birth of quantum discord are investigated. Next we explain this phenomenon from the geometric structure of quantum discord. According to the above results, the states with sudden death and sudden birth can be filtered in three-parameter space. Then we provide two necessary conditions to judge which kind of noise channels can make Bell-diagonal states sudden death and sudden birth. Moreover, the relation between quantum discord and coherence indicates that the sudden death and sudden birth of quantum discord implies the sudden death and sudden birth of coherence in an optimal basis.

The information geometry of chaos

NASA Astrophysics Data System (ADS)

Cafaro, Carlo

2008-10-01

In this Thesis, we propose a new theoretical information-geometric framework (IGAC, Information Geometrodynamical Approach to Chaos) suitable to characterize chaotic dynamical behavior of arbitrary complex systems. First, the problem being investigated is defined; its motivation and relevance are discussed. The basic tools of information physics and the relevant mathematical tools employed in this work are introduced. The basic aspects of Entropic Dynamics (ED) are reviewed. ED is an information-constrained dynamics developed by Ariel Caticha to investigate the possibility that laws of physics---either classical or quantum---may emerge as macroscopic manifestations of underlying microscopic statistical structures. ED is of primary importance in our IGAC. The notion of chaos in classical and quantum physics is introduced. Special focus is devoted to the conventional Riemannian geometrodynamical approach to chaos (Jacobi geometrodynamics) and to the Zurek-Paz quantum chaos criterion of linear entropy growth. After presenting this background material, we show that the ED formalism is not purely an abstract mathematical framework, but is indeed a general theoretical scheme from which conventional Newtonian dynamics is obtained as a special limiting case. The major elements of our IGAC and the novel notion of information geometrodynamical entropy (IGE) are introduced by studying two "toy models". To illustrate the potential power of our IGAC, one application is presented. An information-geometric analogue of the Zurek-Paz quantum chaos criterion of linear entropy growth is suggested. Finally, concluding remarks emphasizing strengths and weak points of our approach are presented and possible further research directions are addressed. At this stage of its development, IGAC remains an ambitious unifying information-geometric theoretical construct for the study of chaotic dynamics with several unsolved problems. However, based on our recent findings, we believe it already provides an interesting, innovative and potentially powerful way to study and understand the very important and challenging problems of classical and quantum chaos.

Designing, programming, and optimizing a (small) quantum computer

NASA Astrophysics Data System (ADS)

Svore, Krysta

In 1982, Richard Feynman proposed to use a computer founded on the laws of quantum physics to simulate physical systems. In the more than thirty years since, quantum computers have shown promise to solve problems in number theory, chemistry, and materials science that would otherwise take longer than the lifetime of the universe to solve on an exascale classical machine. The practical realization of a quantum computer requires understanding and manipulating subtle quantum states while experimentally controlling quantum interference. It also requires an end-to-end software architecture for programming, optimizing, and implementing a quantum algorithm on the quantum device hardware. In this talk, we will introduce recent advances in connecting abstract theory to present-day real-world applications through software. We will highlight recent advancement of quantum algorithms and the challenges in ultimately performing a scalable solution on a quantum device.

Quantum Walk Schemes for Universal Quantum Computation

NASA Astrophysics Data System (ADS)

Underwood, Michael S.

Random walks are a powerful tool for the efficient implementation of algorithms in classical computation. Their quantum-mechanical analogues, called quantum walks, hold similar promise. Quantum walks provide a model of quantum computation that has recently been shown to be equivalent in power to the standard circuit model. As in the classical case, quantum walks take place on graphs and can undergo discrete or continuous evolution, though quantum evolution is unitary and therefore deterministic until a measurement is made. This thesis considers the usefulness of continuous-time quantum walks to quantum computation from the perspectives of both their fundamental power under various formulations, and their applicability in practical experiments. In one extant scheme, logical gates are effected by scattering processes. The results of an exhaustive search for single-qubit operations in this model are presented. It is shown that the number of distinct operations increases exponentially with the number of vertices in the scattering graph. A catalogue of all graphs on up to nine vertices that implement single-qubit unitaries at a specific set of momenta is included in an appendix. I develop a novel scheme for universal quantum computation called the discontinuous quantum walk, in which a continuous-time quantum walker takes discrete steps of evolution via perfect quantum state transfer through small 'widget' graphs. The discontinuous quantum-walk scheme requires an exponentially sized graph, as do prior discrete and continuous schemes. To eliminate the inefficient vertex resource requirement, a computation scheme based on multiple discontinuous walkers is presented. In this model, n interacting walkers inhabiting a graph with 2n vertices can implement an arbitrary quantum computation on an input of length n, an exponential savings over previous universal quantum walk schemes. This is the first quantum walk scheme that allows for the application of quantum error correction. The many-particle quantum walk can be viewed as a single quantum walk undergoing perfect state transfer on a larger weighted graph, obtained via equitable partitioning. I extend this formalism to non-simple graphs. Examples of the application of equitable partitioning to the analysis of quantum walks and many-particle quantum systems are discussed.

Exploration of quantum phases transition in the XXZ model with Dzyaloshinskii-Moriya interaction using trance distance discord

NASA Astrophysics Data System (ADS)

Zhang, Ren-jie; Xu, Shuai; Shi, Jia-dong; Ma, Wen-chao; Ye, Liu

2015-11-01

In the paper, we researched the quantum phase transition (QPT) in the anisotropic spin XXZ model by exploiting the quantum renormalization group (QRG) method. The innovation point is that we adopt a new approach called trace distance discord to indicate the quantum correlation of the system. QPT after several iterations of renormalization in current system has been observed. Consequently, it opened the possibility of investigation of QPR in the geometric discord territory. While the anisotropy suppresses the correlation due to favoring of the alignment of spins, the DM interaction restores the spoiled correlation via creation of the quantum fluctuations. We also apply quantum renormalization group method to probe the thermodynamic limit of the model and emerging of nonanalytic behavior of the correlation.

Conformal invariance and the metrication of the fundamental forces

NASA Astrophysics Data System (ADS)

Mannheim, Philip D.

2016-07-01

We revisit Weyl’s metrication (geometrization) of electromagnetism. We show that by making Weyl’s proposed geometric connection be pure imaginary, not only are we able to metricate electromagnetism, an underlying local conformal invariance makes the geometry be strictly Riemannian and prevents observational gravity from being complex. Via torsion, we achieve an analogous metrication for axial-vector fields. We generalize our procedure to Yang-Mills theories, and achieve a metrication of all the fundamental forces. Only in the gravity sector does our approach differ from the standard picture of fundamental forces, with our approach requiring that standard Einstein gravity be replaced by conformal gravity. We show that quantum conformal gravity is a consistent and unitary quantum gravitational theory, one that, unlike string theory, only requires four spacetime dimensions.

Theory of electronic and optical properties for different shapes of InAs/In0.52Al0.48As quantum wires

NASA Astrophysics Data System (ADS)

Bouazra, A.; Nasrallah, S. Abdi-Ben; Said, M.

2016-01-01

In this work, we propose an efficient method to investigate optical properties as well as their dependence on geometrical parameters in InAs/InAlAs quantum wires. The used method is based on the coordinate transformation and the finite difference method. It provides sufficient accuracy, stability and flexibility with respect to the size and shape of the quantum wire. The electron and hole energy levels as well as their corresponding wave functions are investigated for different shape of quantum wires. The optical transition energies, the emission wavelengths and the oscillator strengths are also studied.

A Theoretical Study of Phosphoryl Transfers of Tyrosyl-DNA Phosphodiesterase I (Tdp1) and the Possibility of a "Dead-End" Phosphohistidine Intermediate.

PubMed

DeYonker, Nathan J; Webster, Charles Edwin

2015-07-14

Tyrosyl-DNA phosphodiesterase I (Tdp1) is a DNA repair enzyme conserved across eukaryotes that catalyzes the hydrolysis of the phosphodiester bond between the tyrosine residue of topoisomerase I and the 3'-phosphate of DNA. Atomic level details of the mechanism of Tdp1 are proposed and analyzed using a fully quantum mechanical, geometrically constrained model. The structural basis for the computational model is the vanadate-inhibited crystal structure of human Tdp1 (hTdp1, Protein Data Bank entry 1RFF ). Density functional theory computations are used to acquire thermodynamic and kinetic data along the catalytic pathway, including the phosphoryl transfer and subsequent hydrolysis. Located transition states and intermediates along the reaction coordinate suggest an associative phosphoryl transfer mechanism with five-coordinate phosphorane intermediates. Similar to both theoretical and experimental results for phospholipase D, the proposed mechanism for hTdp1 also includes the thermodynamically favorable possibility of a four-coordinate phosphohistidine "dead-end" product.

Geometric metasurface enabling polarization independent beam splitting.

PubMed

Yoon, Gwanho; Lee, Dasol; Nam, Ki Tae; Rho, Junsuk

2018-06-21

A polarization independent holographic beam splitter that generates equal-intensity beams based on geometric metasurface is demonstrated. Although conventional geometric metasurfaces have the advantages of working over a broad frequency range and having intuitive design principles, geometric metasurfaces have the limitation that they only work for circular polarization. In this work, Fourier holography is used to overcome this limitation. A perfect overlap resulting from the origin-symmetry of the encoded image enables polarization independent operation of geometric metasurfaces. The designed metasurface beam splitter is experimentally demonstrated by using hydrogenated amorphous silicon, and the device performs consistent beam splitting regardless of incident polarizations as well as wavelengths. Our device can be applied to generate equal-intensity beams for entangled photon light sources in quantum optics, and the design approach provides a way to develop ultra-thin broadband polarization independent components for modern optics.

Step-by-step magic state encoding for efficient fault-tolerant quantum computation

PubMed Central

Goto, Hayato

2014-01-01

Quantum error correction allows one to make quantum computers fault-tolerant against unavoidable errors due to decoherence and imperfect physical gate operations. However, the fault-tolerant quantum computation requires impractically large computational resources for useful applications. This is a current major obstacle to the realization of a quantum computer. In particular, magic state distillation, which is a standard approach to universality, consumes the most resources in fault-tolerant quantum computation. For the resource problem, here we propose step-by-step magic state encoding for concatenated quantum codes, where magic states are encoded step by step from the physical level to the logical one. To manage errors during the encoding, we carefully use error detection. Since the sizes of intermediate codes are small, it is expected that the resource overheads will become lower than previous approaches based on the distillation at the logical level. Our simulation results suggest that the resource requirements for a logical magic state will become comparable to those for a single logical controlled-NOT gate. Thus, the present method opens a new possibility for efficient fault-tolerant quantum computation. PMID:25511387

Step-by-step magic state encoding for efficient fault-tolerant quantum computation.

PubMed

Goto, Hayato

2014-12-16

Quantum error correction allows one to make quantum computers fault-tolerant against unavoidable errors due to decoherence and imperfect physical gate operations. However, the fault-tolerant quantum computation requires impractically large computational resources for useful applications. This is a current major obstacle to the realization of a quantum computer. In particular, magic state distillation, which is a standard approach to universality, consumes the most resources in fault-tolerant quantum computation. For the resource problem, here we propose step-by-step magic state encoding for concatenated quantum codes, where magic states are encoded step by step from the physical level to the logical one. To manage errors during the encoding, we carefully use error detection. Since the sizes of intermediate codes are small, it is expected that the resource overheads will become lower than previous approaches based on the distillation at the logical level. Our simulation results suggest that the resource requirements for a logical magic state will become comparable to those for a single logical controlled-NOT gate. Thus, the present method opens a new possibility for efficient fault-tolerant quantum computation.

Secure entanglement distillation for double-server blind quantum computation.

PubMed

Morimae, Tomoyuki; Fujii, Keisuke

2013-07-12

Blind quantum computation is a new secure quantum computing protocol where a client, who does not have enough quantum technologies at her disposal, can delegate her quantum computation to a server, who has a fully fledged quantum computer, in such a way that the server cannot learn anything about the client's input, output, and program. If the client interacts with only a single server, the client has to have some minimum quantum power, such as the ability of emitting randomly rotated single-qubit states or the ability of measuring states. If the client interacts with two servers who share Bell pairs but cannot communicate with each other, the client can be completely classical. For such a double-server scheme, two servers have to share clean Bell pairs, and therefore the entanglement distillation is necessary in a realistic noisy environment. In this Letter, we show that it is possible to perform entanglement distillation in the double-server scheme without degrading the security of blind quantum computing.

Efficient universal blind quantum computation.

PubMed

Giovannetti, Vittorio; Maccone, Lorenzo; Morimae, Tomoyuki; Rudolph, Terry G

2013-12-06

We give a cheat sensitive protocol for blind universal quantum computation that is efficient in terms of computational and communication resources: it allows one party to perform an arbitrary computation on a second party's quantum computer without revealing either which computation is performed, or its input and output. The first party's computational capabilities can be extremely limited: she must only be able to create and measure single-qubit superposition states. The second party is not required to use measurement-based quantum computation. The protocol requires the (optimal) exchange of O(Jlog2(N)) single-qubit states, where J is the computational depth and N is the number of qubits needed for the computation.

High-speed linear optics quantum computing using active feed-forward.

PubMed

Prevedel, Robert; Walther, Philip; Tiefenbacher, Felix; Böhi, Pascal; Kaltenbaek, Rainer; Jennewein, Thomas; Zeilinger, Anton

2007-01-04

As information carriers in quantum computing, photonic qubits have the advantage of undergoing negligible decoherence. However, the absence of any significant photon-photon interaction is problematic for the realization of non-trivial two-qubit gates. One solution is to introduce an effective nonlinearity by measurements resulting in probabilistic gate operations. In one-way quantum computation, the random quantum measurement error can be overcome by applying a feed-forward technique, such that the future measurement basis depends on earlier measurement results. This technique is crucial for achieving deterministic quantum computation once a cluster state (the highly entangled multiparticle state on which one-way quantum computation is based) is prepared. Here we realize a concatenated scheme of measurement and active feed-forward in a one-way quantum computing experiment. We demonstrate that, for a perfect cluster state and no photon loss, our quantum computation scheme would operate with good fidelity and that our feed-forward components function with very high speed and low error for detected photons. With present technology, the individual computational step (in our case the individual feed-forward cycle) can be operated in less than 150 ns using electro-optical modulators. This is an important result for the future development of one-way quantum computers, whose large-scale implementation will depend on advances in the production and detection of the required highly entangled cluster states.

Phase diagram and quench dynamics of the cluster-XY spin chain

NASA Astrophysics Data System (ADS)

Montes, Sebastián; Hamma, Alioscia

2012-08-01

We study the complete phase space and the quench dynamics of an exactly solvable spin chain, the cluster-XY model. In this chain, the cluster term and the XY couplings compete to give a rich phase diagram. The phase diagram is studied by means of the quantum geometric tensor. We study the time evolution of the system after a critical quantum quench using the Loschmidt echo. The structure of the revivals after critical quantum quenches presents a nontrivial behavior depending on the phase of the initial state and the critical point.

Phase diagram and quench dynamics of the cluster-XY spin chain.

PubMed

Montes, Sebastián; Hamma, Alioscia

2012-08-01

We study the complete phase space and the quench dynamics of an exactly solvable spin chain, the cluster-XY model. In this chain, the cluster term and the XY couplings compete to give a rich phase diagram. The phase diagram is studied by means of the quantum geometric tensor. We study the time evolution of the system after a critical quantum quench using the Loschmidt echo. The structure of the revivals after critical quantum quenches presents a nontrivial behavior depending on the phase of the initial state and the critical point.

A Decoherence-Free Quantum Memory Using Trapped Ions

DTIC Science & Technology

2016-09-22

superpo- sitions. Robust quantum memories are there- fore essential to realizing the potential gains of quantum computing (3). However, inter- action of a...tolerant quantum logic (13, 14). These properties suggest that DFSs will be intrinsic to future quantum computing architectures. Logic gates on DFS...practi- cal quantum computing will in any case re- quire logic gates of a much higher fidelity than those used in this work. We therefore expect that, once

Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning

NASA Astrophysics Data System (ADS)

Fujii, Keisuke; Nakajima, Kohei

2017-08-01

The quantum computer has an amazing potential of fast information processing. However, the realization of a digital quantum computer is still a challenging problem requiring highly accurate controls and key application strategies. Here we propose a platform, quantum reservoir computing, to solve these issues successfully by exploiting the natural quantum dynamics of ensemble systems, which are ubiquitous in laboratories nowadays, for machine learning. This framework enables ensemble quantum systems to universally emulate nonlinear dynamical systems including classical chaos. A number of numerical experiments show that quantum systems consisting of 5-7 qubits possess computational capabilities comparable to conventional recurrent neural networks of 100-500 nodes. This discovery opens up a paradigm for information processing with artificial intelligence powered by quantum physics.

QCCM Center for Quantum Algorithms

DTIC Science & Technology

2008-10-17

algorithms (e.g., quantum walks and adiabatic computing ), as well as theoretical advances relating algorithms to physical implementations (e.g...Park, NC 27709-2211 15. SUBJECT TERMS Quantum algorithms, quantum computing , fault-tolerant error correction Richard Cleve MITACS East Academic...0511200 Algebraic results on quantum automata A. Ambainis, M. Beaudry, M. Golovkins, A. Kikusts, M. Mercer, D. Thrien Theory of Computing Systems 39(2006

Self-guaranteed measurement-based quantum computation

NASA Astrophysics Data System (ADS)

Hayashi, Masahito; Hajdušek, Michal

2018-05-01

In order to guarantee the output of a quantum computation, we usually assume that the component devices are trusted. However, when the total computation process is large, it is not easy to guarantee the whole system when we have scaling effects, unexpected noise, or unaccounted for correlations between several subsystems. If we do not trust the measurement basis or the prepared entangled state, we do need to be worried about such uncertainties. To this end, we propose a self-guaranteed protocol for verification of quantum computation under the scheme of measurement-based quantum computation where no prior-trusted devices (measurement basis or entangled state) are needed. The approach we present enables the implementation of verifiable quantum computation using the measurement-based model in the context of a particular instance of delegated quantum computation where the server prepares the initial computational resource and sends it to the client, who drives the computation by single-qubit measurements. Applying self-testing procedures, we are able to verify the initial resource as well as the operation of the quantum devices and hence the computation itself. The overhead of our protocol scales with the size of the initial resource state to the power of 4 times the natural logarithm of the initial state's size.

Limits on efficient computation in the physical world

NASA Astrophysics Data System (ADS)

Aaronson, Scott Joel

More than a speculative technology, quantum computing seems to challenge our most basic intuitions about how the physical world should behave. In this thesis I show that, while some intuitions from classical computer science must be jettisoned in the light of modern physics, many others emerge nearly unscathed; and I use powerful tools from computational complexity theory to help determine which are which. In the first part of the thesis, I attack the common belief that quantum computing resembles classical exponential parallelism, by showing that quantum computers would face serious limitations on a wider range of problems than was previously known. In particular, any quantum algorithm that solves the collision problem---that of deciding whether a sequence of n integers is one-to-one or two-to-one---must query the sequence O (n1/5) times. This resolves a question that was open for years; previously no lower bound better than constant was known. A corollary is that there is no "black-box" quantum algorithm to break cryptographic hash functions or solve the Graph Isomorphism problem in polynomial time. I also show that relative to an oracle, quantum computers could not solve NP-complete problems in polynomial time, even with the help of nonuniform "quantum advice states"; and that any quantum algorithm needs O (2n/4/n) queries to find a local minimum of a black-box function on the n-dimensional hypercube. Surprisingly, the latter result also leads to new classical lower bounds for the local search problem. Finally, I give new lower bounds on quantum one-way communication complexity, and on the quantum query complexity of total Boolean functions and recursive Fourier sampling. The second part of the thesis studies the relationship of the quantum computing model to physical reality. I first examine the arguments of Leonid Levin, Stephen Wolfram, and others who believe quantum computing to be fundamentally impossible. I find their arguments unconvincing without a "Sure/Shor separator"---a criterion that separates the already-verified quantum states from those that appear in Shor's factoring algorithm. I argue that such a separator should be based on a complexity classification of quantum states, and go on to create such a classification. Next I ask what happens to the quantum computing model if we take into account that the speed of light is finite---and in particular, whether Grover's algorithm still yields a quadratic speedup for searching a database. Refuting a claim by Benioff, I show that the surprising answer is yes. Finally, I analyze hypothetical models of computation that go even beyond quantum computing. I show that many such models would be as powerful as the complexity class PP, and use this fact to give a simple, quantum computing based proof that PP is closed under intersection. On the other hand, I also present one model---wherein we could sample the entire history of a hidden variable---that appears to be more powerful than standard quantum computing, but only slightly so.

Emergent geometric description for a topological phase transition in the Kitaev superconductor model

NASA Astrophysics Data System (ADS)

Kim, Ki-Seok; Park, Miok; Cho, Jaeyoon; Park, Chanyong

2017-10-01

Resorting to Wilsonian renormalization group (RG) transformations, we propose an emergent geometric description for a topological phase transition in the Kitaev superconductor model. An effective field theory consists of an emergent bulk action with an extra dimension, an ultraviolet (UV) boundary condition for an initial value of a coupling function, and an infrared (IR) effective action with a fully renormalized coupling function. The bulk action describes the evolution of the coupling function along the direction of the extra dimension, where the extra dimension is identified with an RG scale and the resulting equation of motion is nothing but a β function. In particular, the IR effective field theory turns out to be consistent with a Callan-Symanzik equation which takes into account both the bulk and IR boundary contributions. This derived Callan-Symanzik equation gives rise to a metric structure. Based on this emergent metric tensor, we uncover the equivalence of the entanglement entropy between the emergent geometric description and the quantum field theory in the vicinity of the quantum critical point.

On the self-interference in electron scattering: Copenhagen, Bohmian and geometrical interpretations of quantum mechanics

NASA Astrophysics Data System (ADS)

Tavernelli, Ivano

2018-06-01

Self-interference embodies the essence of the particle-wave formulation of quantum mechanics (QM). According to the Copenhagen interpretation of QM, self-interference by a double-slit requires a large transverse coherence of the incident wavepacket such that it covers the separation between the slits. Bohmian dynamics provides a first step in the separation of the particle-wave character of matter by introducing deterministic trajectories guided by a pilot wave that follows the time-dependent Schrödinger equation. In this work, I present a new description of the phenomenon of self-interference using the geometrical formulation of QM introduced in Tavernelli (2016). In particular, this formalism removes the need for the concept of wavefunction collapse in the interpretation of the act of measurement i.e., the emergence of the classical world. The three QM formulations (Schrödinger, Bohmian, and geometrical) are applied to the description of the scattering of a free electron by a hydrogen atom and a double-slit. The corresponding interpretations of self-interference are compared and discussed.

Architectures for Quantum Simulation Showing a Quantum Speedup

NASA Astrophysics Data System (ADS)

Bermejo-Vega, Juan; Hangleiter, Dominik; Schwarz, Martin; Raussendorf, Robert; Eisert, Jens

2018-04-01

One of the main aims in the field of quantum simulation is to achieve a quantum speedup, often referred to as "quantum computational supremacy," referring to the experimental realization of a quantum device that computationally outperforms classical computers. In this work, we show that one can devise versatile and feasible schemes of two-dimensional, dynamical, quantum simulators showing such a quantum speedup, building on intermediate problems involving nonadaptive, measurement-based, quantum computation. In each of the schemes, an initial product state is prepared, potentially involving an element of randomness as in disordered models, followed by a short-time evolution under a basic translationally invariant Hamiltonian with simple nearest-neighbor interactions and a mere sampling measurement in a fixed basis. The correctness of the final-state preparation in each scheme is fully efficiently certifiable. We discuss experimental necessities and possible physical architectures, inspired by platforms of cold atoms in optical lattices and a number of others, as well as specific assumptions that enter the complexity-theoretic arguments. This work shows that benchmark settings exhibiting a quantum speedup may require little control, in contrast to universal quantum computing. Thus, our proposal puts a convincing experimental demonstration of a quantum speedup within reach in the near term.

Demonstration of measurement-only blind quantum computing

NASA Astrophysics Data System (ADS)

Greganti, Chiara; Roehsner, Marie-Christine; Barz, Stefanie; Morimae, Tomoyuki; Walther, Philip

2016-01-01

Blind quantum computing allows for secure cloud networks of quasi-classical clients and a fully fledged quantum server. Recently, a new protocol has been proposed, which requires a client to perform only measurements. We demonstrate a proof-of-principle implementation of this measurement-only blind quantum computing, exploiting a photonic setup to generate four-qubit cluster states for computation and verification. Feasible technological requirements for the client and the device-independent blindness make this scheme very applicable for future secure quantum networks.

Quantum machine learning.

PubMed

Biamonte, Jacob; Wittek, Peter; Pancotti, Nicola; Rebentrost, Patrick; Wiebe, Nathan; Lloyd, Seth

2017-09-13

Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Quantum systems produce atypical patterns that classical systems are thought not to produce efficiently, so it is reasonable to postulate that quantum computers may outperform classical computers on machine learning tasks. The field of quantum machine learning explores how to devise and implement quantum software that could enable machine learning that is faster than that of classical computers. Recent work has produced quantum algorithms that could act as the building blocks of machine learning programs, but the hardware and software challenges are still considerable.

Quantum machine learning

NASA Astrophysics Data System (ADS)

Biamonte, Jacob; Wittek, Peter; Pancotti, Nicola; Rebentrost, Patrick; Wiebe, Nathan; Lloyd, Seth

2017-09-01

Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Quantum systems produce atypical patterns that classical systems are thought not to produce efficiently, so it is reasonable to postulate that quantum computers may outperform classical computers on machine learning tasks. The field of quantum machine learning explores how to devise and implement quantum software that could enable machine learning that is faster than that of classical computers. Recent work has produced quantum algorithms that could act as the building blocks of machine learning programs, but the hardware and software challenges are still considerable.

History dependent quantum random walks as quantum lattice gas automata

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shakeel, Asif, E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu; Love, Peter J., E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu; Meyer, David A., E-mail: asif.shakeel@gmail.com, E-mail: dmeyer@math.ucsd.edu, E-mail: plove@haverford.edu

Quantum Random Walks (QRW) were first defined as one-particle sectors of Quantum Lattice Gas Automata (QLGA). Recently, they have been generalized to include history dependence, either on previous coin (internal, i.e., spin or velocity) states or on previous position states. These models have the goal of studying the transition to classicality, or more generally, changes in the performance of quantum walks in algorithmic applications. We show that several history dependent QRW can be identified as one-particle sectors of QLGA. This provides a unifying conceptual framework for these models in which the extra degrees of freedom required to store the historymore » information arise naturally as geometrical degrees of freedom on the lattice.« less

Practical quality control tools for curves and surfaces

NASA Technical Reports Server (NTRS)

Small, Scott G.

1992-01-01

Curves (geometry) and surfaces created by Computer Aided Geometric Design systems in the engineering environment must satisfy two basic quality criteria: the geometric shape must have the desired engineering properties; and the objects must be parameterized in a way which does not cause computational difficulty for geometric processing and engineering analysis. Interactive techniques are described which are in use at Boeing to evaluate the quality of aircraft geometry prior to Computational Fluid Dynamic analysis, including newly developed methods for examining surface parameterization and its effects.

Experimental comparison of two quantum computing architectures

PubMed Central

Linke, Norbert M.; Maslov, Dmitri; Roetteler, Martin; Debnath, Shantanu; Figgatt, Caroline; Landsman, Kevin A.; Wright, Kenneth; Monroe, Christopher

2017-01-01

We run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device (www.research.ibm.com/ibm-q) with limited connectivity, and the other is a fully connected trapped-ion system. Even though the two systems have different native quantum interactions, both can be programed in a way that is blind to the underlying hardware, thus allowing a comparison of identical quantum algorithms between different physical systems. We show that quantum algorithms and circuits that use more connectivity clearly benefit from a better-connected system of qubits. Although the quantum systems here are not yet large enough to eclipse classical computers, this experiment exposes critical factors of scaling quantum computers, such as qubit connectivity and gate expressivity. In addition, the results suggest that codesigning particular quantum applications with the hardware itself will be paramount in successfully using quantum computers in the future. PMID:28325879

Complex Instruction Set Quantum Computing

NASA Astrophysics Data System (ADS)

Sanders, G. D.; Kim, K. W.; Holton, W. C.

1998-03-01

In proposed quantum computers, electromagnetic pulses are used to implement logic gates on quantum bits (qubits). Gates are unitary transformations applied to coherent qubit wavefunctions and a universal computer can be created using a minimal set of gates. By applying many elementary gates in sequence, desired quantum computations can be performed. This reduced instruction set approach to quantum computing (RISC QC) is characterized by serial application of a few basic pulse shapes and a long coherence time. However, the unitary matrix of the overall computation is ultimately a unitary matrix of the same size as any of the elementary matrices. This suggests that we might replace a sequence of reduced instructions with a single complex instruction using an optimally taylored pulse. We refer to this approach as complex instruction set quantum computing (CISC QC). One trades the requirement for long coherence times for the ability to design and generate potentially more complex pulses. We consider a model system of coupled qubits interacting through nearest neighbor coupling and show that CISC QC can reduce the time required to perform quantum computations.

Quantum Error Correction

NASA Astrophysics Data System (ADS)

Lidar, Daniel A.; Brun, Todd A.

2013-09-01

Prologue; Preface; Part I. Background: 1. Introduction to decoherence and noise in open quantum systems Daniel Lidar and Todd Brun; 2. Introduction to quantum error correction Dave Bacon; 3. Introduction to decoherence-free subspaces and noiseless subsystems Daniel Lidar; 4. Introduction to quantum dynamical decoupling Lorenza Viola; 5. Introduction to quantum fault tolerance Panos Aliferis; Part II. Generalized Approaches to Quantum Error Correction: 6. Operator quantum error correction David Kribs and David Poulin; 7. Entanglement-assisted quantum error-correcting codes Todd Brun and Min-Hsiu Hsieh; 8. Continuous-time quantum error correction Ognyan Oreshkov; Part III. Advanced Quantum Codes: 9. Quantum convolutional codes Mark Wilde; 10. Non-additive quantum codes Markus Grassl and Martin Rötteler; 11. Iterative quantum coding systems David Poulin; 12. Algebraic quantum coding theory Andreas Klappenecker; 13. Optimization-based quantum error correction Andrew Fletcher; Part IV. Advanced Dynamical Decoupling: 14. High order dynamical decoupling Zhen-Yu Wang and Ren-Bao Liu; 15. Combinatorial approaches to dynamical decoupling Martin Rötteler and Pawel Wocjan; Part V. Alternative Quantum Computation Approaches: 16. Holonomic quantum computation Paolo Zanardi; 17. Fault tolerance for holonomic quantum computation Ognyan Oreshkov, Todd Brun and Daniel Lidar; 18. Fault tolerant measurement-based quantum computing Debbie Leung; Part VI. Topological Methods: 19. Topological codes Héctor Bombín; 20. Fault tolerant topological cluster state quantum computing Austin Fowler and Kovid Goyal; Part VII. Applications and Implementations: 21. Experimental quantum error correction Dave Bacon; 22. Experimental dynamical decoupling Lorenza Viola; 23. Architectures Jacob Taylor; 24. Error correction in quantum communication Mark Wilde; Part VIII. Critical Evaluation of Fault Tolerance: 25. Hamiltonian methods in QEC and fault tolerance Eduardo Novais, Eduardo Mucciolo and Harold Baranger; 26. Critique of fault-tolerant quantum information processing Robert Alicki; References; Index.

Simple proof of equivalence between adiabatic quantum computation and the circuit model.

PubMed

Mizel, Ari; Lidar, Daniel A; Mitchell, Morgan

2007-08-17

We prove the equivalence between adiabatic quantum computation and quantum computation in the circuit model. An explicit adiabatic computation procedure is given that generates a ground state from which the answer can be extracted. The amount of time needed is evaluated by computing the gap. We show that the procedure is computationally efficient.

Layered Architectures for Quantum Computers and Quantum Repeaters

NASA Astrophysics Data System (ADS)

Jones, Nathan C.

This chapter examines how to organize quantum computers and repeaters using a systematic framework known as layered architecture, where machine control is organized in layers associated with specialized tasks. The framework is flexible and could be used for analysis and comparison of quantum information systems. To demonstrate the design principles in practice, we develop architectures for quantum computers and quantum repeaters based on optically controlled quantum dots, showing how a myriad of technologies must operate synchronously to achieve fault-tolerance. Optical control makes information processing in this system very fast, scalable to large problem sizes, and extendable to quantum communication.

Radio-frequency measurement in semiconductor quantum computation

NASA Astrophysics Data System (ADS)

Han, TianYi; Chen, MingBo; Cao, Gang; Li, HaiOu; Xiao, Ming; Guo, GuoPing

2017-05-01

Semiconductor quantum dots have attracted wide interest for the potential realization of quantum computation. To realize efficient quantum computation, fast manipulation and the corresponding readout are necessary. In the past few decades, considerable progress of quantum manipulation has been achieved experimentally. To meet the requirements of high-speed readout, radio-frequency (RF) measurement has been developed in recent years, such as RF-QPC (radio-frequency quantum point contact) and RF-DGS (radio-frequency dispersive gate sensor). Here we specifically demonstrate the principle of the radio-frequency reflectometry, then review the development and applications of RF measurement, which provides a feasible way to achieve high-bandwidth readout in quantum coherent control and also enriches the methods to study these artificial mesoscopic quantum systems. Finally, we prospect the future usage of radio-frequency reflectometry in scaling-up of the quantum computing models.

Magnetic resonance force microscopy quantum computer with tellurium donors in silicon.

PubMed

Berman, G P; Doolen, G D; Hammel, P C; Tsifrinovich, V I

2001-03-26

We propose a magnetic resonance force microscopy (MRFM)-based nuclear spin quantum computer using tellurium impurities in silicon. This approach to quantum computing combines well-developed silicon technology and expected advances in MRFM. Our proposal does not use electrostatic gates to realize quantum logic operations.

FT-IR and Raman spectra, DFT and SQMFF calculations for geometrical interpretation and vibrational analysis of 3-nitro-p-toluic acid

NASA Astrophysics Data System (ADS)

Nataraj, A.; Balachandran, V.; Karthick, T.

2012-08-01

The Fourier transform infrared (FT-IR) and FT-Raman of 3-nitro-p-toluic acid (NTA) have been recorded and analyzed. The equilibrium geometry, bonding features and harmonic vibrational frequencies have been investigated with the help of ab initio and density functional theory (DFT) methods. The assignments of the vibrational spectra have been carried out with the help of normal coordinate analysis (NCA) following the scaled quantum mechanical force field methodology (SQMFF). The optimized geometric bond lengths and bond angles obtained by computation show good agreement with experimental data of the relative compound. The computed dimer parameters also show good agreement with experimental data. The first hyperpolarizability (β0) of this noval molecular system and related properties (β, α0, and Δα) of NTA are calculated using B3LYP/6-311++G(d,p) method on the finite-field approach. Stability of the molecule arising from hyperconjugative interactions, charge delocalization have been analyzed using natural bond orbital (NBO) analysis. The results show that charge in electron density (ED) in the σ* and π* antibonding orbital and second order delocalization energies E(2) confirms the occurrence of intramolecular charge transfer (ICT) within the molecule. The calculated HOMO and LUMO energies also show that charge transfer occurs within the molecule. Finally the calculations results were applied to simulated infrared and Raman spectra of the title compound which show good agreement with observed spectra.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Andrianov, S N; Moiseev, S A

We propose a scheme of a quantum computer based on nanophotonic elements: two buses in the form of nanowaveguide resonators, two nanosized units of multiatom multiqubit quantum memory and a set of nanoprocessors in the form of photonic quantum transistors, each containing a pair of nanowaveguide ring resonators coupled via a quantum dot. The operation modes of nanoprocessor photonic quantum transistors are theoretically studied and the execution of main logical operations by means of them is demonstrated. We also discuss the prospects of the proposed nanophotonic quantum computer for operating in high-speed optical fibre networks. (quantum computations)

Beyond Moore's law: towards competitive quantum devices

NASA Astrophysics Data System (ADS)

Troyer, Matthias

2015-05-01

A century after the invention of quantum theory and fifty years after Bell's inequality we see the first quantum devices emerge as products that aim to be competitive with the best classical computing devices. While a universal quantum computer of non-trivial size is still out of reach there exist a number commercial and experimental devices: quantum random number generators, quantum simulators and quantum annealers. In this colloquium I will present some of these devices and validation tests we performed on them. Quantum random number generators use the inherent randomness in quantum measurements to produce true random numbers, unlike classical pseudorandom number generators which are inherently deterministic. Optical lattice emulators use ultracold atomic gases in optical lattices to mimic typical models of condensed matter physics. In my talk I will focus especially on the devices built by Canadian company D-Wave systems, which are special purpose quantum simulators for solving hard classical optimization problems. I will review the controversy around the quantum nature of these devices and will compare them to state of the art classical algorithms. I will end with an outlook towards universal quantum computing and end with the question: which important problems that are intractable even for post-exa-scale classical computers could we expect to solve once we have a universal quantum computer?

Vibrational frequency analysis, FT-IR, DFT and M06-2X studies on tert-Butyl N-(thiophen-2yl)carbamate.

PubMed

Sert, Yusuf; Singer, L M; Findlater, M; Doğan, Hatice; Çırak, Ç

2014-07-15

In this study, the experimental and theoretical vibrational frequencies of a newly synthesized tert-Butyl N-(thiophen-2yl)carbamate have been investigated. The experimental FT-IR (4000-400 cm(-1)) spectrum of the molecule in the solid phase have been recorded. The theoretical vibrational frequencies and optimized geometric parameters (bond lengths and bond angles) have been calculated by using density functional theory (DFT/B3LYP: Becke, 3-parameter, Lee-Yang-Parr) and DFT/M06-2X (the highly parametrized, empirical exchange correlation function) quantum chemical methods with the 6-311++G(d,p) basis set by Gaussian 09W software, for the first time. The vibrational frequencies have been assigned using potential energy distribution (PED) analysis by using VEDA 4 software. The computational optimized geometric parameters and vibrational frequencies have been found to be in good agreement with the corresponding experimental data, and with related literature results. In addition, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energies and the other related molecular energy values have been calculated and are depicted. Copyright © 2014 Elsevier B.V. All rights reserved.

Quantum simulation of quantum field theory using continuous variables

DOE PAGES

Marshall, Kevin; Pooser, Raphael C.; Siopsis, George; ...

2015-12-14

Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonicmore » quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.« less

Quantum simulation of quantum field theory using continuous variables

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marshall, Kevin; Pooser, Raphael C.; Siopsis, George

Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonicmore » quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.« less

Gate sequence for continuous variable one-way quantum computation

PubMed Central

Su, Xiaolong; Hao, Shuhong; Deng, Xiaowei; Ma, Lingyu; Wang, Meihong; Jia, Xiaojun; Xie, Changde; Peng, Kunchi

2013-01-01

Measurement-based one-way quantum computation using cluster states as resources provides an efficient model to perform computation and information processing of quantum codes. Arbitrary Gaussian quantum computation can be implemented sufficiently by long single-mode and two-mode gate sequences. However, continuous variable gate sequences have not been realized so far due to an absence of cluster states larger than four submodes. Here we present the first continuous variable gate sequence consisting of a single-mode squeezing gate and a two-mode controlled-phase gate based on a six-mode cluster state. The quantum property of this gate sequence is confirmed by the fidelities and the quantum entanglement of two output modes, which depend on both the squeezing and controlled-phase gates. The experiment demonstrates the feasibility of implementing Gaussian quantum computation by means of accessible gate sequences.

Quantum Computer Games: Quantum Minesweeper

ERIC Educational Resources Information Center

Gordon, Michal; Gordon, Goren

2010-01-01

The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…

Distribution of Bell-inequality violation versus multiparty-quantum-correlation measures

NASA Astrophysics Data System (ADS)

Sharma, Kunal; Das, Tamoghna; Sen (de), Aditi; Sen, Ujjwal

Violation of a Bell inequality guarantees the existence of quantum correlations in a shared quantum state. A pure bipartite quantum state, having nonvanishing quantum correlation, always violates a Bell inequality. Such correspondence is absent for multipartite pure quantum states in the case of multipartite correlation function Bell inequalities with two settings at each site. We establish a connection between the monogamy of Bell-inequality violation and multiparty quantum correlations for shared multisite quantum states. We believe that the relation is generic, as it is true for a number of different multisite measures that are defined from radically different perspectives. Precisely, we quantify the multisite-quantum-correlation content in the states by generalized geometric measure, a genuine multisite entanglement measure, as well as three monogamybased multiparty-quantum-correlation measures, viz., 3-tangle, quantum-discord score, and quantum-work-deficit score. We find that generalized Greenberger-Horne-Zeilinger states and another single-parameter family of states, which we refer to as the special Greenberger-Horne-Zeilinger states, have the status of extremal states in such relations.

Distribution of Bell-inequality violation versus multiparty-quantum-correlation measures

NASA Astrophysics Data System (ADS)

Sharma, Kunal; Das, Tamoghna; SenDe, Aditi; Sen, Ujjwal

2016-06-01

Violation of a Bell inequality guarantees the existence of quantum correlations in a shared quantum state. A pure bipartite quantum state, having nonvanishing quantum correlation, always violates a Bell inequality. Such correspondence is absent for multipartite pure quantum states in the case of multipartite correlation function Bell inequalities with two settings at each site. We establish a connection between the monogamy of Bell-inequality violation and multiparty quantum correlations for shared multisite quantum states. We believe that the relation is generic, as it is true for a number of different multisite measures that are defined from radically different perspectives. Precisely, we quantify the multisite-quantum-correlation content in the states by generalized geometric measure, a genuine multisite entanglement measure, as well as three monogamy-based multiparty-quantum-correlation measures, viz., 3-tangle, quantum-discord score, and quantum-work-deficit score. We find that generalized Greenberger-Horne-Zeilinger states and another single-parameter family of states, which we refer to as the special Greenberger-Horne-Zeilinger states, have the status of extremal states in such relations.

GeoBuilder: a geometric algorithm visualization and debugging system for 2D and 3D geometric computing.

PubMed

Wei, Jyh-Da; Tsai, Ming-Hung; Lee, Gen-Cher; Huang, Jeng-Hung; Lee, Der-Tsai

2009-01-01

Algorithm visualization is a unique research topic that integrates engineering skills such as computer graphics, system programming, database management, computer networks, etc., to facilitate algorithmic researchers in testing their ideas, demonstrating new findings, and teaching algorithm design in the classroom. Within the broad applications of algorithm visualization, there still remain performance issues that deserve further research, e.g., system portability, collaboration capability, and animation effect in 3D environments. Using modern technologies of Java programming, we develop an algorithm visualization and debugging system, dubbed GeoBuilder, for geometric computing. The GeoBuilder system features Java's promising portability, engagement of collaboration in algorithm development, and automatic camera positioning for tracking 3D geometric objects. In this paper, we describe the design of the GeoBuilder system and demonstrate its applications.

Toward a superconducting quantum computer. Harnessing macroscopic quantum coherence.

PubMed

Tsai, Jaw-Shen

2010-01-01

Intensive research on the construction of superconducting quantum computers has produced numerous important achievements. The quantum bit (qubit), based on the Josephson junction, is at the heart of this research. This macroscopic system has the ability to control quantum coherence. This article reviews the current state of quantum computing as well as its history, and discusses its future. Although progress has been rapid, the field remains beset with unsolved issues, and there are still many new research opportunities open to physicists and engineers.

Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedom

NASA Astrophysics Data System (ADS)

Plenio, M. B.; Hartley, J.; Eisert, J.

2004-03-01

We study the entanglement dynamics of a system consisting of a large number of coupled harmonic oscillators in various configurations and for different types of nearest-neighbour interactions. For a one-dimensional chain, we provide compact analytical solutions and approximations to the dynamical evolution of the entanglement between spatially separated oscillators. Key properties such as the speed of entanglement propagation, the maximum amount of transferred entanglement and the efficiency for the entanglement transfer are computed. For harmonic oscillators coupled by springs, corresponding to a phonon model, we observe a non-monotonic transfer efficiency in the initially prepared amount of entanglement, i.e. an intermediate amount of initial entanglement is transferred with the highest efficiency. In contrast, within the framework of the rotating-wave approximation (as appropriate, e.g. in quantum optical settings) one finds a monotonic behaviour. We also study geometrical configurations that are analogous to quantum optical devices (such as beamsplitters and interferometers) and observe characteristic differences when initially thermal or squeezed states are entering these devices. We show that these devices may be switched on and off by changing the properties of an individual oscillator. They may therefore be used as building blocks of large fixed and pre-fabricated but programmable structures in which quantum information is manipulated through propagation. We discuss briefly possible experimental realizations of systems of interacting harmonic oscillators in which these effects may be confirmed experimentally.

Quantum Control of Spins in Diamond for Nanoscale Magnetic Sensing and Imaging

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dutt, Gurudev

Our research activities during the grant period focused on the challenges of highly accurate and precise magnetometry and magnetic imaging using quantum spins inside diamond. Our work has resulted in 6 papers published in peer-reviewed journals, with two more currently under consideration by referees. We showed that through the use of novel phase estimation algorithms inspired by quantum information science we can carry out accurate and high dynamic range DC magnetometry as well as lock-in detection of oscillating (AC) magnetic fields. We investigated the geometric phase as a route to higher precision quantum information and magnetic sensing applications, and probedmore » the experimental limits to the fidelity of such geometric phase gates. We also demonstrated that there is a spin dependent signal in the charge state flipping of the NV defect center in diamond, which could potentialy be useful for higher fidelity spin readout at room temperature. Some of these projects have now led to further investigation in our lab on multi-photon spectroscopy (manuscript in preparation), and plasmonic guiding of light in metal nanowires (manuscript available on arxiv). In addition, several invited talks were given by the PI, and conference presentations were given by the graduate students and postdocs.« less

Novel symmetries in an interacting 𝒩 = 2 supersymmetric quantum mechanical model

NASA Astrophysics Data System (ADS)

Krishna, S.; Shukla, D.; Malik, R. P.

2016-07-01

In this paper, we demonstrate the existence of a set of novel discrete symmetry transformations in the case of an interacting 𝒩 = 2 supersymmetric quantum mechanical model of a system of an electron moving on a sphere in the background of a magnetic monopole and establish its interpretation in the language of differential geometry. These discrete symmetries are, over and above, the usual three continuous symmetries of the theory which together provide the physical realizations of the de Rham cohomological operators of differential geometry. We derive the nilpotent 𝒩 = 2 SUSY transformations by exploiting our idea of supervariable approach and provide geometrical meaning to these transformations in the language of Grassmannian translational generators on a (1, 2)-dimensional supermanifold on which our 𝒩 = 2 SUSY quantum mechanical model is generalized. We express the conserved supercharges and the invariance of the Lagrangian in terms of the supervariables (obtained after the imposition of the SUSY invariant restrictions) and provide the geometrical meaning to (i) the nilpotency property of the 𝒩 = 2 supercharges, and (ii) the SUSY invariance of the Lagrangian of our 𝒩 = 2 SUSY theory.

Novel Image Encryption based on Quantum Walks

PubMed Central

Yang, Yu-Guang; Pan, Qing-Xiang; Sun, Si-Jia; Xu, Peng

2015-01-01

Quantum computation has achieved a tremendous success during the last decades. In this paper, we investigate the potential application of a famous quantum computation model, i.e., quantum walks (QW) in image encryption. It is found that QW can serve as an excellent key generator thanks to its inherent nonlinear chaotic dynamic behavior. Furthermore, we construct a novel QW-based image encryption algorithm. Simulations and performance comparisons show that the proposal is secure enough for image encryption and outperforms prior works. It also opens the door towards introducing quantum computation into image encryption and promotes the convergence between quantum computation and image processing. PMID:25586889

Characterizing quantum supremacy in near-term devices

NASA Astrophysics Data System (ADS)

Boixo, Sergio; Isakov, Sergei V.; Smelyanskiy, Vadim N.; Babbush, Ryan; Ding, Nan; Jiang, Zhang; Bremner, Michael J.; Martinis, John M.; Neven, Hartmut

2018-06-01

A critical question for quantum computing in the near future is whether quantum devices without error correction can perform a well-defined computational task beyond the capabilities of supercomputers. Such a demonstration of what is referred to as quantum supremacy requires a reliable evaluation of the resources required to solve tasks with classical approaches. Here, we propose the task of sampling from the output distribution of random quantum circuits as a demonstration of quantum supremacy. We extend previous results in computational complexity to argue that this sampling task must take exponential time in a classical computer. We introduce cross-entropy benchmarking to obtain the experimental fidelity of complex multiqubit dynamics. This can be estimated and extrapolated to give a success metric for a quantum supremacy demonstration. We study the computational cost of relevant classical algorithms and conclude that quantum supremacy can be achieved with circuits in a two-dimensional lattice of 7 × 7 qubits and around 40 clock cycles. This requires an error rate of around 0.5% for two-qubit gates (0.05% for one-qubit gates), and it would demonstrate the basic building blocks for a fault-tolerant quantum computer.

STIC: Photonic Quantum Computation through Cavity Assisted Interaction

DTIC Science & Technology

2007-12-28

PRA ; available as quant-ph/06060791. Report for the grant “Photonic Quantum Computation through Cavity Assisted Interaction” from DTO Luming Duan...cavity •B. Wang, L.-M. Duan, PRA 72 (in press, 2005) Single-photon source Photonic Quantum Computation through Cavity-Assisted Interaction H. Jeff Kimble...interaction [Duan, Wang, Kimble, PRA 05] • “Investigate more efficient methods for combating noise in photonic quantum computation ” • Partial progress

Robust Quantum Computing using Molecules with Switchable Dipole

DTIC Science & Technology

2010-06-15

REPORT Robust quantum computing using molecules with switchable dipole 14. ABSTRACT 16. SECURITY CLASSIFICATION OF: Of the many systems studied to...Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 15. SUBJECT TERMS Ultracold polar molecules, quantum computing , phase gates...From - To) 30-Aug-2006 Standard Form 298 (Rev 8/98) Prescribed by ANSI Std. Z39.18 - 31-Aug-2009 Robust quantum computing using molecules with

Effects of hydrostatic pressure on the donor impurity in a cylindrical quantum dot with Morse confining potential

NASA Astrophysics Data System (ADS)

Hayrapetyan, David B.; Kotanjyan, Tigran V.; Tevosyan, Hovhannes Kh.; Kazaryan, Eduard M.

2016-12-01

The effects of hydrostatic pressure and size quantization on the binding energies of a hydrogen-like donor impurity in cylindrical GaAs quantum dot (QD) with Morse confining potential are studied using the variational method and effective-mass approximation. In the cylindrical QD, the effect of hydrostatic pressure on the binding energy of electron has been investigated and it has been found that the application of the hydrostatic pressure leads to the blue shift. The dependence of the absorption edge on geometrical parameters of cylindrical QD is obtained. Selection rules are revealed for transitions between levels with different quantum numbers. It is shown that for the radial quantum number, transitions are allowed between the levels with the same quantum numbers, and any transitions between different levels are allowed for the principal quantum number.

Second-Order Asymptotics for the Classical Capacity of Image-Additive Quantum Channels

NASA Astrophysics Data System (ADS)

Tomamichel, Marco; Tan, Vincent Y. F.

2015-08-01

We study non-asymptotic fundamental limits for transmitting classical information over memoryless quantum channels, i.e. we investigate the amount of classical information that can be transmitted when a quantum channel is used a finite number of times and a fixed, non-vanishing average error is permissible. In this work we consider the classical capacity of quantum channels that are image-additive, including all classical to quantum channels, as well as the product state capacity of arbitrary quantum channels. In both cases we show that the non-asymptotic fundamental limit admits a second-order approximation that illustrates the speed at which the rate of optimal codes converges to the Holevo capacity as the blocklength tends to infinity. The behavior is governed by a new channel parameter, called channel dispersion, for which we provide a geometrical interpretation.

Bath-induced correlations in an infinite-dimensional Hilbert space

NASA Astrophysics Data System (ADS)

Nizama, Marco; Cáceres, Manuel O.

2017-09-01

Quantum correlations between two free spinless dissipative distinguishable particles (interacting with a thermal bath) are studied analytically using the quantum master equation and tools of quantum information. Bath-induced coherence and correlations in an infinite-dimensional Hilbert space are shown. We show that for temperature T> 0 the time-evolution of the reduced density matrix cannot be written as the direct product of two independent particles. We have found a time-scale that characterizes the time when the bath-induced coherence is maximum before being wiped out by dissipation (purity, relative entropy, spatial dispersion, and mirror correlations are studied). The Wigner function associated to the Wannier lattice (where the dissipative quantum walks move) is studied as an indirect measure of the induced correlations among particles. We have supported the quantum character of the correlations by analyzing the geometric quantum discord.

Trapped-Ion Quantum Logic with Global Radiation Fields.

PubMed

Weidt, S; Randall, J; Webster, S C; Lake, K; Webb, A E; Cohen, I; Navickas, T; Lekitsch, B; Retzker, A; Hensinger, W K

2016-11-25

Trapped ions are a promising tool for building a large-scale quantum computer. However, the number of required radiation fields for the realization of quantum gates in any proposed ion-based architecture scales with the number of ions within the quantum computer, posing a major obstacle when imagining a device with millions of ions. Here, we present a fundamentally different approach for trapped-ion quantum computing where this detrimental scaling vanishes. The method is based on individually controlled voltages applied to each logic gate location to facilitate the actual gate operation analogous to a traditional transistor architecture within a classical computer processor. To demonstrate the key principle of this approach we implement a versatile quantum gate method based on long-wavelength radiation and use this method to generate a maximally entangled state of two quantum engineered clock qubits with fidelity 0.985(12). This quantum gate also constitutes a simple-to-implement tool for quantum metrology, sensing, and simulation.

Quantum Computing and Second Quantization

DOE PAGES

Makaruk, Hanna Ewa

2017-02-10

Quantum computers are by their nature many particle quantum systems. Both the many-particle arrangement and being quantum are necessary for the existence of the entangled states, which are responsible for the parallelism of the quantum computers. Second quantization is a very important approximate method of describing such systems. This lecture will present the general idea of the second quantization, and discuss shortly some of the most important formulations of second quantization.

Quantum Computing and Second Quantization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Makaruk, Hanna Ewa

Quantum computers are by their nature many particle quantum systems. Both the many-particle arrangement and being quantum are necessary for the existence of the entangled states, which are responsible for the parallelism of the quantum computers. Second quantization is a very important approximate method of describing such systems. This lecture will present the general idea of the second quantization, and discuss shortly some of the most important formulations of second quantization.

Numerical characteristics of quantum computer simulation

NASA Astrophysics Data System (ADS)

Chernyavskiy, A.; Khamitov, K.; Teplov, A.; Voevodin, V.; Voevodin, Vl.

2016-12-01

The simulation of quantum circuits is significantly important for the implementation of quantum information technologies. The main difficulty of such modeling is the exponential growth of dimensionality, thus the usage of modern high-performance parallel computations is relevant. As it is well known, arbitrary quantum computation in circuit model can be done by only single- and two-qubit gates, and we analyze the computational structure and properties of the simulation of such gates. We investigate the fact that the unique properties of quantum nature lead to the computational properties of the considered algorithms: the quantum parallelism make the simulation of quantum gates highly parallel, and on the other hand, quantum entanglement leads to the problem of computational locality during simulation. We use the methodology of the AlgoWiki project (algowiki-project.org) to analyze the algorithm. This methodology consists of theoretical (sequential and parallel complexity, macro structure, and visual informational graph) and experimental (locality and memory access, scalability and more specific dynamic characteristics) parts. Experimental part was made by using the petascale Lomonosov supercomputer (Moscow State University, Russia). We show that the simulation of quantum gates is a good base for the research and testing of the development methods for data intense parallel software, and considered methodology of the analysis can be successfully used for the improvement of the algorithms in quantum information science.

Experimental Blind Quantum Computing for a Classical Client.

PubMed

Huang, He-Liang; Zhao, Qi; Ma, Xiongfeng; Liu, Chang; Su, Zu-En; Wang, Xi-Lin; Li, Li; Liu, Nai-Le; Sanders, Barry C; Lu, Chao-Yang; Pan, Jian-Wei

2017-08-04

To date, blind quantum computing demonstrations require clients to have weak quantum devices. Here we implement a proof-of-principle experiment for completely classical clients. Via classically interacting with two quantum servers that share entanglement, the client accomplishes the task of having the number 15 factorized by servers who are denied information about the computation itself. This concealment is accompanied by a verification protocol that tests servers' honesty and correctness. Our demonstration shows the feasibility of completely classical clients and thus is a key milestone towards secure cloud quantum computing.

Experimental Blind Quantum Computing for a Classical Client

NASA Astrophysics Data System (ADS)

Huang, He-Liang; Zhao, Qi; Ma, Xiongfeng; Liu, Chang; Su, Zu-En; Wang, Xi-Lin; Li, Li; Liu, Nai-Le; Sanders, Barry C.; Lu, Chao-Yang; Pan, Jian-Wei

2017-08-01

To date, blind quantum computing demonstrations require clients to have weak quantum devices. Here we implement a proof-of-principle experiment for completely classical clients. Via classically interacting with two quantum servers that share entanglement, the client accomplishes the task of having the number 15 factorized by servers who are denied information about the computation itself. This concealment is accompanied by a verification protocol that tests servers' honesty and correctness. Our demonstration shows the feasibility of completely classical clients and thus is a key milestone towards secure cloud quantum computing.

Mathematical Theory of Generalized Duality Quantum Computers Acting on Vector-States

NASA Astrophysics Data System (ADS)

Cao, Huai-Xin; Long, Gui-Lu; Guo, Zhi-Hua; Chen, Zheng-Li

2013-06-01

Following the idea of duality quantum computation, a generalized duality quantum computer (GDQC) acting on vector-states is defined as a tuple consisting of a generalized quantum wave divider (GQWD) and a finite number of unitary operators as well as a generalized quantum wave combiner (GQWC). It is proved that the GQWD and GQWC of a GDQC are an isometry and a co-isometry, respectively, and mutually dual. It is also proved that every GDQC gives a contraction, called a generalized duality quantum gate (GDQG). A classification of GDQCs is given and the properties of GDQGs are discussed. Some applications are obtained, including two orthogonal duality quantum computer algorithms for unsorted database search and an understanding of the Mach-Zehnder interferometer.

Semiquantum key distribution with secure delegated quantum computation

PubMed Central

Li, Qin; Chan, Wai Hong; Zhang, Shengyu

2016-01-01

Semiquantum key distribution allows a quantum party to share a random key with a “classical” party who only can prepare and measure qubits in the computational basis or reorder some qubits when he has access to a quantum channel. In this work, we present a protocol where a secret key can be established between a quantum user and an almost classical user who only needs the quantum ability to access quantum channels, by securely delegating quantum computation to a quantum server. We show the proposed protocol is robust even when the delegated quantum server is a powerful adversary, and is experimentally feasible with current technology. As one party of our protocol is the most quantum-resource efficient, it can be more practical and significantly widen the applicability scope of quantum key distribution. PMID:26813384

Parallel Photonic Quantum Computation Assisted by Quantum Dots in One-Side Optical Microcavities

PubMed Central

Luo, Ming-Xing; Wang, Xiaojun

2014-01-01

Universal quantum logic gates are important elements for a quantum computer. In contrast to previous constructions on one degree of freedom (DOF) of quantum systems, we investigate the possibility of parallel quantum computations dependent on two DOFs of photon systems. We construct deterministic hyper-controlled-not (hyper-CNOT) gates operating on the spatial-mode and the polarization DOFs of two-photon or one-photon systems by exploring the giant optical circular birefringence induced by quantum-dot spins in one-sided optical microcavities. These hyper-CNOT gates show that the quantum states of two DOFs can be viewed as independent qubits without requiring auxiliary DOFs in theory. This result can reduce the quantum resources by half for quantum applications with large qubit systems, such as the quantum Shor algorithm. PMID:25030424

Parallel photonic quantum computation assisted by quantum dots in one-side optical microcavities.

PubMed

Luo, Ming-Xing; Wang, Xiaojun

2014-07-17

Universal quantum logic gates are important elements for a quantum computer. In contrast to previous constructions on one degree of freedom (DOF) of quantum systems, we investigate the possibility of parallel quantum computations dependent on two DOFs of photon systems. We construct deterministic hyper-controlled-not (hyper-CNOT) gates operating on the spatial-mode and the polarization DOFs of two-photon or one-photon systems by exploring the giant optical circular birefringence induced by quantum-dot spins in one-sided optical microcavities. These hyper-CNOT gates show that the quantum states of two DOFs can be viewed as independent qubits without requiring auxiliary DOFs in theory. This result can reduce the quantum resources by half for quantum applications with large qubit systems, such as the quantum Shor algorithm.

Open quantum systems and error correction

NASA Astrophysics Data System (ADS)

Shabani Barzegar, Alireza

Quantum effects can be harnessed to manipulate information in a desired way. Quantum systems which are designed for this purpose are suffering from harming interaction with their surrounding environment or inaccuracy in control forces. Engineering different methods to combat errors in quantum devices are highly demanding. In this thesis, I focus on realistic formulations of quantum error correction methods. A realistic formulation is the one that incorporates experimental challenges. This thesis is presented in two sections of open quantum system and quantum error correction. Chapters 2 and 3 cover the material on open quantum system theory. It is essential to first study a noise process then to contemplate methods to cancel its effect. In the second chapter, I present the non-completely positive formulation of quantum maps. Most of these results are published in [Shabani and Lidar, 2009b,a], except a subsection on geometric characterization of positivity domain of a quantum map. The real-time formulation of the dynamics is the topic of the third chapter. After introducing the concept of Markovian regime, A new post-Markovian quantum master equation is derived, published in [Shabani and Lidar, 2005a]. The section of quantum error correction is presented in three chapters of 4, 5, 6 and 7. In chapter 4, we introduce a generalized theory of decoherence-free subspaces and subsystems (DFSs), which do not require accurate initialization (published in [Shabani and Lidar, 2005b]). In Chapter 5, we present a semidefinite program optimization approach to quantum error correction that yields codes and recovery procedures that are robust against significant variations in the noise channel. Our approach allows us to optimize the encoding, recovery, or both, and is amenable to approximations that significantly improve computational cost while retaining fidelity (see [Kosut et al., 2008] for a published version). Chapter 6 is devoted to a theory of quantum error correction (QEC) that applies to any linear map, in particular maps that are not completely positive (CP). This is a complementary to the second chapter which is published in [Shabani and Lidar, 2007]. In the last chapter 7 before the conclusion, a formulation for evaluating the performance of quantum error correcting codes for a general error model is presented, also published in [Shabani, 2005]. In this formulation, the correlation between errors is quantified by a Hamiltonian description of the noise process. In particular, we consider Calderbank-Shor-Steane codes and observe a better performance in the presence of correlated errors depending on the timing of the error recovery.

Geometric phase in entangled systems: A single-neutron interferometer experiment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sponar, S.; Klepp, J.; Loidl, R.

2010-04-15

The influence of the geometric phase on a Bell measurement, as proposed by Bertlmann et al. [Phys. Rev. A 69, 032112 (2004)] and expressed by the Clauser-Horne-Shimony-Holt (CHSH) inequality, has been observed for a spin-path-entangled neutron state in an interferometric setup. It is experimentally demonstrated that the effect of geometric phase can be balanced by a change in Bell angles. The geometric phase is acquired during a time-dependent interaction with a radiofrequency field. Two schemes, polar and azimuthal adjustment of the Bell angles, are realized and analyzed in detail. The former scheme yields a sinusoidal oscillation of the correlation functionmore » S, dependent on the geometric phase, such that it varies in the range between 2 and 2{radical}(2) and therefore always exceeds the boundary value 2 between quantum mechanic and noncontextual theories. The latter scheme results in a constant, maximal violation of the Bell-like CHSH inequality, where S remains 2{radical}(2) for all settings of the geometric phase.« less

Analytic Expression of Geometric Discord in Arbitrary Mixture of any Two Bi-qubit Product Pure States

NASA Astrophysics Data System (ADS)

Xie, Chuan-Mei; Liu, Yi-Min; Xing, Hang; Zhang, Zhan-Jun

2015-04-01

Quantum correlations in a family of states comprising any mixture of a pair of arbitrary bi-qubit product pure states are studied by employing geometric discord [Phys. Rev. Lett. 105 (2010) 190502] as the quantifier. First, the inherent symmetry in the family of states about local unitary transformations is revealed. Then, the analytic expression of geometric discords in the states is worked out. Some concrete discussions and analyses on the captured geometric discords are made so that their distinct features are exposed. It is found that, the more averagely the two bi-qubit product states are mixed, the bigger geometric discord the mixed state owns. Moreover, the monotonic relationships of geometric discord with different parameters are revealed. Supported by the National Natural Science Foundation of China (NNSFC) under Grant Nos. 11375011 and 11372122, the Natural Science Foundation of Anhui Province under Grant No. 1408085MA12, and the 211 Project of Anhui University

Acausal measurement-based quantum computing

NASA Astrophysics Data System (ADS)

Morimae, Tomoyuki

2014-07-01

In measurement-based quantum computing, there is a natural "causal cone" among qubits of the resource state, since the measurement angle on a qubit has to depend on previous measurement results in order to correct the effect of by-product operators. If we respect the no-signaling principle, by-product operators cannot be avoided. Here we study the possibility of acausal measurement-based quantum computing by using the process matrix framework [Oreshkov, Costa, and Brukner, Nat. Commun. 3, 1092 (2012), 10.1038/ncomms2076]. We construct a resource process matrix for acausal measurement-based quantum computing restricting local operations to projective measurements. The resource process matrix is an analog of the resource state of the standard causal measurement-based quantum computing. We find that if we restrict local operations to projective measurements the resource process matrix is (up to a normalization factor and trivial ancilla qubits) equivalent to the decorated graph state created from the graph state of the corresponding causal measurement-based quantum computing. We also show that it is possible to consider a causal game whose causal inequality is violated by acausal measurement-based quantum computing.

Performing quantum computing experiments in the cloud

NASA Astrophysics Data System (ADS)

Devitt, Simon J.

2016-09-01

Quantum computing technology has reached a second renaissance in the past five years. Increased interest from both the private and public sector combined with extraordinary theoretical and experimental progress has solidified this technology as a major advancement in the 21st century. As anticipated my many, some of the first realizations of quantum computing technology has occured over the cloud, with users logging onto dedicated hardware over the classical internet. Recently, IBM has released the Quantum Experience, which allows users to access a five-qubit quantum processor. In this paper we take advantage of this online availability of actual quantum hardware and present four quantum information experiments. We utilize the IBM chip to realize protocols in quantum error correction, quantum arithmetic, quantum graph theory, and fault-tolerant quantum computation by accessing the device remotely through the cloud. While the results are subject to significant noise, the correct results are returned from the chip. This demonstrates the power of experimental groups opening up their technology to a wider audience and will hopefully allow for the next stage of development in quantum information technology.

Geometrization of quantum physics

NASA Astrophysics Data System (ADS)

Ol'Khov, O. A.

2009-12-01

It is shown that the Dirac equation for free particle can be considered as a description of specific distortion of the space euclidean geometry (space topological defect). This approach is based on possibility of interpretation of the wave function as vector realizing representation of the fundamental group of the closed topological space-time 4-manifold. Mass and spin appear to be topological invariants. Such concept explains all so called “strange” properties of quantum formalism: probabilities, wave-particle duality, nonlocal instantaneous correlation between noninteracting particles (EPR-paradox) and so on. Acceptance of suggested geometrical concept means rejection of atomistic concept where all matter is considered as consisting of more and more small elementary particles. There is no any particles a priori, before measurement: the notions of particles appear as a result of classical interpretation of the contact of the region of the curved space with a device.

PREFACE: Preface

NASA Astrophysics Data System (ADS)

Hotta, Takashi

2016-02-01

This volume of Journal of Physics: Conference Series contains both invited and contributed papers presented at the International Symposium on "New Quantum Phases Emerging from Novel Crystal Structure", which was held from 24-25 September 2015 at the Minami-Osawa Campus of Tokyo Metropolitan University (TMU). The Graduate School of Science and Engineering of TMU is now promoting a research project on "New Quantum Phases Emerging from Novel Crystal Structure" with the support of the university. This is the cooperative project involving the electrical and electronic engineering and physics departments to discover new quantum phases in strongly correlated electron systems on novel crystal structures, with geometrically characteristic properties such as cage, layered, and geometrical frustrated structures. In this international symposium, we have mainly picked up BiS2-based layered superconductors, cage-structure materials such as 1-2-20 and filled skutterudites, geometrically frustrated systems such as pyrochlore compounds, and noncentrosymmetric materials. Topics on other materials with exotic crystal structure have been also discussed. I believe that this symposium provides a good opportunity to present recent research results on magnetism and superconductivity in such materials, and to discuss future directions of research on strongly correlated electron systems with novel crystal structure. I would like to give thanks, on behalf of the organizing committee, to all participants of the TMU International Symposium and all members of the Advisory Committee, who have contributed to the success of this symposium. I further thank the TMU Research Organization for the financial support of this symposium.

Greenberger-Horne-Zeilinger states-based blind quantum computation with entanglement concentration.

PubMed

Zhang, Xiaoqian; Weng, Jian; Lu, Wei; Li, Xiaochun; Luo, Weiqi; Tan, Xiaoqing

2017-09-11

In blind quantum computation (BQC) protocol, the quantum computability of servers are complicated and powerful, while the clients are not. It is still a challenge for clients to delegate quantum computation to servers and keep the clients' inputs, outputs and algorithms private. Unfortunately, quantum channel noise is unavoidable in the practical transmission. In this paper, a novel BQC protocol based on maximally entangled Greenberger-Horne-Zeilinger (GHZ) states is proposed which doesn't need a trusted center. The protocol includes a client and two servers, where the client only needs to own quantum channels with two servers who have full-advantage quantum computers. Two servers perform entanglement concentration used to remove the noise, where the success probability can almost reach 100% in theory. But they learn nothing in the process of concentration because of the no-signaling principle, so this BQC protocol is secure and feasible.

From transistor to trapped-ion computers for quantum chemistry.

PubMed

Yung, M-H; Casanova, J; Mezzacapo, A; McClean, J; Lamata, L; Aspuru-Guzik, A; Solano, E

2014-01-07

Over the last few decades, quantum chemistry has progressed through the development of computational methods based on modern digital computers. However, these methods can hardly fulfill the exponentially-growing resource requirements when applied to large quantum systems. As pointed out by Feynman, this restriction is intrinsic to all computational models based on classical physics. Recently, the rapid advancement of trapped-ion technologies has opened new possibilities for quantum control and quantum simulations. Here, we present an efficient toolkit that exploits both the internal and motional degrees of freedom of trapped ions for solving problems in quantum chemistry, including molecular electronic structure, molecular dynamics, and vibronic coupling. We focus on applications that go beyond the capacity of classical computers, but may be realizable on state-of-the-art trapped-ion systems. These results allow us to envision a new paradigm of quantum chemistry that shifts from the current transistor to a near-future trapped-ion-based technology.

From transistor to trapped-ion computers for quantum chemistry

PubMed Central

Yung, M.-H.; Casanova, J.; Mezzacapo, A.; McClean, J.; Lamata, L.; Aspuru-Guzik, A.; Solano, E.

2014-01-01

Over the last few decades, quantum chemistry has progressed through the development of computational methods based on modern digital computers. However, these methods can hardly fulfill the exponentially-growing resource requirements when applied to large quantum systems. As pointed out by Feynman, this restriction is intrinsic to all computational models based on classical physics. Recently, the rapid advancement of trapped-ion technologies has opened new possibilities for quantum control and quantum simulations. Here, we present an efficient toolkit that exploits both the internal and motional degrees of freedom of trapped ions for solving problems in quantum chemistry, including molecular electronic structure, molecular dynamics, and vibronic coupling. We focus on applications that go beyond the capacity of classical computers, but may be realizable on state-of-the-art trapped-ion systems. These results allow us to envision a new paradigm of quantum chemistry that shifts from the current transistor to a near-future trapped-ion-based technology. PMID:24395054

Analyzing Three-Player Quantum Games in an EPR Type Setup

PubMed Central

Chappell, James M.; Iqbal, Azhar; Abbott, Derek

2011-01-01

We use the formalism of Clifford Geometric Algebra (GA) to develop an analysis of quantum versions of three-player non-cooperative games. The quantum games we explore are played in an Einstein-Podolsky-Rosen (EPR) type setting. In this setting, the players' strategy sets remain identical to the ones in the mixed-strategy version of the classical game that is obtained as a proper subset of the corresponding quantum game. Using GA we investigate the outcome of a realization of the game by players sharing GHZ state, W state, and a mixture of GHZ and W states. As a specific example, we study the game of three-player Prisoners' Dilemma. PMID:21818260

On Fock-space representations of quantized enveloping algebras related to noncommutative differential geometry

NASA Astrophysics Data System (ADS)

Jurčo, B.; Schlieker, M.

1995-07-01

In this paper explicitly natural (from the geometrical point of view) Fock-space representations (contragradient Verma modules) of the quantized enveloping algebras are constructed. In order to do so, one starts from the Gauss decomposition of the quantum group and introduces the differential operators on the corresponding q-deformed flag manifold (assumed as a left comodule for the quantum group) by a projection to it of the right action of the quantized enveloping algebra on the quantum group. Finally, the representatives of the elements of the quantized enveloping algebra corresponding to the left-invariant vector fields on the quantum group are expressed as first-order differential operators on the q-deformed flag manifold.

Protecting Information

NASA Astrophysics Data System (ADS)

Loepp, Susan; Wootters, William K.

2006-09-01

For many everyday transmissions, it is essential to protect digital information from noise or eavesdropping. This undergraduate introduction to error correction and cryptography is unique in devoting several chapters to quantum cryptography and quantum computing, thus providing a context in which ideas from mathematics and physics meet. By covering such topics as Shor's quantum factoring algorithm, this text informs the reader about current thinking in quantum information theory and encourages an appreciation of the connections between mathematics and science.Of particular interest are the potential impacts of quantum physics:(i) a quantum computer, if built, could crack our currently used public-key cryptosystems; and (ii) quantum cryptography promises to provide an alternative to these cryptosystems, basing its security on the laws of nature rather than on computational complexity. No prior knowledge of quantum mechanics is assumed, but students should have a basic knowledge of complex numbers, vectors, and matrices. Accessible to readers familiar with matrix algebra, vector spaces and complex numbers First undergraduate text to cover cryptography, error-correction, and quantum computation together Features exercises designed to enhance understanding, including a number of computational problems, available from www.cambridge.org/9780521534765

Universal measurement-based quantum computation in two-dimensional symmetry-protected topological phases

NASA Astrophysics Data System (ADS)

Wei, Tzu-Chieh; Huang, Ching-Yu

2017-09-01

Recent progress in the characterization of gapped quantum phases has also triggered the search for a universal resource for quantum computation in symmetric gapped phases. Prior works in one dimension suggest that it is a feature more common than previously thought, in that nontrivial one-dimensional symmetry-protected topological (SPT) phases provide quantum computational power characterized by the algebraic structure defining these phases. Progress in two and higher dimensions so far has been limited to special fixed points. Here we provide two families of two-dimensional Z2 symmetric wave functions such that there exists a finite region of the parameter in the SPT phases that supports universal quantum computation. The quantum computational power appears to lose its universality at the boundary between the SPT and the symmetry-breaking phases.

Towards quantum chemistry on a quantum computer.

PubMed

Lanyon, B P; Whitfield, J D; Gillett, G G; Goggin, M E; Almeida, M P; Kassal, I; Biamonte, J D; Mohseni, M; Powell, B J; Barbieri, M; Aspuru-Guzik, A; White, A G

2010-02-01

Exact first-principles calculations of molecular properties are currently intractable because their computational cost grows exponentially with both the number of atoms and basis set size. A solution is to move to a radically different model of computing by building a quantum computer, which is a device that uses quantum systems themselves to store and process data. Here we report the application of the latest photonic quantum computer technology to calculate properties of the smallest molecular system: the hydrogen molecule in a minimal basis. We calculate the complete energy spectrum to 20 bits of precision and discuss how the technique can be expanded to solve large-scale chemical problems that lie beyond the reach of modern supercomputers. These results represent an early practical step toward a powerful tool with a broad range of quantum-chemical applications.

Surface Segregation Energies of BCC Binaries from Ab Initio and Quantum Approximate Calculations

NASA Technical Reports Server (NTRS)

Good, Brian S.

2003-01-01

We compare dilute-limit segregation energies for selected BCC transition metal binaries computed using ab initio and quantum approximate energy method. Ab initio calculations are carried out using the CASTEP plane-wave pseudopotential computer code, while quantum approximate results are computed using the Bozzolo-Ferrante-Smith (BFS) method with the most recent parameterization. Quantum approximate segregation energies are computed with and without atomistic relaxation. The ab initio calculations are performed without relaxation for the most part, but predicted relaxations from quantum approximate calculations are used in selected cases to compute approximate relaxed ab initio segregation energies. Results are discussed within the context of segregation models driven by strain and bond-breaking effects. We compare our results with other quantum approximate and ab initio theoretical work, and available experimental results.

Optical rectification using geometrical field enhancement in gold nano-arrays

NASA Astrophysics Data System (ADS)

Piltan, S.; Sievenpiper, D.

2017-11-01

Conversion of photons to electrical energy has a wide variety of applications including imaging, solar energy harvesting, and IR detection. A rectenna device consists of an antenna in addition to a rectifying element to absorb the incident radiation within a certain frequency range. We designed, fabricated, and measured an optical rectifier taking advantage of asymmetrical field enhancement for forward and reverse currents due to geometrical constraints. The gold nano-structures as well as the geometrical parameters offer enhanced light-matter interaction at 382 THz. Using the Taylor expansion of the time-dependent current as a function of the external bias and oscillating optical excitation, we obtained responsivities close to quantum limit of operation. This geometrical approach can offer an efficient, broadband, and scalable solution for energy conversion and detection in the future.

Universal Quantum Computing with Arbitrary Continuous-Variable Encoding.

PubMed

Lau, Hoi-Kwan; Plenio, Martin B

2016-09-02

Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal quantum computation with a fixed set of operations but arbitrary encoding. By storing a qubit in the parity of two or four qumodes, all computing processes can be implemented by basis state preparations, continuous-variable exponential-swap operations, and swap tests. Our formalism inherits the advantages that the quantum information is decoupled from collective noise, and logical qubits with different encodings can be brought to interact without decoding. We also propose a possible implementation of the required operations by using interactions that are available in a variety of continuous-variable systems. Our work separates the "hardware" problem of engineering quantum-computing-universal interactions, from the "software" problem of designing encodings for specific purposes. The development of quantum computer architecture could hence be simplified.

Universal Quantum Computing with Arbitrary Continuous-Variable Encoding

NASA Astrophysics Data System (ADS)

Lau, Hoi-Kwan; Plenio, Martin B.

2016-09-01

Implementing a qubit quantum computer in continuous-variable systems conventionally requires the engineering of specific interactions according to the encoding basis states. In this work, we present a unified formalism to conduct universal quantum computation with a fixed set of operations but arbitrary encoding. By storing a qubit in the parity of two or four qumodes, all computing processes can be implemented by basis state preparations, continuous-variable exponential-swap operations, and swap tests. Our formalism inherits the advantages that the quantum information is decoupled from collective noise, and logical qubits with different encodings can be brought to interact without decoding. We also propose a possible implementation of the required operations by using interactions that are available in a variety of continuous-variable systems. Our work separates the "hardware" problem of engineering quantum-computing-universal interactions, from the "software" problem of designing encodings for specific purposes. The development of quantum computer architecture could hence be simplified.

Two-Dimensional Arrays of Neutral Atom Quantum Gates

DTIC Science & Technology

2012-10-20

Box 12211 Research Triangle Park, NC 27709-2211 15. SUBJECT TERMS quantum computing , Rydberg atoms, entanglement Mark Saffman University of...Nature Physics, (01 2009): 0. doi: 10.1038/nphys1178 10/19/2012 9.00 K. Mølmer, M. Saffman. Scaling the neutral-atom Rydberg gate quantum computer by...Saffman, E. Brion, K. Mølmer. Error Correction in Ensemble Registers for Quantum Repeaters and Quantum Computers , Physical Review Letters, (3 2008): 0

QUANTUM COMPUTING: Quantum Entangled Bits Step Closer to IT.

PubMed

Zeilinger, A

2000-07-21

In contrast to today's computers, quantum computers and information technologies may in future be able to store and transmit information not only in the state "0" or "1," but also in superpositions of the two; information will then be stored and transmitted in entangled quantum states. Zeilinger discusses recent advances toward using this principle for quantum cryptography and highlights studies into the entanglement (or controlled superposition) of several photons, atoms, or ions.

Integrated Visible Photonics for Trapped-Ion Quantum Computing

DTIC Science & Technology

2017-06-10

necessarily reflect the views of the Department of Defense. Abstract- A scalable trapped-ion-based quantum - computing architecture requires the... Quantum Computing Dave Kharas, Cheryl Sorace-Agaskar, Suraj Bramhavar, William Loh, Jeremy M. Sage, Paul W. Juodawlkis, and John...coherence times, strong coulomb interactions, and optical addressability, hold great promise for implementation of practical quantum information

Algorithms Bridging Quantum Computation and Chemistry

NASA Astrophysics Data System (ADS)

McClean, Jarrod Ryan

The design of new materials and chemicals derived entirely from computation has long been a goal of computational chemistry, and the governing equation whose solution would permit this dream is known. Unfortunately, the exact solution to this equation has been far too expensive and clever approximations fail in critical situations. Quantum computers offer a novel solution to this problem. In this work, we develop not only new algorithms to use quantum computers to study hard problems in chemistry, but also explore how such algorithms can help us to better understand and improve our traditional approaches. In particular, we first introduce a new method, the variational quantum eigensolver, which is designed to maximally utilize the quantum resources available in a device to solve chemical problems. We apply this method in a real quantum photonic device in the lab to study the dissociation of the helium hydride (HeH+) molecule. We also enhance this methodology with architecture specific optimizations on ion trap computers and show how linear-scaling techniques from traditional quantum chemistry can be used to improve the outlook of similar algorithms on quantum computers. We then show how studying quantum algorithms such as these can be used to understand and enhance the development of classical algorithms. In particular we use a tool from adiabatic quantum computation, Feynman's Clock, to develop a new discrete time variational principle and further establish a connection between real-time quantum dynamics and ground state eigenvalue problems. We use these tools to develop two novel parallel-in-time quantum algorithms that outperform competitive algorithms as well as offer new insights into the connection between the fermion sign problem of ground states and the dynamical sign problem of quantum dynamics. Finally we use insights gained in the study of quantum circuits to explore a general notion of sparsity in many-body quantum systems. In particular we use developments from the field of compressed sensing to find compact representations of ground states. As an application we study electronic systems and find solutions dramatically more compact than traditional configuration interaction expansions, offering hope to extend this methodology to challenging systems in chemical and material design.

Models of optical quantum computing

NASA Astrophysics Data System (ADS)

Krovi, Hari

2017-03-01

I review some work on models of quantum computing, optical implementations of these models, as well as the associated computational power. In particular, we discuss the circuit model and cluster state implementations using quantum optics with various encodings such as dual rail encoding, Gottesman-Kitaev-Preskill encoding, and coherent state encoding. Then we discuss intermediate models of optical computing such as boson sampling and its variants. Finally, we review some recent work in optical implementations of adiabatic quantum computing and analog optical computing. We also provide a brief description of the relevant aspects from complexity theory needed to understand the results surveyed.

Quantum correlation properties in Matrix Product States of finite-number spin rings

NASA Astrophysics Data System (ADS)

Zhu, Jing-Min; He, Qi-Kai

2018-02-01

The organization and structure of quantum correlation (QC) of quantum spin-chains are very rich and complex. Hence the depiction and measures about the QC of finite-number spin rings deserved to be investigated intensively by using Matrix Product States(MPSs) in addition to the case with infinite-number. Here the dependencies of the geometric quantum discord(GQD) of two spin blocks on the total spin number, the spacing spin number and the environment parameter are presented in detail. We also compare the GQD with the total correlation(TC) and the classical correlation(CC) and illustrate its characteristics. Predictably, our findings may provide the potential of designing the optimal QC experimental detection proposals and pave the way for the designation of optimal quantum information processing schemes.

On the 'principle of the quantumness', the quantumness of Relativity, and the computational grand-unification

DOE Office of Scientific and Technical Information (OSTI.GOV)

D'Ariano, Giacomo Mauro

2010-05-04

I will argue that the proposal of establishing operational foundations of Quantum Theory should have top-priority, and that the Lucien Hardy's program on Quantum Gravity should be paralleled by an analogous program on Quantum Field Theory (QFT), which needs to be reformulated, notwithstanding its experimental success. In this paper, after reviewing recently suggested operational 'principles of the quantumness', I address the problem on whether Quantum Theory and Special Relativity are unrelated theories, or instead, if the one implies the other. I show how Special Relativity can be indeed derived from causality of Quantum Theory, within the computational paradigm 'the universemore » is a huge quantum computer', reformulating QFT as a Quantum-Computational Field Theory (QCFT). In QCFT Special Relativity emerges from the fabric of the computational network, which also naturally embeds gauge invariance. In this scheme even the quantization rule and the Planck constant can in principle be derived as emergent from the underlying causal tapestry of space-time. In this way Quantum Theory remains the only theory operating the huge computer of the universe.Is the computational paradigm only a speculative tautology (theory as simulation of reality), or does it have a scientific value? The answer will come from Occam's razor, depending on the mathematical simplicity of QCFT. Here I will just start scratching the surface of QCFT, analyzing simple field theories, including Dirac's. The number of problems and unmotivated recipes that plague QFT strongly motivates us to undertake the QCFT project, since QCFT makes all such problems manifest, and forces a re-foundation of QFT.« less

Ancilla-driven quantum computation for qudits and continuous variables

NASA Astrophysics Data System (ADS)

Proctor, Timothy; Giulian, Melissa; Korolkova, Natalia; Andersson, Erika; Kendon, Viv

2017-05-01

Although qubits are the leading candidate for the basic elements in a quantum computer, there are also a range of reasons to consider using higher-dimensional qudits or quantum continuous variables (QCVs). In this paper, we use a general "quantum variable" formalism to propose a method of quantum computation in which ancillas are used to mediate gates on a well-isolated "quantum memory" register and which may be applied to the setting of qubits, qudits (for d >2 ), or QCVs. More specifically, we present a model in which universal quantum computation may be implemented on a register using only repeated applications of a single fixed two-body ancilla-register interaction gate, ancillas prepared in a single state, and local measurements of these ancillas. In order to maintain determinism in the computation, adaptive measurements via a classical feed forward of measurement outcomes are used, with the method similar to that in measurement-based quantum computation (MBQC). We show that our model has the same hybrid quantum-classical processing advantages as MBQC, including the power to implement any Clifford circuit in essentially one layer of quantum computation. In some physical settings, high-quality measurements of the ancillas may be highly challenging or not possible, and hence we also present a globally unitary model which replaces the need for measurements of the ancillas with the requirement for ancillas to be prepared in states from a fixed orthonormal basis. Finally, we discuss settings in which these models may be of practical interest.

Research on Quantum Authentication Methods for the Secure Access Control Among Three Elements of Cloud Computing

NASA Astrophysics Data System (ADS)

Dong, Yumin; Xiao, Shufen; Ma, Hongyang; Chen, Libo

2016-12-01

Cloud computing and big data have become the developing engine of current information technology (IT) as a result of the rapid development of IT. However, security protection has become increasingly important for cloud computing and big data, and has become a problem that must be solved to develop cloud computing. The theft of identity authentication information remains a serious threat to the security of cloud computing. In this process, attackers intrude into cloud computing services through identity authentication information, thereby threatening the security of data from multiple perspectives. Therefore, this study proposes a model for cloud computing protection and management based on quantum authentication, introduces the principle of quantum authentication, and deduces the quantum authentication process. In theory, quantum authentication technology can be applied in cloud computing for security protection. This technology cannot be cloned; thus, it is more secure and reliable than classical methods.

Digitized adiabatic quantum computing with a superconducting circuit.

PubMed

Barends, R; Shabani, A; Lamata, L; Kelly, J; Mezzacapo, A; Las Heras, U; Babbush, R; Fowler, A G; Campbell, B; Chen, Yu; Chen, Z; Chiaro, B; Dunsworth, A; Jeffrey, E; Lucero, E; Megrant, A; Mutus, J Y; Neeley, M; Neill, C; O'Malley, P J J; Quintana, C; Roushan, P; Sank, D; Vainsencher, A; Wenner, J; White, T C; Solano, E; Neven, H; Martinis, John M

2016-06-09

Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable.

Quantum market games: implementing tactics via measurements

NASA Astrophysics Data System (ADS)

Pakula, I.; Piotrowski, E. W.; Sladkowski, J.

2006-02-01

A major development in applying quantum mechanical formalism to various fields has been made during the last few years. Quantum counterparts of Game Theory, Economy, as well as diverse approaches to Quantum Information Theory have been found and currently are being explored. Using connections between Quantum Game Theory and Quantum Computations, an application of the universality of a measurement based computation in Quantum Market Theory is presented.

Benchmarking gate-based quantum computers

NASA Astrophysics Data System (ADS)

Michielsen, Kristel; Nocon, Madita; Willsch, Dennis; Jin, Fengping; Lippert, Thomas; De Raedt, Hans

2017-11-01

With the advent of public access to small gate-based quantum processors, it becomes necessary to develop a benchmarking methodology such that independent researchers can validate the operation of these processors. We explore the usefulness of a number of simple quantum circuits as benchmarks for gate-based quantum computing devices and show that circuits performing identity operations are very simple, scalable and sensitive to gate errors and are therefore very well suited for this task. We illustrate the procedure by presenting benchmark results for the IBM Quantum Experience, a cloud-based platform for gate-based quantum computing.

Quantum Hash function and its application to privacy amplification in quantum key distribution, pseudo-random number generation and image encryption

NASA Astrophysics Data System (ADS)

Yang, Yu-Guang; Xu, Peng; Yang, Rui; Zhou, Yi-Hua; Shi, Wei-Min

2016-01-01

Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information.

Quantum Hash function and its application to privacy amplification in quantum key distribution, pseudo-random number generation and image encryption

PubMed Central

Yang, Yu-Guang; Xu, Peng; Yang, Rui; Zhou, Yi-Hua; Shi, Wei-Min

2016-01-01

Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information. PMID:26823196

Quantum Hash function and its application to privacy amplification in quantum key distribution, pseudo-random number generation and image encryption.

PubMed

Yang, Yu-Guang; Xu, Peng; Yang, Rui; Zhou, Yi-Hua; Shi, Wei-Min

2016-01-29

Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information.

A Gaussian wave packet phase-space representation of quantum canonical statistics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coughtrie, David J.; Tew, David P.

2015-07-28

We present a mapping of quantum canonical statistical averages onto a phase-space average over thawed Gaussian wave-packet (GWP) parameters, which is exact for harmonic systems at all temperatures. The mapping invokes an effective potential surface, experienced by the wave packets, and a temperature-dependent phase-space integrand, to correctly transition from the GWP average at low temperature to classical statistics at high temperature. Numerical tests on weakly and strongly anharmonic model systems demonstrate that thermal averages of the system energy and geometric properties are accurate to within 1% of the exact quantum values at all temperatures.

Laterally coupled circular quantum dots under applied electric field

NASA Astrophysics Data System (ADS)

Duque, C. M.; Correa, J. D.; Morales, A. L.; Mora-Ramos, M. E.; Duque, C. A.

2016-03-01

The optical response of a system of two laterally coupled quantum dots with circular cross-sectional shape is investigated within the effective mass approximation, taking into account the effects of the change in the geometrical configuration, the application of an external static electric field, and the presence of a donor impurity center. The first-order dielectric susceptibility is calculated in order to derive the corresponding light absorption and relative refractive index coefficients. The possibility of tuning these optical properties by means of changes in the quantum dot symmetry and the electric field intensity is particularly discussed.