Physical and Constructive (Limiting) Criterions of Gear Wheels Wear

NASA Astrophysics Data System (ADS)

Fedorov, S. V.

2018-01-01

We suggest using a generalized model of friction - the model of elastic-plastic deformation of the body element, which is located on the surface of the friction pairs. This model is based on our new engineering approach to the problem of friction-triboergodynamics. Friction is examined as transformative and dissipative process. Structural-energetic interpretation of friction as a process of elasto-plastic deformation and fracture contact volumes is proposed. The model of Hertzian (heavy-loaded) friction contact evolution is considered. The least wear particle principle is formulated. It is mechanical (nano) quantum. Mechanical quantum represents the least structural form of solid material body in conditions of friction. It is dynamic oscillator of dissipative friction structure and it can be examined as the elementary nanostructure of metal’s solid body. At friction in state of most complete evolution of elementary tribosystem (tribocontact) all mechanical quanta (subtribosystems) with the exception of one, elasticity and reversibly transform energy of outer impact (mechanic movement). In these terms only one mechanical quantum is the lost - standard of wear. From this position we can consider the physical criterion of wear and the constructive (limiting) criterion of gear teeth and other practical examples of tribosystems efficiency with new tribology notion - mechanical (nano) quantum.

Bialgebra cohomology, deformations, and quantum groups.

PubMed Central

Gerstenhaber, M; Schack, S D

1990-01-01

We introduce cohomology and deformation theories for a bialgebra A (over a commutative unital ring k) such that the second cohomology group is the space of infinitesimal deformations. Our theory gives a natural identification between the underlying k-modules of the original and the deformed bialgebra. Certain explicit deformation formulas are given for the construction of quantum groups--i.e., Hopf algebras that are neither commutative nor cocommutative (whether or not they arise from quantum Yang-Baxter operators). These formulas yield, in particular, all GLq(n) and SLq(n) as deformations of GL(n) and SL(n). Using a Hodge decomposition of the underlying cochain complex, we compute our cohomology for GL(n). With this, we show that every deformation of GL(n) is equivalent to one in which the comultiplication is unchanged, not merely on elements of degree one but on all elements (settling in the strongest way a decade-old conjecture) and in which the quantum determinant, as an element of the underlying k-module, is identical with the usual one. PMID:11607053

The Hopf algebra structure of the h-deformed Z3-graded quantum supergroup GLh,j(1|1)

NASA Astrophysics Data System (ADS)

Yasar, Ergün

2016-07-01

In this work, we define a new proper singular g matrix to construct a Z3-graded calculus on the h-deformed quantum superplane. Using the obtained calculus, we construct a new h-deformed Z3-graded quantum supergroup and give some features of it. Finally, we build up the Hopf algebra structure of this supergroup.

Ab Initio Path Integral Molecular Dynamics Study of the Nuclear Quantum Effect on Out-of-Plane Ring Deformation of Hydrogen Maleate Anion.

PubMed

Kawashima, Yukio; Tachikawa, Masanori

2014-01-14

Ab initio path integral molecular dynamics (PIMD) simulation was performed to understand the nuclear quantum effect on the out-of-plane ring deformation of hydrogen maleate anion and investigate the existence of a stable structure with ring deformation, which was suggested in experimental observation (Fillaux et al., Chem. Phys. 1999, 120, 387-403). The isotope effect and the temperature effect are studied as well. We first investigated the nuclear quantum effect on the proton transfer. In static calculation and classical ab initio molecular dynamics simulations, the proton in the hydrogen bond is localized to either oxygen atom. On the other hand, the proton is located at the center of two oxygen atoms in quantum ab initio PIMD simulations. The nuclear quantum effect washes out the barrier of proton transfer. We next examined the nuclear quantum effect on the motion of hydrogen maleate anion. Principal component analysis revealed that the out-of-plane ring bending modes have dominant contribution to the entire molecular motion. In quantum ab initio PIMD simulations, structures with ring deformation were the global minimum for the deuterated isotope at 300 K. We analyzed the out-of-plane ring bending mode further and found that there are three minima along a ring distortion mode. We successfully found a stable structure with ring deformation of hydrogen maleate for the first time, to our knowledge, using theoretical calculation. The structures with ring deformation found in quantum simulation of the deuterated isotope allowed the proton transfer to occur more frequently than the planar structure. Static ab initio electronic structure calculation found that the structures with ring deformation have very small proton transfer barrier compared to the planar structure. We suggest that the "proton transfer driven" mechanism is the origin of stabilization for the structure with out-of-plane ring deformation.

Perturbatively deformed defects in Pöschl-Teller-driven scenarios for quantum mechanics

NASA Astrophysics Data System (ADS)

Bernardini, Alex E.; da Rocha, Roldão

2016-07-01

Pöschl-Teller-driven solutions for quantum mechanical fluctuations are triggered off by single scalar field theories obtained through a systematic perturbative procedure for generating deformed defects. The analytical properties concerning the quantum fluctuations in one-dimension, zero-mode states, first- and second-excited states, and energy density profiles are all obtained from deformed topological and non-topological structures supported by real scalar fields. Results are firstly derived from an integrated λϕ4 theory, with corresponding generalizations applied to starting λχ4 and sine-Gordon theories. By focusing our calculations on structures supported by the λϕ4 theory, the outcome of our study suggests an exact quantitative correspondence to Pöschl-Teller-driven systems. Embedded into the perturbative quantum mechanics framework, such a correspondence turns into a helpful tool for computing excited states and continuous mode solutions, as well as their associated energy spectrum, for quantum fluctuations of perturbatively deformed structures. Perturbative deformations create distinct physical scenarios in the context of exactly solvable quantum systems and may also work as an analytical support for describing novel braneworld universes embedded into a 5-dimensional gravity bulk.

Asymptotic inference in system identification for the atom maser.

PubMed

Catana, Catalin; van Horssen, Merlijn; Guta, Madalin

2012-11-28

System identification is closely related to control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However, for quantum dynamical systems such as quantum Markov processes, it is more natural to consider the estimation based on continuous measurements of the output, with a given input that may be stationary. We address this problem using asymptotic statistics tools, for the specific example of estimating the Rabi frequency of an atom maser. We compute the Fisher information of different measurement processes as well as the quantum Fisher information of the atom maser, and establish the local asymptotic normality of these statistical models. The statistical notions can be expressed in terms of spectral properties of certain deformed Markov generators, and the connection to large deviations is briefly discussed.

Pseudo Landau levels and quantum oscillations in strained Weyl semimetals

NASA Astrophysics Data System (ADS)

Alisultanov, Z. Z.

2018-05-01

The crystal lattice deformation in Weyl materials where the two chiralities are separated in momentum space leads to the appearance of gauge pseudo-fields. We investigated the pseudo-magnetic field induced quantum oscillations in strained Weyl semimetal (WSM). In contrast to all previous works on this problem, we use here a more general tilted Hamiltonian. Such Hamiltonian, seems to be is more suitable for a strained WSMs. We have shown that a pseudo-magnetic field induced magnetization of strained WSM is nonzero due to the fact that electric field (gradient of the deformation potential) is induced simultaneously with the pseudo-magnetic field. This related with fact that the pseudo Landau levels (LLs) in strained WSM are differ in vicinities of different WPs due to the presence of tilt in spectrum. Such violation of the equivalence between Weyl points (WPs) leads to modulation of quantum oscillations. We also showed that magnetization magnitude can be changed by application of an external electric field. In particular, it can be reduced to zero. The possibility of controlling of the magnetization by an electric field is interesting both from a fundamental point of view (a new type of magneto-electric effect) and application point of view (additional possibility to control diamagnetism of deformed WSMs). Finally, a coexistence of type-I and type-II Weyl fermions is possible in the system under investigation. Such phase is absolutely new for physics of topological systems.

Quantum Sheaf Cohomology on Grassmannians

NASA Astrophysics Data System (ADS)

Guo, Jirui; Lu, Zhentao; Sharpe, Eric

2017-05-01

In this paper we study the quantum sheaf cohomology of Grassmannians with deformations of the tangent bundle. Quantum sheaf cohomology is a (0,2) deformation of the ordinary quantum cohomology ring, realized as the OPE ring in A/2-twisted theories. Quantum sheaf cohomology has previously been computed for abelian gauged linear sigma models (GLSMs); here, we study (0,2) deformations of nonabelian GLSMs, for which previous methods have been intractable. Combined with the classical result, the quantum ring structure is derived from the one-loop effective potential. We also utilize recent advances in supersymmetric localization to compute A/2 correlation functions and check the general result in examples. In this paper we focus on physics derivations and examples; in a companion paper, we will provide a mathematically rigorous derivation of the classical sheaf cohomology ring.

Could quantum gravity phenomenology be tested with high intensity lasers?

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

Magueijo, Joao; Canadian Institute for Theoretical Astrophysics, 60 St. George Street, Toronto M5S 3H8; Theoretical Physics Group, Imperial College, Prince Consort Road, London SW7 2BZ

2006-06-15

In phenomenological quantum gravity theories, Planckian behavior is triggered by the energy of elementary particles approaching the Planck energy, E{sub P}, but it is also possible that anomalous behavior strikes systems of particles with total energy near E{sub P}. This is usually perceived to be pathological and has been labeled 'the soccer ball problem'. We point out that there is no obvious contradiction with experiment if coherent collections of particles with bulk energy of order E{sub P} do indeed display Planckian behavior, a possibility that would open a new experimental window. Unfortunately, field theory realizations of 'doubly' (or deformed) specialmore » relativity never exhibit a soccer ball problem; we present several formulations where this is undeniably true. Upon closer scrutiny we discover that the only chance for Planckian behavior to be triggered by large coherent energies involves the details of second quantization. We find a formulation where the quanta have their energy-momentum (mass-shell) relations deformed as a function of the bulk energy of the coherent packet to which they belong, rather than the frequency. Given ongoing developments in laser technology, such a possibility would be of great experimental interest.« less

Towards the map of quantum gravity

NASA Astrophysics Data System (ADS)

Mielczarek, Jakub; Trześniewski, Tomasz

2018-06-01

In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between loop quantum gravity, causal dynamical triangulations, Hořava-Lifshitz gravity, asymptotic safety scenario, Quantum Graphity, deformations of relativistic symmetries and nonlinear phase space models are discussed. The main focus is on quantum deformations of the Hypersurface Deformations Algebra and Poincaré algebra, nonlinear structure of phase space, the running dimension of spacetime and nontrivial phase diagram of quantum gravity. We present an attempt to arrange the observed relations in the form of a graph, highlighting different aspects of quantum gravity. The analysis is performed in the spirit of a mind map, which represents the architectural approach to the studied theory, being a natural way to describe the properties of a complex system. We hope that the constructed graphs (maps) will turn out to be helpful in uncovering the global picture of quantum gravity as a particular complex system and serve as a useful guide for the researchers.

Self-adjointness of deformed unbounded operators

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

Much, Albert

2015-09-15

We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem, we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain condition. This condition proves itself to be necessary for the oscillatory integral to be well-defined. Moreover, different proofs are given for self-adjointness of deformed unbounded operators in the context of quantum mechanics and quantum field theory.

Deformed D1D5 CFT: A Holographic Probe of Quantum Gravity

NASA Astrophysics Data System (ADS)

Jardine, Ian Theodore

One of the big unsolved questions in gravity research is the black hole information problem. This problem, which pits the unitarity of quantum field theory against smooth classical spacetime, must have a solution in a complete theory of quantum gravity. This thesis will explore aspects of one approach to this problem in the context of string theory. The approach imagines black hole microstates as string theoretic objects. We look at a prototype system, the D1D5 system, and exploit holography to examine the dual conformal field theory (CFT). Specifically, we examine the CFT deformed from the free orbifold point, dual to a very stringy bulk, using a twisted operator that will take us towards the point with the supergravity description. The effects of twisted operators in the CFT are key to understanding physical processes such as emission and thermalization in black hole microstates. We will propose a component twist method for examining the effects of bare twist operators for higher twists in the continuum limit. Our method builds higher twists from simple 2-cycle twists, whose effects are known. We will find that, in this limit, the coefficients describing general states will follow a conjectured general functional form. We then explore the deformed CFT directly by examining operator mixing for untwisted operators. We will exploit the operator product expansion on the covering space, where twist operators of the orbifold are resolved. We use this to examine the mixing of a general supergravity operator, specifically examine the dilaton, and finish with the mixing of a non-supersymmetric candidate operator. We conjecture that this method could be extended to include twisted operators. We will also examine the mixing of the non-supersymmetric candidate operator by examining three point functions. To automate the lengthy and repetitive computations, we wrote a Mathematica package to compute correlation functions and OPEs in the D1D5 CFT. We will explain some of the main functions of this package and how it can be applied to computations. Finally, we will end with a short discussion on future directions.

Integrability of the Ad{{S}_{5}}\\times {{S}^{5}} superstring and its deformations

NASA Astrophysics Data System (ADS)

van Tongeren, Stijn J.

2014-10-01

This article reviews the application of integrability to the spectral problem of strings on Ad{{S}5}× {{S}5} and its deformations. We begin with a pedagogical introduction to integrable field theories culminating in the description of their finite-volume spectra through the thermodynamic Bethe ansatz (TBA). Next, we apply these ideas to the Ad{{S}5}× {{S}5} string and in later sections discuss how to account for particular integrable deformations. Through the AdS/CFT correspondence this gives an exact description of anomalous scaling dimensions of single trace operators in planar N=4 supersymmetry Yang-Mills theory, its ‘orbifolds’, and β and γ-deformed supersymmetric Yang-Mills theory. We also touch upon some subtleties arising in these deformed theories. Furthermore, we consider complex excited states (bound states) in the su(2) sector and give their TBA description. Finally we discuss the TBA for a quantum deformation of the Ad{{S}5}× {{S}5} superstring S-matrix, with close relations to among others Pohlmeyer reduced string theory, and briefly indicate more recent developments in this area.

Observables and dispersion relations in κ-Minkowski spacetime

NASA Astrophysics Data System (ADS)

Aschieri, Paolo; Borowiec, Andrzej; Pachoł, Anna

2017-10-01

We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on noncommutative spaces are derived from a quantum Hodge star operator. This general noncommutative geometry construction is then exemplified in the case of κ-Minkowski spacetime. The corresponding quantum Poincaré-Weyl Lie algebra of in-finitesimal translations, rotations and dilatations is obtained. The d'Alembert wave operator coincides with the quadratic Casimir of quantum translations and it is deformed as in Deformed Special Relativity theories. Also momenta (infinitesimal quantum translations) are deformed, and correspondingly the Einstein-Planck relation and the de Broglie one. The energy-momentum relations (dispersion relations) are consequently deduced. These results complement those of the phenomenological literature on the subject.

Gröbner bases for finite-temperature quantum computing and their complexity

NASA Astrophysics Data System (ADS)

Crompton, P. R.

2011-11-01

Following the recent approach of using order domains to construct Gröbner bases from general projective varieties, we examine the parity and time-reversal arguments relating to the Wightman axioms of quantum field theory and propose that the definition of associativity in these axioms should be introduced a posteriori to the cluster property in order to generalize the anyon conjecture for quantum computing to indefinite metrics. We then show that this modification, which we define via ideal quotients, does not admit a faithful representation of the Braid group, because the generalized twisted inner automorphisms that we use to reintroduce associativity are only parity invariant for the prime spectra of the exterior algebra. We then use a coordinate prescription for the quantum deformations of toric varieties to show how a faithful representation of the Braid group can be reconstructed and argue that for a degree reverse lexicographic (monomial) ordered Gröbner basis, the complexity class of this problem is bounded quantum polynomial.

Squeezing the Efimov effect

NASA Astrophysics Data System (ADS)

Sandoval, J. H.; Bellotti, F. F.; Yamashita, M. T.; Frederico, T.; Fedorov, D. V.; Jensen, A. S.; Zinner, N. T.

2018-03-01

The quantum mechanical three-body problem is a source of continuing interest due to its complexity and not least due to the presence of fascinating solvable cases. The prime example is the Efimov effect where infinitely many bound states of identical bosons can arise at the threshold where the two-body problem has zero binding energy. An important aspect of the Efimov effect is the effect of spatial dimensionality; it has been observed in three dimensional systems, yet it is believed to be impossible in two dimensions. Using modern experimental techniques, it is possible to engineer trap geometry and thus address the intricate nature of quantum few-body physics as function of dimensionality. Here we present a framework for studying the three-body problem as one (continuously) changes the dimensionality of the system all the way from three, through two, and down to a single dimension. This is done by considering the Efimov favorable case of a mass-imbalanced system and with an external confinement provided by a typical experimental case with a (deformed) harmonic trap.

Deformed Calogero-Sutherland model and fractional quantum Hall effect

NASA Astrophysics Data System (ADS)

Atai, Farrokh; Langmann, Edwin

2017-01-01

The deformed Calogero-Sutherland (CS) model is a quantum integrable system with arbitrary numbers of two types of particles and reducing to the standard CS model in special cases. We show that a known collective field description of the CS model, which is based on conformal field theory (CFT), is actually a collective field description of the deformed CS model. This provides a natural application of the deformed CS model in Wen's effective field theory of the fractional quantum Hall effect (FQHE), with the two kinds of particles corresponding to electrons and quasi-hole excitations. In particular, we use known mathematical results about super-Jack polynomials to obtain simple explicit formulas for the orthonormal CFT basis proposed by van Elburg and Schoutens in the context of the FQHE.

Deformation of supersymmetric and conformal quantum mechanics through affine transformations

NASA Technical Reports Server (NTRS)

Spiridonov, Vyacheslav

1993-01-01

Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional N = 2 supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e. the spectrum of one can be obtained from another (with possible exception of the lowest level) by q(sup 2)-factor scaling. This construction allows easily to rederive a special self-similar potential found by Shabat and to show that for the latter a q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane serves as the spectrum generating algebra. A general class of potentials related to the quantum conformal algebra su(sub q)(1,1) is described. Further possibilities for q-deformation of known solvable potentials are outlined.

A Cohomological Perspective on Algebraic Quantum Field Theory

NASA Astrophysics Data System (ADS)

Hawkins, Eli

2018-05-01

Algebraic quantum field theory is considered from the perspective of the Hochschild cohomology bicomplex. This is a framework for studying deformations and symmetries. Deformation is a possible approach to the fundamental challenge of constructing interacting QFT models. Symmetry is the primary tool for understanding the structure and properties of a QFT model. This perspective leads to a generalization of the algebraic quantum field theory framework, as well as a more general definition of symmetry. This means that some models may have symmetries that were not previously recognized or exploited. To first order, a deformation of a QFT model is described by a Hochschild cohomology class. A deformation could, for example, correspond to adding an interaction term to a Lagrangian. The cohomology class for such an interaction is computed here. However, the result is more general and does not require the undeformed model to be constructed from a Lagrangian. This computation leads to a more concrete version of the construction of perturbative algebraic quantum field theory.

Conformal quantum mechanics and holography in noncommutative space-time

NASA Astrophysics Data System (ADS)

Gupta, Kumar S.; Harikumar, E.; Zuhair, N. S.

2017-09-01

We analyze the effects of noncommutativity in conformal quantum mechanics (CQM) using the κ-deformed space-time as a prototype. Up to the first order in the deformation parameter, the symmetry structure of the CQM algebra is preserved but the coupling in a canonical model of the CQM gets deformed. We show that the boundary conditions that ensure a unitary time evolution in the noncommutative CQM can break the scale invariance, leading to a quantum mechanical scaling anomaly. We calculate the scaling dimensions of the two and three point functions in the noncommutative CQM which are shown to be deformed. The AdS2 / CFT1 duality for the CQM suggests that the corresponding correlation functions in the holographic duals are modified. In addition, the Breitenlohner-Freedman bound also picks up a noncommutative correction. The strongly attractive regime of a canonical model of the CQM exhibit quantum instability. We show that the noncommutativity softens this singular behaviour and its implications for the corresponding holographic duals are discussed.

Short distance modification of the quantum virial theorem

NASA Astrophysics Data System (ADS)

Zhao, Qin; Faizal, Mir; Zaz, Zaid

2017-07-01

In this letter, we will analyse the deformation of a semi-classical gravitational system from minimal measurable length scale. In the semi-classical approximation, the gravitational field will be analysed as a classical field, and the matter fields will be treated quantum mechanically. Thus, using this approximation, this system will be represented by a deformation of Schrödinger-Newton equation by the generalised uncertainty principle (GUP). We will analyse the effects of this GUP deformed Schrödinger-Newton equation on the behaviour of such a semi-classical gravitational system. As the quantum mechanical virial theorem can be obtained using the Schrödinger-Newton equation, a short distance modification of the Schrödinger-Newton equation will also result in a short distance modification of the quantum mechanical virial theorem.

Decoherence and discrete symmetries in deformed relativistic kinematics

NASA Astrophysics Data System (ADS)

Arzano, Michele

2018-01-01

Models of deformed Poincaré symmetries based on group valued momenta have long been studied as effective modifications of relativistic kinematics possibly capturing quantum gravity effects. In this contribution we show how they naturally lead to a generalized quantum time evolution of the type proposed to model fundamental decoherence for quantum systems in the presence of an evaporating black hole. The same structures which determine such generalized evolution also lead to a modification of the action of discrete symmetries and of the CPT operator. These features can in principle be used to put phenomenological constraints on models of deformed relativistic symmetries using precision measurements of neutral kaons.

Quantum field theory and coalgebraic logic in theoretical computer science.

PubMed

Basti, Gianfranco; Capolupo, Antonio; Vitiello, Giuseppe

2017-11-01

We suggest that in the framework of the Category Theory it is possible to demonstrate the mathematical and logical dual equivalence between the category of the q-deformed Hopf Coalgebras and the category of the q-deformed Hopf Algebras in quantum field theory (QFT), interpreted as a thermal field theory. Each pair algebra-coalgebra characterizes a QFT system and its mirroring thermal bath, respectively, so to model dissipative quantum systems in far-from-equilibrium conditions, with an evident significance also for biological sciences. Our study is in fact inspired by applications to neuroscience where the brain memory capacity, for instance, has been modeled by using the QFT unitarily inequivalent representations. The q-deformed Hopf Coalgebras and the q-deformed Hopf Algebras constitute two dual categories because characterized by the same functor T, related with the Bogoliubov transform, and by its contravariant application T op , respectively. The q-deformation parameter is related to the Bogoliubov angle, and it is effectively a thermal parameter. Therefore, the different values of q identify univocally, and label the vacua appearing in the foliation process of the quantum vacuum. This means that, in the framework of Universal Coalgebra, as general theory of dynamic and computing systems ("labelled state-transition systems"), the so labelled infinitely many quantum vacua can be interpreted as the Final Coalgebra of an "Infinite State Black-Box Machine". All this opens the way to the possibility of designing a new class of universal quantum computing architectures based on this coalgebraic QFT formulation, as its ability of naturally generating a Fibonacci progression demonstrates. Copyright © 2017 Elsevier Ltd. All rights reserved.

Generalized Ehrenfest Relations, Deformation Quantization, and the Geometry of Inter-model Reduction

NASA Astrophysics Data System (ADS)

Rosaler, Joshua

2018-03-01

This study attempts to spell out more explicitly than has been done previously the connection between two types of formal correspondence that arise in the study of quantum-classical relations: one the one hand, deformation quantization and the associated continuity between quantum and classical algebras of observables in the limit \\hbar → 0, and, on the other, a certain generalization of Ehrenfest's Theorem and the result that expectation values of position and momentum evolve approximately classically for narrow wave packet states. While deformation quantization establishes a direct continuity between the abstract algebras of quantum and classical observables, the latter result makes in-eliminable reference to the quantum and classical state spaces on which these structures act—specifically, via restriction to narrow wave packet states. Here, we describe a certain geometrical re-formulation and extension of the result that expectation values evolve approximately classically for narrow wave packet states, which relies essentially on the postulates of deformation quantization, but describes a relationship between the actions of quantum and classical algebras and groups over their respective state spaces that is non-trivially distinct from deformation quantization. The goals of the discussion are partly pedagogical in that it aims to provide a clear, explicit synthesis of known results; however, the particular synthesis offered aspires to some novelty in its emphasis on a certain general type of mathematical and physical relationship between the state spaces of different models that represent the same physical system, and in the explicitness with which it details the above-mentioned connection between quantum and classical models.

Studies of Entanglement Entropy, and Relativistic Fluids for Thermal Field Theories

NASA Astrophysics Data System (ADS)

Spillane, Michael

In this dissertation we consider physical consequences of adding a finite temperature to quantum field theories. At small length scales entanglement is a critically important feature. It is therefore unsurprising that entanglement entropy and Renyi entropy are useful tools in studying quantum phase transition, and quantum information. In this thesis we consider the corrections to entanglement and Renyi entropies due to addition of a finite temperature. More specifically, we investigate the entanglement entropy of a massive scalar field in 1+1 dimensions at nonzero temperature. In the small mass ( m) and temperature (T) limit, we put upper and lower bounds on the two largest eigenvalues of the covariance matrix used to compute the entanglement entropy. We argue that the entanglement entropy has e-m/T scaling in the limit T << m.. Additionally, we calculate thermal corrections to Renyi entropies for free massless fermions on R x S d-1. By expanding the density matrix in a Boltzmann sum, the problem of finding the Renyi entropies can be mapped to the problem of calculating a two point function on an n-sheeted cover of the sphere. We map the problem on the sphere to a conical region in Euclidean space. By using the method of images, we calculate the two point function and recover the Renyi entropies. At large length scales hydrodynamics is a useful way to study quantum field theories. We review recent interest in the Riemann problem as a method for generating a non-equilibrium steady state. The initial conditions consist of a planar interface between two halves of a system held at different temperatures in a hydrodynamic regime. The resulting fluid flow contains a fixed temperature region with a nonzero flux. We briefly discuss the effects of a conserved charge. Next we discuss deforming the relativistic equations with a nonlinear term and how that deformation affects the temperature and velocity in the region connecting the asymptotic fluids. Finally, we study properties of a non-equilibrium steady state generated when two heat baths are initially in contact with one another. The dynamics of the system in question are governed by holographic duality to a blackhole. We discuss the "phase diagram" associated with the steady state of the dual, dynamical black hole and its relation to the fluid/gravity correspondence.

Noncommutativity and Humanity — Julius Wess and his Legacy

NASA Astrophysics Data System (ADS)

Djordjevic, Goran S.

2012-03-01

A personal view on Julius Wess's human and scientific legacy in Serbia and the Balkan region is given. Motivation for using noncommutative and nonarchimedean geometry on very short distances is presented. In addition to some mathematical preliminaries, we present a short introduction in adelic quantum mechanics in a way suitable for its noncommutative generalization. We also review the basic ideas and tools embedded in q-deformed and noncommutative quantum mechanics. A rather fundamental approach, called deformation quantization, is noted. A few relations between noncommutativity and nonarchimedean spaces, as well as similarities between corresponding quantum theories, in particular, quantum cosmology are pointed out. An extended Moyal product in a frame of an adelic noncommutative quantum mechanics is also considered.

The GUP and quantum Raychaudhuri equation

NASA Astrophysics Data System (ADS)

Vagenas, Elias C.; Alasfar, Lina; Alsaleh, Salwa M.; Ali, Ahmed Farag

2018-06-01

In this paper, we compare the quantum corrections to the Schwarzschild black hole temperature due to quadratic and linear-quadratic generalised uncertainty principle, with the corrections from the quantum Raychaudhuri equation. The reason for this comparison is to connect the deformation parameters β0 and α0 with η which is the parameter that characterises the quantum Raychaudhuri equation. The derived relation between the parameters appears to depend on the relative scale of the system (black hole), which could be read as a beta function equation for the quadratic deformation parameter β0. This study shows a correspondence between the two phenomenological approaches and indicates that quantum Raychaudhuri equation implies the existence of a crystal-like structure of spacetime.

Quantum deformations of conformal algebras with mass-like deformation parameters

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

Frydryszak, Andrzej; Lukierski, Jerzy; Mozrzymas, Marek

1998-12-15

We recall the mathematical apparatus necessary for the quantum deformation of Lie algebras, namely the notions of coboundary Lie algebras, classical r-matrices, classical Yang-Baxter equations (CYBE), Froebenius algebras and parabolic subalgebras. Then we construct the quantum deformation of D=1, D=2 and D=3 conformal algebras, showing that this quantization introduce fundamental mass parameters. Finally we consider with more details the quantization of D=4 conformal algebra. We build three classes of sl(4,C) classical r-matrices, satisfying CYBE and depending respectively on 8, 10 and 12 generators of parabolic subalgebras. We show that only the 8-dimensional r-matrices allow to impose the D=4 conformal o(4,2){approx_equal}su(2,2)more » reality conditions. Weyl reflections and Dynkin diagram automorphisms for o(4,2) define the class of admissible bases for given classical r-matrices.« less

Multi-objective optimization in quantum parameter estimation

NASA Astrophysics Data System (ADS)

Gong, BeiLi; Cui, Wei

2018-04-01

We investigate quantum parameter estimation based on linear and Kerr-type nonlinear controls in an open quantum system, and consider the dissipation rate as an unknown parameter. We show that while the precision of parameter estimation is improved, it usually introduces a significant deformation to the system state. Moreover, we propose a multi-objective model to optimize the two conflicting objectives: (1) maximizing the Fisher information, improving the parameter estimation precision, and (2) minimizing the deformation of the system state, which maintains its fidelity. Finally, simulations of a simplified ɛ-constrained model demonstrate the feasibility of the Hamiltonian control in improving the precision of the quantum parameter estimation.

The behaviour of resonances in Hecke triangular billiards under deformation

NASA Astrophysics Data System (ADS)

Howard, P. J.; O'Mahony, P. F.

2007-08-01

The right-hand boundary of Artin's billiard on the Poincaré half-plane is continuously deformed to generate a class of chaotic billiards which includes fundamental domains of the Hecke groups Γ(2, n) at certain values of the deformation parameter. The quantum scattering problem in these open chaotic billiards is described and the distributions of both real and imaginary parts of the resonant eigenvalues are investigated. The transitions to arithmetic chaos in the cases n ∈ {4, 6} are closely examined and the explicit analytic form for the scattering matrix is given together with the Fourier coefficients for the scattered wavefunction. The n = 4 and 6 cases have an additional set of regular equally spaced resonances compared to Artin's billiard (n = 3). For a general deformation, a numerical procedure is presented which generates the resonance eigenvalues and the evolution of the eigenvalues is followed as the boundary is varied continuously which leads to dramatic changes in their distribution. For deformations away from the non-generic arithmetic cases, including that of the tiling Hecke triangular billiard n = 5, the distributions of the positions and widths of the resonances are consistent with the predictions of a random matrix theory.

Novel characteristics of energy spectrum for 3D Dirac oscillator analyzed via Lorentz covariant deformed algebra

PubMed Central

Betrouche, Malika; Maamache, Mustapha; Choi, Jeong Ryeol

2013-01-01

We investigate the Lorentz-covariant deformed algebra for Dirac oscillator problem, which is a generalization of Kempf deformed algebra in 3 + 1 dimension of space-time, where Lorentz symmetry are preserved. The energy spectrum of the system is analyzed by taking advantage of the corresponding wave functions with explicit spin state. We obtained entirely new results from our development based on Kempf algebra in comparison to the studies carried out with the non-Lorentz-covariant deformed one. A novel result of this research is that the quantized relativistic energy of the system in the presence of minimal length cannot grow indefinitely as quantum number n increases, but converges to a finite value, where c is the speed of light and β is a parameter that determines the scale of noncommutativity in space. If we consider the fact that the energy levels of ordinary oscillator is equally spaced, which leads to monotonic growth of quantized energy with the increment of n, this result is very interesting. The physical meaning of this consequence is discussed in detail. PMID:24225900

Novel characteristics of energy spectrum for 3D Dirac oscillator analyzed via Lorentz covariant deformed algebra.

PubMed

Betrouche, Malika; Maamache, Mustapha; Choi, Jeong Ryeol

2013-11-14

We investigate the Lorentz-covariant deformed algebra for Dirac oscillator problem, which is a generalization of Kempf deformed algebra in 3 + 1 dimension of space-time, where Lorentz symmetry are preserved. The energy spectrum of the system is analyzed by taking advantage of the corresponding wave functions with explicit spin state. We obtained entirely new results from our development based on Kempf algebra in comparison to the studies carried out with the non-Lorentz-covariant deformed one. A novel result of this research is that the quantized relativistic energy of the system in the presence of minimal length cannot grow indefinitely as quantum number n increases, but converges to a finite value, where c is the speed of light and β is a parameter that determines the scale of noncommutativity in space. If we consider the fact that the energy levels of ordinary oscillator is equally spaced, which leads to monotonic growth of quantized energy with the increment of n, this result is very interesting. The physical meaning of this consequence is discussed in detail.

3D quantum gravity and effective noncommutative quantum field theory.

PubMed

Freidel, Laurent; Livine, Etera R

2006-06-09

We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.

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.

Study of the statistical physics bases on superstatistics from the β-fluctuated to the T-fluctuated form

NASA Astrophysics Data System (ADS)

Sargolzaeipor, S.; Hassanabadi, H.; Chung, W. S.

2018-04-01

In this paper, we study the T -fluctuated form of superstatistics. In this form, some thermodynamic quantities such as the Helmholtz energy, the entropy and the internal energy, are expressed in terms of the T -fluctuated form for a canonical ensemble. In addition, the partition functions in the formalism for 2-level and 3-level distributions are derived. Then we make use of the T -fluctuated superstatistics for a quantum harmonic oscillator problem and the thermal properties of the system for three statistics of the Bose-Einstein, Maxwell-Boltzmann and Fermi-Dirac statistics are calculated. The effect of the deformation parameter on these properties is examined. All the results recover the well-known results by removing the deformation parameter.

Dolan Grady relations and noncommutative quasi-exactly solvable systems

NASA Astrophysics Data System (ADS)

Klishevich, Sergey M.; Plyushchay, Mikhail S.

2003-11-01

We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the {\\mathfrak{su}}(2) and {\\mathfrak{sl}}(2,{\\bb {R}}) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems.

Adiabatic quantum computation along quasienergies

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

Tanaka, Atushi; Nemoto, Kae; National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda ku, Tokyo 101-8430

2010-02-15

The parametric deformations of quasienergies and eigenvectors of unitary operators are applied to the design of quantum adiabatic algorithms. The conventional, standard adiabatic quantum computation proceeds along eigenenergies of parameter-dependent Hamiltonians. By contrast, discrete adiabatic computation utilizes adiabatic passage along the quasienergies of parameter-dependent unitary operators. For example, such computation can be realized by a concatenation of parameterized quantum circuits, with an adiabatic though inevitably discrete change of the parameter. A design principle of adiabatic passage along quasienergy was recently proposed: Cheon's quasienergy and eigenspace anholonomies on unitary operators is available to realize anholonomic adiabatic algorithms [A. Tanaka and M.more » Miyamoto, Phys. Rev. Lett. 98, 160407 (2007)], which compose a nontrivial family of discrete adiabatic algorithms. It is straightforward to port a standard adiabatic algorithm to an anholonomic adiabatic one, except an introduction of a parameter |v>, which is available to adjust the gaps of the quasienergies to control the running time steps. In Grover's database search problem, the costs to prepare |v> for the qualitatively different (i.e., power or exponential) running time steps are shown to be qualitatively different.« less

Deformation dependence of proton decay rates and angular distributions in a time-dependent approach

NASA Astrophysics Data System (ADS)

Carjan, N.; Talou, P.; Strottman, D.

1998-12-01

A new, time-dependent, approach to proton decay from axially symmetric deformed nuclei is presented. The two-dimensional time-dependent Schrödinger equation for the interaction between the emitted proton and the rest of the nucleus is solved numerically for well defined initial quasi-stationary proton states. Applied to the hypothetical proton emission from excited states in deformed nuclei of 208Pb, this approach shows that the problem cannot be reduced to one dimension. There are in general more than one directions of emission with wide distributions around them, determined mainly by the quantum numbers of the initial wave function rather than by the potential landscape. The distribution of the "residual" angular momentum and its variation in time play a major role in the determination of the decay rate. In a couple of cases, no exponential decay was found during the calculated time evolution (2×10-21 sec) although more than half of the wave function escaped during that time.

Phase space deformations in phantom cosmology

NASA Astrophysics Data System (ADS)

López, J. L.; Sabido, M.; Yee-Romero, C.

2018-03-01

We discuss the physical consequences of general phase space deformations on the minisuperspace of phantom cosmology. Based on the principle of physically equivalent descriptions in the deformed theory, we investigate for what values of the deformation parameters the arising descriptions are physically equivalent. We also construct and solve the quantum model and derive the semiclassical dynamics.

Perturbative computation in a generalized quantum field theory

NASA Astrophysics Data System (ADS)

Bezerra, V. B.; Curado, E. M.; Rego-Monteiro, M. A.

2002-10-01

We consider a quantum field theory that creates at any point of the space-time particles described by a q-deformed Heisenberg algebra which is interpreted as a phenomenological quantum theory describing the scattering of spin-0 composed particles. We discuss the generalization of Wick's expansion for this case and we compute perturbatively the scattering 1+2-->1'+2' to second order in the coupling constant. The result we find shows that the structure of a composed particle, described here phenomenologically by the deformed algebraic structure, can modify in a simple but nontrivial way the perturbation expansion for the process under consideration.

A simple method for constructing the inhomogeneous quantum group IGLq(n) and its universal enveloping algebra Uq(igl(n))

NASA Astrophysics Data System (ADS)

Shariati, A.; Aghamohammadi, A.

1995-12-01

We propose a simple and concise method to construct the inhomogeneous quantum group IGLq(n) and its universal enveloping algebra Uq(igl(n)). Our technique is based on embedding an n-dimensional quantum space in an n+1-dimensional one as the set xn+1=1. This is possible only if one considers the multiparametric quantum space whose parameters are fixed in a specific way. The quantum group IGLq(n) is then the subset of GLq(n+1), which leaves the xn+1=1 subset invariant. For the deformed universal enveloping algebra Uq(igl(n)), we will show that it can also be embedded in Uq(gl(n+1)), provided one uses the multiparametric deformation of U(gl(n+1)) with a specific choice of its parameters.

Quantum information aspects of noncommutative quantum mechanics

NASA Astrophysics Data System (ADS)

Bertolami, Orfeu; Bernardini, Alex E.; Leal, Pedro

2018-01-01

Some fundamental aspects related with the construction of Robertson-Schrödinger-like uncertainty-principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum systems in the noncommutative phase-space. Some consequences of the deformed noncommutative algebra are also considered in physical systems of interest.

More on quantum groups from the quantization point of view

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

1994-12-01

Star products on the classical double group of a simple Lie group and on corresponding symplectic groupoids are given so that the quantum double and the “quantized tangent bundle” are obtained in the deformation description. “Complex” quantum groups and bicovariant quantum Lie algebras are discussed from this point of view. Further we discuss the quantization of the Poisson structure on the symmetric algebra S(g) leading to the quantized enveloping algebra U h (g) as an example of biquantization in the sense of Turaev. Description of U h (g) in terms of the generators of the bicovariant differential calculus on F(G q ) is very convenient for this purpose. Finaly we interpret in the deformation framework some well known properties of compact quantum groups as simple consequences of corresponding properties of classical compact Lie groups. An analogue of the classical Kirillov's universal character formula is given for the unitary irreducble representation in the compact case.

Hypersurface-deformation algebroids and effective spacetime models

NASA Astrophysics Data System (ADS)

Bojowald, Martin; Büyükçam, Umut; Brahma, Suddhasattwa; D'Ambrosio, Fabio

2016-11-01

In canonical gravity, covariance is implemented by brackets of hypersurface-deformation generators forming a Lie algebroid. Lie-algebroid morphisms, therefore, allow one to relate different versions of the brackets that correspond to the same spacetime structure. An application to examples of modified brackets found mainly in models of loop quantum gravity can, in some cases, map the spacetime structure back to the classical Riemannian form after a field redefinition. For one type of quantum corrections (holonomies), signature change appears to be a generic feature of effective spacetime, and it is shown here to be a new quantum spacetime phenomenon which cannot be mapped to an equivalent classical structure. In low-curvature regimes, our constructions not only prove the existence of classical spacetime structures assumed elsewhere in models of loop quantum cosmology, they also show the existence of additional quantum corrections that have not always been included.

Fractional quantum Hall effect in strained graphene: Stability of Laughlin states in disordered pseudomagnetic fields

NASA Astrophysics Data System (ADS)

Bagrov, Andrey A.; Principi, Alessandro; Katsnelson, Mikhail I.

2017-03-01

We address the question of the stability of the fractional quantum Hall effect in the presence of pseudomagnetic disorder generated by mechanical deformations of a graphene sheet. Neglecting the potential disorder and taking into account only strain-induced random pseudomagnetic fields, it is possible to write down a Laughlin-like trial ground-state wave function explicitly. Exploiting the Laughlin plasma analogy, we demonstrate that in the case of fluctuating pseudomagnetic fluxes of a relatively small amplitude, the fractional quantum Hall effect is always stable upon the deformations. By contrast, in the case of bubble-induced pseudomagnetic fields in graphene on a substrate (a small number of large fluxes) the disorder can be strong enough to cause a glass transition in the corresponding classical Coulomb plasma, resulting in the destruction of the fractional quantum Hall regime and in a quantum phase transition to a nonergodic state of the lowest Landau level.

Quantum-corrected Geometry of Horizon Vicinity

NASA Astrophysics Data System (ADS)

Park, I. Y.

2017-12-01

We study the deformation of the horizon-vicinity geometry caused by quantum gravitational effects. Departure from the semi-classical picture is noted, and the fact that the matter part of the action comes at a higher order in Newton's constant than does the Einstein-Hilbert term is crucial for the departure. The analysis leads to a Firewall-type energy measured by an infalling observer for which quantum generation of the cosmological constant is critical. The analysis seems to suggest that the Firewall should be a part of such deformation and that the information be stored both in the horizon-vicinity and asymptotic boundary region. We also examine the behavior near the cosmological horizon.

Quantum corrections to newtonian potential and generalized uncertainty principle

NASA Astrophysics Data System (ADS)

Scardigli, Fabio; Lambiase, Gaetano; Vagenas, Elias

2017-08-01

We use the leading quantum corrections to the newtonian potential to compute the deformation parameter of the generalized uncertainty principle. By assuming just only General Relativity as theory of Gravitation, and the thermal nature of the GUP corrections to the Hawking spectrum, our calculation gives, to first order, a specific numerical result. We briefly discuss the physical meaning of this value, and compare it with the previously obtained bounds on the generalized uncertainty principle deformation parameter.

Hidden symmetries for ellipsoid-solitonic deformations of Kerr-Sen black holes and quantum anomalies

NASA Astrophysics Data System (ADS)

Vacaru, Sergiu I.

2013-02-01

We prove the existence of hidden symmetries in the general relativity theory defined by exact solutions with generic off-diagonal metrics, nonholonomic (non-integrable) constraints, and deformations of the frame and linear connection structure. A special role in characterization of such spacetimes is played by the corresponding nonholonomic generalizations of Stackel-Killing and Killing-Yano tensors. There are constructed new classes of black hole solutions and we study hidden symmetries for ellipsoidal and/or solitonic deformations of "prime" Kerr-Sen black holes into "target" off-diagonal metrics. In general, the classical conserved quantities (integrable and not-integrable) do not transfer to the quantized systems and produce quantum gravitational anomalies. We prove that such anomalies can be eliminated via corresponding nonholonomic deformations of fundamental geometric objects (connections and corresponding Riemannian and Ricci tensors) and by frame transforms.

Moduli space potentials for heterotic non-Abelian flux tubes: Weak deformation

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

Shifman, M.; Yung, A.; Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg 188300

2010-09-15

We consider N=2 supersymmetric QCD with the U(N) gauge group (with no Fayet-Iliopoulos term) and N{sub f} flavors of massive quarks deformed by the mass term {mu} for the adjoint matter, W={mu}A{sup 2}, assuming that N{<=}N{sub f}<2N. This deformation breaks N=2 supersymmetry down to N=1. This theory supports non-Abelian flux tubes (strings) which are stabilized by W. They are referred to as F-term stabilized strings. We focus on the studies of such strings in the vacuum in which N squarks condense, at small {mu}, so that the Z{sub N} strings preserve, in a sense, their Bogomol'nyi-Prasad-Sommerfield nature. The (s)quark massesmore » are assumed to be nondegenerate. We calculate string tensions both in the classical and quantum regimes. Then we translate our results for the tensions in terms of the effective low-energy weighted CP(N{sub f}-1) model on the string world sheet. The bulk {mu} deformation makes this theory N=(0,2) supersymmetric heterotic weighted CP(N{sub f}-1) model in two dimensions. We find the deformation potential on the world sheet. This significantly expands the class of the heterotically deformed CP models emerging on the string world sheet compared to that suggested by Edalati and Tong. Among other things, we show that nonperturbative quantum effects in the bulk theory are exactly reproduced by the quantum effects in the world-sheet theory.« less

Generalized Quantum Field Theory Based on a Nonlinear Deformed Heisenberg Algebra

NASA Astrophysics Data System (ADS)

Ribeiro-Silva, C. I.; Oliveira-Neto, N. M.

We consider a quantum field theory based on a nonlinear Heisenberg algebra which describes phenomenologically a composite particle. Perturbative computation, considering the λϕ4 interaction was done and we also performed some comparison with a quantum field theory based on the q-oscillator algebra.

Generalization of multifractal theory within quantum calculus

NASA Astrophysics Data System (ADS)

Olemskoi, A.; Shuda, I.; Borisyuk, V.

2010-03-01

On the basis of the deformed series in quantum calculus, we generalize the partition function and the mass exponent of a multifractal, as well as the average of a random variable distributed over a self-similar set. For the partition function, such expansion is shown to be determined by binomial-type combinations of the Tsallis entropies related to manifold deformations, while the mass exponent expansion generalizes the known relation τq=Dq(q-1). We find the equation for the set of averages related to ordinary, escort, and generalized probabilities in terms of the deformed expansion as well. Multifractals related to the Cantor binomial set, exchange currency series, and porous-surface condensates are considered as examples.

GUP parameter from quantum corrections to the Newtonian potential

NASA Astrophysics Data System (ADS)

Scardigli, Fabio; Lambiase, Gaetano; Vagenas, Elias C.

2017-04-01

We propose a technique to compute the deformation parameter of the generalized uncertainty principle by using the leading quantum corrections to the Newtonian potential. We just assume General Relativity as theory of Gravitation, and the thermal nature of the GUP corrections to the Hawking spectrum. With these minimal assumptions our calculation gives, to first order, a specific numerical result. The physical meaning of this value is discussed, and compared with the previously obtained bounds on the generalized uncertainty principle deformation parameter.

Bialgebra deformations and algebras of trees

NASA Technical Reports Server (NTRS)

Grossman, Robert; Radford, David

1991-01-01

Let A denote a bialgebra over a field k and let A sub t = A((t)) denote the ring of formal power series with coefficients in A. Assume that A is also isomorphic to a free, associative algebra over k. A simple construction is given which makes A sub t a bialgebra deformation of A. In typical applications, A sub t is neither commutative nor cocommutative. In the terminology of Drinfeld, (1987), A sub t is a quantum group. This construction yields quantum groups associated with families of trees.

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition

DOE PAGES

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar; ...

2016-09-08

We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on R 1,d-1. We show that in addition to the usual boost generator, there is a contribution to the modular Hamiltonian at first order in the shape deformation, proportional to the integral of the null components of the stress tensor along the Rindler horizon. We use this fact along with monotonicity of relative entropy to prove the averaged null energy condition in Minkowski space-time. This subsequently gives a new proof of the Hofman-Maldacena bounds on the parameters appearing in CFT three-point functions. Ourmore » main technical advance involves adapting newly developed perturbative methods for calculating entanglement entropy to the problem at hand. Our methods were recently used to prove certain results on the shape dependence of entanglement in CFTs and here we generalize these results to excited states and real time dynamics. Finally, we discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.« less

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition

NASA Astrophysics Data System (ADS)

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar; Wang, Huajia

2016-09-01

We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on {{R}}^{1,d-1} . We show that in addition to the usual boost generator, there is a contribution to the modular Hamiltonian at first order in the shape deformation, proportional to the integral of the null components of the stress tensor along the Rindler horizon. We use this fact along with monotonicity of relative entropy to prove the averaged null energy condition in Minkowski space-time. This subsequently gives a new proof of the Hofman-Maldacena bounds on the parameters appearing in CFT three-point functions. Our main technical advance involves adapting newly developed perturbative methods for calculating entanglement entropy to the problem at hand. These methods were recently used to prove certain results on the shape dependence of entanglement in CFTs and here we generalize these results to excited states and real time dynamics. We also discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.

Modular Hamiltonians for deformed half-spaces and the averaged null energy condition

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

Faulkner, Thomas; Leigh, Robert G.; Parrikar, Onkar

We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on R 1,d-1. We show that in addition to the usual boost generator, there is a contribution to the modular Hamiltonian at first order in the shape deformation, proportional to the integral of the null components of the stress tensor along the Rindler horizon. We use this fact along with monotonicity of relative entropy to prove the averaged null energy condition in Minkowski space-time. This subsequently gives a new proof of the Hofman-Maldacena bounds on the parameters appearing in CFT three-point functions. Ourmore » main technical advance involves adapting newly developed perturbative methods for calculating entanglement entropy to the problem at hand. Our methods were recently used to prove certain results on the shape dependence of entanglement in CFTs and here we generalize these results to excited states and real time dynamics. Finally, we discuss the AdS/CFT counterpart of this result, making connection with the recently proposed gravitational dual for modular Hamiltonians in holographic theories.« less

Yang Baxter and anisotropic sigma and lambda models, cyclic RG and exact S-matrices

NASA Astrophysics Data System (ADS)

Appadu, Calan; Hollowood, Timothy J.; Price, Dafydd; Thompson, Daniel C.

2017-09-01

Integrable deformation of SU(2) sigma and lambda models are considered at the classical and quantum levels. These are the Yang-Baxter and XXZ-type anisotropic deformations. The XXZ type deformations are UV safe in one regime, while in another regime, like the Yang-Baxter deformations, they exhibit cyclic RG behaviour. The associ-ated affine quantum group symmetry, realized classically at the Poisson bracket level, has q a complex phase in the UV safe regime and q real in the cyclic RG regime, where q is an RG invariant. Based on the symmetries and RG flow we propose exact factorizable S-matrices to describe the scattering of states in the lambda models, from which the sigma models follow by taking a limit and non-abelian T-duality. In the cyclic RG regimes, the S-matrices are periodic functions of rapidity, at large rapidity, and in the Yang-Baxter case violate parity.

q-Derivatives, quantization methods and q-algebras

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

Twarock, Reidun

1998-12-15

Using the example of Borel quantization on S{sup 1}, we discuss the relation between quantization methods and q-algebras. In particular, it is shown that a q-deformation of the Witt algebra with generators labeled by Z is realized by q-difference operators. This leads to a discrete quantum mechanics. Because of Z, the discretization is equidistant. As an approach to a non-equidistant discretization of quantum mechanics one can change the Witt algebra using not the number field Z as labels but a quadratic extension of Z characterized by an irrational number {tau}. This extension is denoted as quasi-crystal Lie algebra, because thismore » is a relation to one-dimensional quasicrystals. The q-deformation of this quasicrystal Lie algebra is discussed. It is pointed out that quasicrystal Lie algebras can be considered also as a 'deformed' Witt algebra with a 'deformation' of the labeling number field. Their application to the theory is discussed.« less

Multiple feature fusion via covariance matrix for visual tracking

NASA Astrophysics Data System (ADS)

Jin, Zefenfen; Hou, Zhiqiang; Yu, Wangsheng; Wang, Xin; Sun, Hui

2018-04-01

Aiming at the problem of complicated dynamic scenes in visual target tracking, a multi-feature fusion tracking algorithm based on covariance matrix is proposed to improve the robustness of the tracking algorithm. In the frame-work of quantum genetic algorithm, this paper uses the region covariance descriptor to fuse the color, edge and texture features. It also uses a fast covariance intersection algorithm to update the model. The low dimension of region covariance descriptor, the fast convergence speed and strong global optimization ability of quantum genetic algorithm, and the fast computation of fast covariance intersection algorithm are used to improve the computational efficiency of fusion, matching, and updating process, so that the algorithm achieves a fast and effective multi-feature fusion tracking. The experiments prove that the proposed algorithm can not only achieve fast and robust tracking but also effectively handle interference of occlusion, rotation, deformation, motion blur and so on.

Microscopic model of quasiparticle wave packets in superfluids, superconductors, and paired Hall states.

PubMed

Parameswaran, S A; Kivelson, S A; Shankar, R; Sondhi, S L; Spivak, B Z

2012-12-07

We study the structure of Bogoliubov quasiparticles, bogolons, the fermionic excitations of paired superfluids that arise from fermion (BCS) pairing, including neutral superfluids, superconductors, and paired quantum Hall states. The naive construction of a stationary quasiparticle in which the deformation of the pair field is neglected leads to a contradiction: it carries a net electrical current even though it does not move. However, treating the pair field self-consistently resolves this problem: in a neutral superfluid, a dipolar current pattern is associated with the quasiparticle for which the total current vanishes. When Maxwell electrodynamics is included, as appropriate to a superconductor, this pattern is confined over a penetration depth. For paired quantum Hall states of composite fermions, the Maxwell term is replaced by a Chern-Simons term, which leads to a dipolar charge distribution and consequently to a dipolar current pattern.

Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equations

NASA Astrophysics Data System (ADS)

He, Wei

2015-02-01

The Gauge/Bethe correspondence relates Omega-deformed N = 2 supersymmetric gauge theories to some quantum integrable models, in simple cases the integrable models can be treated as solvable quantum mechanics models. For SU(2) gauge theory with an adjoint matter, or with 4 fundamental matters, the potential of corresponding quantum model is the elliptic function. If the mass of matter takes special value then the potential is an elliptic solution of KdV hierarchy. We show that the deformed prepotential of gauge theory can be obtained from the average densities of conserved charges of the classical KdV solution, the UV gauge coupling dependence is assembled into the Eisenstein series. The gauge theory with adjoint mass is taken as the example.

Bilinear covariants and spinor fields duality in quantum Clifford algebras

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

Abłamowicz, Rafał, E-mail: rablamowicz@tntech.edu; Gonçalves, Icaro, E-mail: icaro.goncalves@ufabc.edu.br; Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-170 Santo André, SP

Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields, the duality between spinor and quantum spinor fields can be discussed. Thus, by endowing the underlying spacetime with an arbitrary bilinear form with an antisymmetric part in addition to a symmetric spacetime metric, quantum algebraic spinor fields and deformed bilinear covariants can be constructed. They are thus compared to the classical (non quantum) ones. Classes of quantum spinor fields classes are introduced and compared with Lounesto'smore » spinor field classification. A physical interpretation of the deformed parts and the underlying Z-grading is proposed. The existence of an arbitrary bilinear form endowing the spacetime already has been explored in the literature in the context of quantum gravity [S. W. Hawking, “The unpredictability of quantum gravity,” Commun. Math. Phys. 87, 395 (1982)]. Here, it is shown further to play a prominent role in the structure of Dirac, Weyl, and Majorana spinor fields, besides the most general flagpoles and flag-dipoles. We introduce a new duality between the standard and the quantum spinor fields, by showing that when Clifford algebras over vector spaces endowed with an arbitrary bilinear form are taken into account, a mixture among the classes does occur. Consequently, novel features regarding the spinor fields can be derived.« less

Thermodynamics of BTZ black holes in gravity’s rainbow

NASA Astrophysics Data System (ADS)

Alsaleh, Salwa

2017-05-01

In this paper, we deform the thermodynamics of a BTZ black hole from rainbow functions in gravity’s rainbow. The rainbow functions will be motivated from the results in loop quantum gravity and noncommutative geometry. It will be observed that the thermodynamics gets deformed due to these rainbow functions, indicating the existence of a remnant. However, the Gibbs free energy does not get deformed due to these rainbow functions, and so the critical behavior from Gibbs does not change by this deformation. This is because the deformation in the entropy cancels out the temperature deformation.

Parity Deformed Jaynes-Cummings Model: “Robust Maximally Entangled States”

PubMed Central

Dehghani, A.; Mojaveri, B.; Shirin, S.; Faseghandis, S. Amiri

2016-01-01

The parity-deformations of the quantum harmonic oscillator are used to describe the generalized Jaynes-Cummings model based on the λ-analog of the Heisenberg algebra. The behavior is interestingly that of a coupled system comprising a two-level atom and a cavity field assisted by a continuous external classical field. The dynamical characters of the system is explored under the influence of the external field. In particular, we analytically study the generation of robust and maximally entangled states formed by a two-level atom trapped in a lossy cavity interacting with an external centrifugal field. We investigate the influence of deformation and detuning parameters on the degree of the quantum entanglement and the atomic population inversion. Under the condition of a linear interaction controlled by an external field, the maximally entangled states may emerge periodically along with time evolution. In the dissipation regime, the entanglement of the parity deformed JCM are preserved more with the increase of the deformation parameter, i.e. the stronger external field induces better degree of entanglement. PMID:27917882

Topological BF Theories

NASA Astrophysics Data System (ADS)

Sǎraru, Silviu-Constantin

Topological field theories originate in the papers of Schwarz and Witten. Initially, Schwarz shown that one of the topological invariants, namely the Ray-Singer torsion, can be represented as the partition function of a certain quantum field theory. Subsequently, Witten constructed a framework for understanding Morse theory in terms of supersymmetric quantum mechanics. These two constructions represent the prototypes of all topological field theories. The model used by Witten has been applied to classical index theorems and, moreover, suggested some generalizations that led to new mathematical results on holomorphic Morse inequalities. Starting with these results, further developments in the domain of topological field theories have been achieved. The Becchi-Rouet-Stora-Tyutin (BRST) symmetry allowed for a new definition of topological ...eld theories as theories whose BRST-invariant Hamiltonian is also BRST-exact. An important class of topological theories of Schwarz type is the class of BF models. This type of models describes three-dimensional quantum gravity and is useful at the study of four-dimensional quantum gravity in Ashtekar-Rovelli-Smolin formulation. Two-dimensional BF models are correlated to Poisson sigma models from various two-dimensional gravities. The analysis of Poisson sigma models, including their relationship to two-dimensional gravity and the study of classical solutions, has been intensively studied in the literature. In this thesis we approach the problem of construction of some classes of interacting BF models in the context of the BRST formalism. In view of this, we use the method of the deformation of the BRST charge and BRST-invariant Hamiltonian. Both methods rely on specific techniques of local BRST cohomology. The main hypotheses in which we construct the above mentioned interactions are: space-time locality, Poincare invariance, smoothness of deformations in the coupling constant and the preservation of the number of derivatives on each field. The first two hypotheses implies that the resulting interacting theory must be local in space-time and Poincare invariant. The smoothness of deformations means that the deformed objects that contribute to the construction of interactions must be smooth in the coupling constant and reduce to the objects corresponding to the free theory in the zero limit of the coupling constant. The preservation of the number of derivatives on each field imp! lies two aspects that must be simultaneously fulfilled: (i) the differential order of each free field equation must coincide with that of the corresponding interacting field equation; (ii) the maximum number of space-time derivatives from the interacting vertices cannot exceed the maximum number of derivatives from the free Lagrangian. The main results obtained can be synthesized into: obtaining self-interactions for certain classes of BF models; generation of couplings between some classes of BF theories and matter theories; construction of interactions between a class of BF models and a system of massless vector fields.

Quantum effect on the nucleation of plastic deformation carriers and destruction in crystals

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

Khon, Yury A., E-mail: khon@ispms.tsc.ru; Kaminskii, Petr P., E-mail: ppk@ispms.tsc.ru

2015-10-27

New concepts on the irreversible crystal deformation as a structure transformation caused by a change in interatomic interactions at fluctuations of the electron density under loading are described. The change in interatomic interactions lead to the excitation of dynamical displacements of atoms. A model and a theory of a deformable pristine crystal taking into account the excitation of thermally activated and dynamical displacements of atoms are suggested. New mechanisms of the nucleation of plastic deformation carriers and destruction in pristine crystals at the real value of the deforming stress are studied.

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

Kawaguchi, Io; Yoshida, Kentaroh

We proceed to study infinite-dimensional symmetries in two-dimensional squashed Wess-Zumino-Novikov-Witten models at the classical level. The target space is given by squashed S³ and the isometry is SU(2){sub L}×U(1){sub R}. It is known that SU(2){sub L} is enhanced to a couple of Yangians. We reveal here that an infinite-dimensional extension of U(1){sub R} is a deformation of quantum affine algebra, where a new deformation parameter is provided with the coefficient of the Wess-Zumino term. Then we consider the relation between the deformed quantum affine algebra and the pair of Yangians from the viewpoint of the left-right duality of monodromy matrices.more » The integrable structure is also discussed by computing the r/s-matrices that satisfy the extended classical Yang-Baxter equation. Finally, two degenerate limits are discussed.« less

Scalar field propagation in the ϕ 4 κ-Minkowski model

NASA Astrophysics Data System (ADS)

Meljanac, S.; Samsarov, A.; Trampetić, J.; Wohlgenannt, M.

2011-12-01

In this article we use the noncommutative (NC) κ-Minkowski ϕ 4 model based on the κ-deformed star product, (★ h ). The action is modified by expanding up to linear order in the κ-deformation parameter a, producing an effective model on commutative spacetime. For the computation of the tadpole diagram contributions to the scalar field propagation/self-energy, we anticipate that statistics on the κ-Minkowski is specifically κ-deformed. Thus our prescription in fact represents hybrid approach between standard quantum field theory (QFT) and NCQFT on the κ-deformed Minkowski spacetime, resulting in a κ-effective model. The propagation is analyzed in the framework of the two-point Green's function for low, intermediate, and for the Planckian propagation energies, respectively. Semiclassical/hybrid behavior of the first order quantum correction do show up due to the κ-deformed momentum conservation law. For low energies, the dependence of the tadpole contribution on the deformation parameter a drops out completely, while for Planckian energies, it tends to a fixed finite value. The mass term of the scalar field is shifted and these shifts are very different at different propagation energies. At the Planck-ian energies we obtain the direction dependent κ-modified dispersion relations. Thus our κ-effective model for the massive scalar field shows a birefringence effect.

On a Class of Hairy Square Barriers and Gamow Vectors

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

Fernandez-Garcia, N.

The second order Darboux-Gamow transformation is applied to deform square one dimensional barriers in non-relativistic quantum mechanics. The initial and the new 'hairy' potentials have the same transmission probabilities (for the appropriate parameters). In general, new Gamow vectors are constructed as Darboux deformations of the initial ones.

Real lasers and other deformed objects

NASA Technical Reports Server (NTRS)

Solomon, Allan I.

1995-01-01

In this talk we re-examine three important properties of quantum laser systems: (1) photon counting statistics; (2) squeezing; and (3) signal-to-quantum noise ratio. None of these phenomena depends on the choice of hamiltonian; indeed, we analyze them initially without restriction to any specific form of the commutation relations.

Approximation solution of Schrodinger equation for Q-deformed Rosen-Morse using supersymmetry quantum mechanics (SUSY QM)

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

Alemgadmi, Khaled I. K., E-mail: azozkied@yahoo.com; Suparmi; Cari

2015-09-30

The approximate analytical solution of Schrodinger equation for Q-Deformed Rosen-Morse potential was investigated using Supersymmetry Quantum Mechanics (SUSY QM) method. The approximate bound state energy is given in the closed form and the corresponding approximate wave function for arbitrary l-state given for ground state wave function. The first excited state obtained using upper operator and ground state wave function. The special case is given for the ground state in various number of q. The existence of Rosen-Morse potential reduce energy spectra of system. The larger value of q, the smaller energy spectra of system.

ZnO nanostructures with different morphology for enhanced photocatalytic activity

NASA Astrophysics Data System (ADS)

Peter, I. John; Praveen, E.; Vignesh, G.; Nithiananthi, P.

2017-12-01

ZnO nanomaterials of different morphologies have been synthesized and the effect of morphology on Photocatalytic activity on natural dye has been investigated. Crystalline size and lattice strain of the synthesized particles are determined by XRD analysis and Williamson-Hall (W-H) method respectively. All other important physical parameters such as strain, stress and energy density values are also calculated using W-H analysis using different models such as uniform deformation model, uniform deformation stress model and uniform deformation energy density model. A shift in the peak of FTIR spectrum of ZnO is observed due to morphology effects. The SEM analysis reveals that the synthesized ZnO nanoparticles appear as flake, rod and dot. ZnO quantum dot exhibits higher photocatalytic activity comparing to the other morphologies. Larger surface area, high adsorption rate, large charge separation and the slow recombination of electrons/holes in ZnO dots establish dots as favorable morphology for good photocatalysis. Among the three, ZnO quantum dot shows three-times enhancement in the kinetic rate constants of photocatalysis. The results confirm that availability of specific (active) surface area, photocatalytic potential and quantum confinement of photo-induced carriers differ with morphology.

Noncommutative spherically symmetric spacetimes at semiclassical order

NASA Astrophysics Data System (ADS)

Fritz, Christopher; Majid, Shahn

2017-07-01

Working within the recent formalism of Poisson-Riemannian geometry, we completely solve the case of generic spherically symmetric metric and spherically symmetric Poisson-bracket to find a unique answer for the quantum differential calculus, quantum metric and quantum Levi-Civita connection at semiclassical order O(λ) . Here λ is the deformation parameter, plausibly the Planck scale. We find that r, t, d r, d t are all forced to be central, i.e. undeformed at order λ, while for each value of r, t we are forced to have a fuzzy sphere of radius r with a unique differential calculus which is necessarily nonassociative at order λ2 . We give the spherically symmetric quantisation of the FLRW cosmology in detail and also recover a previous analysis for the Schwarzschild black hole, now showing that the quantum Ricci tensor for the latter vanishes at order λ. The quantum Laplace-Beltrami operator for spherically symmetric models turns out to be undeformed at order λ while more generally in Poisson-Riemannian geometry we show that it deforms to □f+λ2ωαβ(Ricγα-Sγα)(∇^βdf)γ+O(λ2) in terms of the classical Levi-Civita connection \\widehat\

Quantum criticality and duality in the Sachdev-Ye-Kitaev/AdS2 chain

NASA Astrophysics Data System (ADS)

Jian, Shao-Kai; Xian, Zhuo-Yu; Yao, Hong

2018-05-01

We show that the quantum critical point (QCP) between a diffusive metal and ferromagnetic (or antiferromagnetic) phases in the SYK chain has a gravitational description corresponding to the double-trace deformation in an AdS2 chain. Specifically, by studying a double-trace deformation of a Z2 scalar in an AdS2 chain where the Z2 scalar is dual to the order parameter in the SYK chain, we find that the susceptibility and renormalization group equation describing the QCP in the SYK chain can be exactly reproduced in the holographic model. Our results suggest that the infrared geometry in the gravity theory dual to the diffusive metal of the SYK chain is also an AdS2 chain. We further show that the transition in SYK model captures universal information about double-trace deformation in generic black holes with near horizon AdS2 space-time.

Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries

NASA Astrophysics Data System (ADS)

Meljanac, Daniel; Meljanac, Stjepan; Pikutić, Danijel

2017-12-01

Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincaré-Weyl generators or gl(n) generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) κ -Minkowski spaces and (iii) κ -Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and non-commutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed.

Half-Lives of Proton Emitters With a Deformed Density-Dependent Model

NASA Astrophysics Data System (ADS)

Qian, Yi-Bin; Ren, Zhong-Zhou; Ni, Dong-Dong; Sheng, Zong-Qiang

2010-11-01

Half-lives of proton radioactivity are investigated with a deformed density-dependent model. The single folding potential which is dependent on deformation and orientation is employed to calculate the proton decay width through the deformed potential barrier. In addition, the spectroscopic factor is taken into account in the calculation, which is obtained in the relativistic mean field theory with NL3. The calculated results of semi-spherical nuclei are found to be in good agreement with the experimental data, and the results of well-deformed nuclei are also satisfactory. Moreover, a formula for the spherical proton emission half-life based on the Gamow quantum tunneling theory is presented.

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

Choudhury, Sourav; Das, Tushar Kanti; Chatterjee, Prasanta

The influence of exchange-correlation potential, quantum Bohm term, and degenerate pressure on the nature of solitary waves in a quantum semiconductor plasma is investigated. It is found that an amplitude and a width of the solitary waves change with variation of different parameters for different semiconductors. A deformed Korteweg-de Vries equation is obtained for propagation of nonlinear waves in a quantum semiconductor plasma, and the effects of different plasma parameters on the solution of the equation are also presented.

Deformed quantum double realization of the toric code and beyond

NASA Astrophysics Data System (ADS)

Padmanabhan, Pramod; Ibieta-Jimenez, Juan Pablo; Bernabe Ferreira, Miguel Jorge; Teotonio-Sobrinho, Paulo

2016-09-01

Quantum double models, such as the toric code, can be constructed from transfer matrices of lattice gauge theories with discrete gauge groups and parametrized by the center of the gauge group algebra and its dual. For general choices of these parameters the transfer matrix contains operators acting on links which can also be thought of as perturbations to the quantum double model driving it out of its topological phase and destroying the exact solvability of the quantum double model. We modify these transfer matrices with perturbations and extract exactly solvable models which remain in a quantum phase, thus nullifying the effect of the perturbation. The algebra of the modified vertex and plaquette operators now obey a deformed version of the quantum double algebra. The Abelian cases are shown to be in the quantum double phase whereas the non-Abelian phases are shown to be in a modified phase of the corresponding quantum double phase. These are illustrated with the groups Zn and S3. The quantum phases are determined by studying the excitations of these systems namely their fusion rules and the statistics. We then go further to construct a transfer matrix which contains the other Z2 phase namely the double semion phase. More generally for other discrete groups these transfer matrices contain the twisted quantum double models. These transfer matrices can be thought of as being obtained by introducing extra parameters into the transfer matrix of lattice gauge theories. These parameters are central elements belonging to the tensor products of the algebra and its dual and are associated to vertices and volumes of the three dimensional lattice. As in the case of the lattice gauge theories we construct the operators creating the excitations in this case and study their braiding and fusion properties.

Bell's Inequalities, Superquantum Correlations, and String Theory

DOE PAGES

Chang, Lay Nam; Lewis, Zachary; Minic, Djordje; ...

2011-01-01

We offermore » an interpretation of superquantum correlations in terms of a “doubly” quantum theory. We argue that string theory, viewed as a quantum theory with two deformation parameters, the string tension α ' , and the string coupling constant g s , is such a superquantum theory that transgresses the usual quantum violations of Bell's inequalities. We also discuss the ℏ → ∞ limit of quantum mechanics in this context. As a superquantum theory, string theory should display distinct experimentally observable supercorrelations of entangled stringy states.« less

Numerical analysis of some problems related to the mechanics of pneumatic tires: Finite deformation/rolling contact of a viscoelastic cylinder and finite deformation of cord-reinforced rubber composites

NASA Technical Reports Server (NTRS)

Oden, J. T.; Becker, E. B.; Lin, T. L.; Hsieh, K. T.

1984-01-01

The formulation and numerical analysis of several problems related to the behavior of pneumatic tires are considered. These problems include the general rolling contact problem of a rubber-like viscoelastic cylinder undergoing finite deformations and the finite deformation of cord-reinforced rubber composites. New finite element models are developed for these problems. Numerical results obtained for several representative cases are presented.

Two-dimensional character of internal rotation of furfural and other five-member heterocyclic aromatic aldehydes

NASA Astrophysics Data System (ADS)

Bataev, Vadim A.; Pupyshev, Vladimir I.; Godunov, Igor A.

2016-05-01

The features of nuclear motion corresponding to the rotation of the formyl group (CHO) are studied for the molecules of furfural and some other five-member heterocyclic aromatic aldehydes by the use of MP2/6-311G** quantum chemical approximation. It is demonstrated that the traditional one-dimensional models of internal rotation for the molecules studied have only limited applicability. The reason is the strong kinematic interaction of the rotation of the CHO group and out-of-plane CHO deformation that is realized for the molecules under consideration. The computational procedure based on the two-dimensional approximation is considered for low lying vibrational states as more adequate to the problem.

On coherent states for the simplest quantum groups

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

1991-01-01

The coherent states for the simplest quantum groups ( q-Heisenberg-Weyl, SU q (2) and the discrete series of representations of SU q (1, 1)) are introduced and their properties investigated. The corresponding analytic representations, path integrals, and q-deformation of Berezin's quantization on ℂ, a sphere, and the Lobatchevsky plane are discussed.

Estimation of the Young’s modulus of cellulose Iß by MM3 and quantum mechanics

USDA-ARS?s Scientific Manuscript database

Young’s modulus provides a measure of the resistance to deformation of an elastic material. In this study, modulus estimations for models of cellulose Iß relied on calculations performed with molecular mechanics (MM) and quantum mechanics (QM) programs. MM computations used the second generation emp...

Hadamard States for the Linearized Yang-Mills Equation on Curved Spacetime

NASA Astrophysics Data System (ADS)

Gérard, C.; Wrochna, M.

2015-07-01

We construct Hadamard states for the Yang-Mills equation linearized around a smooth, space-compact background solution. We assume the spacetime is globally hyperbolic and its Cauchy surface is compact or equal . We first consider the case when the spacetime is ultra-static, but the background solution depends on time. By methods of pseudodifferential calculus we construct a parametrix for the associated vectorial Klein-Gordon equation. We then obtain Hadamard two-point functions in the gauge theory, acting on Cauchy data. A key role is played by classes of pseudodifferential operators that contain microlocal or spectral type low-energy cutoffs. The general problem is reduced to the ultra-static spacetime case using an extension of the deformation argument of Fulling, Narcowich and Wald. As an aside, we derive a correspondence between Hadamard states and parametrices for the Cauchy problem in ordinary quantum field theory.

Hidden Entanglement and Unitarity at the Planck Scale

NASA Astrophysics Data System (ADS)

Arzano, Michele; Hamma, Alioscia; Severini, Simone

Attempts to go beyond the framework of local quantum field theory include scenarios in which the action of external symmetries on the quantum fields Hilbert space is deformed. We show how the Fock spaces of such theories exhibit a richer structure in their multi-particle sectors. When the deformation scale is proportional to the Planck energy, such new structure leads to the emergence of a "planckian" mode-entanglement, invisible to an observer that cannot probe the Planck scale. To the same observer, certain unitary processes would appear non-unitary. We show how entanglement transfer to the additional degrees of freedom can provide a potential way out of the black hole information paradox.

The anelastic Ericksen problem: universal eigenstrains and deformations in compressible isotropic elastic solids.

PubMed

Yavari, Arash; Goriely, Alain

2016-12-01

The elastic Ericksen problem consists of finding deformations in isotropic hyperelastic solids that can be maintained for arbitrary strain-energy density functions. In the compressible case, Ericksen showed that only homogeneous deformations are possible. Here, we solve the anelastic version of the same problem, that is, we determine both the deformations and the eigenstrains such that a solution to the anelastic problem exists for arbitrary strain-energy density functions. Anelasticity is described by finite eigenstrains. In a nonlinear solid, these eigenstrains can be modelled by a Riemannian material manifold whose metric depends on their distribution. In this framework, we show that the natural generalization of the concept of homogeneous deformations is the notion of covariantly homogeneous deformations -deformations with covariantly constant deformation gradients. We prove that these deformations are the only universal deformations and that they put severe restrictions on possible universal eigenstrains . We show that, in a simply-connected body, for any distribution of universal eigenstrains the material manifold is a symmetric Riemannian manifold and that in dimensions 2 and 3 the universal eigenstrains are zero-stress.

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.

Advances in Quantum Mechanochemistry: Electronic Structure Methods and Force Analysis.

PubMed

Stauch, Tim; Dreuw, Andreas

2016-11-23

In quantum mechanochemistry, quantum chemical methods are used to describe molecules under the influence of an external force. The calculation of geometries, energies, transition states, reaction rates, and spectroscopic properties of molecules on the force-modified potential energy surfaces is the key to gain an in-depth understanding of mechanochemical processes at the molecular level. In this review, we present recent advances in the field of quantum mechanochemistry and introduce the quantum chemical methods used to calculate the properties of molecules under an external force. We place special emphasis on quantum chemical force analysis tools, which can be used to identify the mechanochemically relevant degrees of freedom in a deformed molecule, and spotlight selected applications of quantum mechanochemical methods to point out their synergistic relationship with experiments.

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

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.

Study of phase transition of even and odd nuclei based on q-deforme SU(1,1) algebraic model

NASA Astrophysics Data System (ADS)

Jafarizadeh, M. A.; Amiri, N.; Fouladi, N.; Ghapanvari, M.; Ranjbar, Z.

2018-04-01

The q-deformed Hamiltonian for the SO (6) ↔ U (5) transitional case in s, d interaction boson model (IBM) can be constructed by using affine SUq (1 , 1) Lie algebra in the both IBM-1 and 2 versions and IBFM. In this research paper, we have studied the energy spectra of 120-128Xe isotopes and 123-131Xe isotopes and B(E2) transition probabilities of 120-128Xe isotopes in the shape phase transition region between the spherical and gamma unstable deformed shapes of the theory of quantum deformation. The theoretical results agree with the experimental data fairly well. It is shown that the q-deformed SO (6) ↔ U (5) transitional dynamical symmetry remains after deformation.

Generalized uncertainty principles and quantum field theory

NASA Astrophysics Data System (ADS)

Husain, Viqar; Kothawala, Dawood; Seahra, Sanjeev S.

2013-01-01

Quantum mechanics with a generalized uncertainty principle arises through a representation of the commutator [x^,p^]=if(p^). We apply this deformed quantization to free scalar field theory for f±=1±βp2. The resulting quantum field theories have a rich fine scale structure. For small wavelength modes, the Green’s function for f+ exhibits a remarkable transition from Lorentz to Galilean invariance, whereas for f- such modes effectively do not propagate. For both cases Lorentz invariance is recovered at long wavelengths.

Effects of quantum noise in 4D-CT on deformable image registration and derived ventilation data

NASA Astrophysics Data System (ADS)

Latifi, Kujtim; Huang, Tzung-Chi; Feygelman, Vladimir; Budzevich, Mikalai M.; Moros, Eduardo G.; Dilling, Thomas J.; Stevens, Craig W.; van Elmpt, Wouter; Dekker, Andre; Zhang, Geoffrey G.

2013-11-01

Quantum noise is common in CT images and is a persistent problem in accurate ventilation imaging using 4D-CT and deformable image registration (DIR). This study focuses on the effects of noise in 4D-CT on DIR and thereby derived ventilation data. A total of six sets of 4D-CT data with landmarks delineated in different phases, called point-validated pixel-based breathing thorax models (POPI), were used in this study. The DIR algorithms, including diffeomorphic morphons (DM), diffeomorphic demons (DD), optical flow and B-spline, were used to register the inspiration phase to the expiration phase. The DIR deformation matrices (DIRDM) were used to map the landmarks. Target registration errors (TRE) were calculated as the distance errors between the delineated and the mapped landmarks. Noise of Gaussian distribution with different standard deviations (SD), from 0 to 200 Hounsfield Units (HU) in amplitude, was added to the POPI models to simulate different levels of quantum noise. Ventilation data were calculated using the ΔV algorithm which calculates the volume change geometrically based on the DIRDM. The ventilation images with different added noise levels were compared using Dice similarity coefficient (DSC). The root mean square (RMS) values of the landmark TRE over the six POPI models for the four DIR algorithms were stable when the noise level was low (SD <150 HU) and increased with added noise when the level is higher. The most accurate DIR was DD with a mean RMS of 1.5 ± 0.5 mm with no added noise and 1.8 ± 0.5 mm with noise (SD = 200 HU). The DSC values between the ventilation images with and without added noise decreased with the noise level, even when the noise level was relatively low. The DIR algorithm most robust with respect to noise was DM, with mean DSC = 0.89 ± 0.01 and 0.66 ± 0.02 for the top 50% ventilation volumes, as compared between 0 added noise and SD = 30 and 200 HU, respectively. Although the landmark TRE were stable with low noise, the differences between ventilation images increased with noise level, even when the noise was low, indicating ventilation imaging from 4D-CT was sensitive to image noise. Therefore, high quality 4D-CT is essential for accurate ventilation images.

Non-geometric fluxes, quasi-Hopf twist deformations, and nonassociative quantum mechanics

NASA Astrophysics Data System (ADS)

Mylonas, Dionysios; Schupp, Peter; Szabo, Richard J.

2014-12-01

We analyse the symmetries underlying nonassociative deformations of geometry in non-geometric R-flux compactifications which arise via T-duality from closed strings with constant geometric fluxes. Starting from the non-abelian Lie algebra of translations and Bopp shifts in phase space, together with a suitable cochain twist, we construct the quasi-Hopf algebra of symmetries that deforms the algebra of functions and the exterior differential calculus in the phase space description of nonassociative R-space. In this setting, nonassociativity is characterised by the associator 3-cocycle which controls non-coassociativity of the quasi-Hopf algebra. We use abelian 2-cocycle twists to construct maps between the dynamical nonassociative star product and a family of associative star products parametrized by constant momentum surfaces in phase space. We define a suitable integration on these nonassociative spaces and find that the usual cyclicity of associative noncommutative deformations is replaced by weaker notions of 2-cyclicity and 3-cyclicity. Using this star product quantization on phase space together with 3-cyclicity, we formulate a consistent version of nonassociative quantum mechanics, in which we calculate the expectation values of area and volume operators, and find coarse-graining of the string background due to the R-flux.

Exploiting Quantum Resonance to Solve Combinatorial Problems

NASA Technical Reports Server (NTRS)

Zak, Michail; Fijany, Amir

2006-01-01

Quantum resonance would be exploited in a proposed quantum-computing approach to the solution of combinatorial optimization problems. In quantum computing in general, one takes advantage of the fact that an algorithm cannot be decoupled from the physical effects available to implement it. Prior approaches to quantum computing have involved exploitation of only a subset of known quantum physical effects, notably including parallelism and entanglement, but not including resonance. In the proposed approach, one would utilize the combinatorial properties of tensor-product decomposability of unitary evolution of many-particle quantum systems for physically simulating solutions to NP-complete problems (a class of problems that are intractable with respect to classical methods of computation). In this approach, reinforcement and selection of a desired solution would be executed by means of quantum resonance. Classes of NP-complete problems that are important in practice and could be solved by the proposed approach include planning, scheduling, search, and optimal design.

Affine q-deformed symmetry and the classical Yang-Baxter σ-model

NASA Astrophysics Data System (ADS)

Delduc, F.; Kameyama, T.; Magro, M.; Vicedo, B.

2017-03-01

The Yang-Baxter σ-model is an integrable deformation of the principal chiral model on a Lie group G. The deformation breaks the G × G symmetry to U(1)rank( G) × G. It is known that there exist non-local conserved charges which, together with the unbroken U(1)rank( G) local charges, form a Poisson algebra [InlineMediaObject not available: see fulltext.], which is the semiclassical limit of the quantum group {U}_q(g) , with g the Lie algebra of G. For a general Lie group G with rank( G) > 1, we extend the previous result by constructing local and non-local conserved charges satisfying all the defining relations of the infinite-dimensional Poisson algebra [InlineMediaObject not available: see fulltext.], the classical analogue of the quantum loop algebra {U}_q(Lg) , where Lg is the loop algebra of g. Quite unexpectedly, these defining relations are proved without encountering any ambiguity related to the non-ultralocality of this integrable σ-model.

Multiparticle states in deformed special relativity

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

Hossenfelder, S.

2007-05-15

We investigate the properties of multiparticle states in deformed special relativity (DSR). Starting from the Lagrangian formalism with an energy dependent metric, the conserved Noether current can be derived which is additive in the usual way. The integrated Noether current had previously been discarded as a conserved quantity, because it was correctly realized that it does no longer obey the DSR transformations. We identify the reason for this mismatch in the fact that DSR depends only on the extensive quantity of total four momentum instead of the energy-momentum densities as would be appropriate for a field theory. We argue thatmore » the reason for the failure of DSR to reproduce the standard transformation behavior in the well established limits is due to the missing sensitivity to the volume inside which energy is accumulated. We show that the soccer-ball problem is absent if one formulates DSR instead for the field densities. As a consequence, estimates for predicted effects have to be corrected by many orders of magnitude. Further, we derive that the modified quantum field theory implies a locality bound.« less

The anelastic Ericksen problem: universal eigenstrains and deformations in compressible isotropic elastic solids

PubMed Central

2016-01-01

The elastic Ericksen problem consists of finding deformations in isotropic hyperelastic solids that can be maintained for arbitrary strain-energy density functions. In the compressible case, Ericksen showed that only homogeneous deformations are possible. Here, we solve the anelastic version of the same problem, that is, we determine both the deformations and the eigenstrains such that a solution to the anelastic problem exists for arbitrary strain-energy density functions. Anelasticity is described by finite eigenstrains. In a nonlinear solid, these eigenstrains can be modelled by a Riemannian material manifold whose metric depends on their distribution. In this framework, we show that the natural generalization of the concept of homogeneous deformations is the notion of covariantly homogeneous deformations—deformations with covariantly constant deformation gradients. We prove that these deformations are the only universal deformations and that they put severe restrictions on possible universal eigenstrains. We show that, in a simply-connected body, for any distribution of universal eigenstrains the material manifold is a symmetric Riemannian manifold and that in dimensions 2 and 3 the universal eigenstrains are zero-stress. PMID:28119554

Study of Quantum Chaos in the Framework of Triaxial Rotator Models

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

Proskurins, J.; Bavrins, K.; Andrejevs, A.

2009-01-28

Dynamical quantum chaos criteria--a perturbed wave function entropy W({psi}{sub i}) and a fragmentation width {kappa}({phi}{sub k}) of basis states were studied in two cases of nuclear rigid triaxial rotator models. The first model is characterized by deformation angle {gamma} only, while the second model depends on both quadrupole deformation parameters ({beta},{gamma}). The degree of chaoticity has been determined in the studies of the dependence of criteria W({psi}{sub i}) and {kappa}({phi}{sub k}) from nuclear spin values up to I{<=}101 for model parameters {gamma} and ({beta},{gamma}) correspondingly. The transition from librational to rotational type energy spectra has been considered for both modelsmore » as well.« less

Friedreich's Ataxia

MedlinePlus

... and heart problems can be treated with medications. Orthopedic problems such as foot deformities and scoliosis can ... and heart problems can be treated with medications. Orthopedic problems such as foot deformities and scoliosis can ...

Efficient classical simulation of the Deutsch-Jozsa and Simon's algorithms

NASA Astrophysics Data System (ADS)

Johansson, Niklas; Larsson, Jan-Åke

2017-09-01

A long-standing aim of quantum information research is to understand what gives quantum computers their advantage. This requires separating problems that need genuinely quantum resources from those for which classical resources are enough. Two examples of quantum speed-up are the Deutsch-Jozsa and Simon's problem, both efficiently solvable on a quantum Turing machine, and both believed to lack efficient classical solutions. Here we present a framework that can simulate both quantum algorithms efficiently, solving the Deutsch-Jozsa problem with probability 1 using only one oracle query, and Simon's problem using linearly many oracle queries, just as expected of an ideal quantum computer. The presented simulation framework is in turn efficiently simulatable in a classical probabilistic Turing machine. This shows that the Deutsch-Jozsa and Simon's problem do not require any genuinely quantum resources, and that the quantum algorithms show no speed-up when compared with their corresponding classical simulation. Finally, this gives insight into what properties are needed in the two algorithms and calls for further study of oracle separation between quantum and classical computation.

Nonequilibrium dynamics of the O( N ) model on dS3 and AdS crunches

NASA Astrophysics Data System (ADS)

Kumar, S. Prem; Vaganov, Vladislav

2018-03-01

We study the nonperturbative quantum evolution of the interacting O( N ) vector model at large- N , formulated on a spatial two-sphere, with time dependent couplings which diverge at finite time. This model - the so-called "E-frame" theory, is related via a conformal transformation to the interacting O( N ) model in three dimensional global de Sitter spacetime with time independent couplings. We show that with a purely quartic, relevant deformation the quantum evolution of the E-frame model is regular even when the classical theory is rendered singular at the end of time by the diverging coupling. Time evolution drives the E-frame theory to the large- N Wilson-Fisher fixed point when the classical coupling diverges. We study the quantum evolution numerically for a variety of initial conditions and demonstrate the finiteness of the energy at the classical "end of time". With an additional (time dependent) mass deformation, quantum backreaction lowers the mass, with a putative smooth time evolution only possible in the limit of infinite quartic coupling. We discuss the relevance of these results for the resolution of crunch singularities in AdS geometries dual to E-frame theories with a classical gravity dual.

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

Two-dimensional character of internal rotation of furfural and other five-member heterocyclic aromatic aldehydes.

PubMed

Bataev, Vadim A; Pupyshev, Vladimir I; Godunov, Igor A

2016-05-15

The features of nuclear motion corresponding to the rotation of the formyl group (CHO) are studied for the molecules of furfural and some other five-member heterocyclic aromatic aldehydes by the use of MP2/6-311G** quantum chemical approximation. It is demonstrated that the traditional one-dimensional models of internal rotation for the molecules studied have only limited applicability. The reason is the strong kinematic interaction of the rotation of the CHO group and out-of-plane CHO deformation that is realized for the molecules under consideration. The computational procedure based on the two-dimensional approximation is considered for low lying vibrational states as more adequate to the problem. Copyright © 2016 Elsevier B.V. All rights reserved.

A case study in programming a quantum annealer for hard operational planning problems

NASA Astrophysics Data System (ADS)

Rieffel, Eleanor G.; Venturelli, Davide; O'Gorman, Bryan; Do, Minh B.; Prystay, Elicia M.; Smelyanskiy, Vadim N.

2015-01-01

We report on a case study in programming an early quantum annealer to attack optimization problems related to operational planning. While a number of studies have looked at the performance of quantum annealers on problems native to their architecture, and others have examined performance of select problems stemming from an application area, ours is one of the first studies of a quantum annealer's performance on parametrized families of hard problems from a practical domain. We explore two different general mappings of planning problems to quadratic unconstrained binary optimization (QUBO) problems, and apply them to two parametrized families of planning problems, navigation-type and scheduling-type. We also examine two more compact, but problem-type specific, mappings to QUBO, one for the navigation-type planning problems and one for the scheduling-type planning problems. We study embedding properties and parameter setting and examine their effect on the efficiency with which the quantum annealer solves these problems. From these results, we derive insights useful for the programming and design of future quantum annealers: problem choice, the mapping used, the properties of the embedding, and the annealing profile all matter, each significantly affecting the performance.

Ultrafast Independent N-H and N-C Bond Deformation Investigated with Resonant Inelastic X-Ray Scattering

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

Eckert, Sebastian; Norell, Jesper; Miedema, Piter S.

Here, the femtosecond excited-state dynamics following resonant photoexcitation enable the selective deformation of N-H and N-C chemical bonds in 2-thiopyridone in aqueous solution with optical or X-ray pulses. In combination with multiconfigurational quantum-chemical calculations, the orbital-specific electronic structure and its ultrafast dynamics accessed with resonant inelastic X-ray scattering at the N 1s level using synchrotron radiation and the soft X-ray free-electron laser LCLS provide direct evidence for this controlled photoinduced molecular deformation and its ultrashort timescale.

Ultrafast Independent N-H and N-C Bond Deformation Investigated with Resonant Inelastic X-Ray Scattering

DOE PAGES

Eckert, Sebastian; Norell, Jesper; Miedema, Piter S.; ...

2017-04-04

Here, the femtosecond excited-state dynamics following resonant photoexcitation enable the selective deformation of N-H and N-C chemical bonds in 2-thiopyridone in aqueous solution with optical or X-ray pulses. In combination with multiconfigurational quantum-chemical calculations, the orbital-specific electronic structure and its ultrafast dynamics accessed with resonant inelastic X-ray scattering at the N 1s level using synchrotron radiation and the soft X-ray free-electron laser LCLS provide direct evidence for this controlled photoinduced molecular deformation and its ultrashort timescale.

Quantum Heterogeneous Computing for Satellite Positioning Optimization

NASA Astrophysics Data System (ADS)

Bass, G.; Kumar, V.; Dulny, J., III

2016-12-01

Hard optimization problems occur in many fields of academic study and practical situations. We present results in which quantum heterogeneous computing is used to solve a real-world optimization problem: satellite positioning. Optimization problems like this can scale very rapidly with problem size, and become unsolvable with traditional brute-force methods. Typically, such problems have been approximately solved with heuristic approaches; however, these methods can take a long time to calculate and are not guaranteed to find optimal solutions. Quantum computing offers the possibility of producing significant speed-up and improved solution quality. There are now commercially available quantum annealing (QA) devices that are designed to solve difficult optimization problems. These devices have 1000+ quantum bits, but they have significant hardware size and connectivity limitations. We present a novel heterogeneous computing stack that combines QA and classical machine learning and allows the use of QA on problems larger than the quantum hardware could solve in isolation. We begin by analyzing the satellite positioning problem with a heuristic solver, the genetic algorithm. The classical computer's comparatively large available memory can explore the full problem space and converge to a solution relatively close to the true optimum. The QA device can then evolve directly to the optimal solution within this more limited space. Preliminary experiments, using the Quantum Monte Carlo (QMC) algorithm to simulate QA hardware, have produced promising results. Working with problem instances with known global minima, we find a solution within 8% in a matter of seconds, and within 5% in a few minutes. Future studies include replacing QMC with commercially available quantum hardware and exploring more problem sets and model parameters. Our results have important implications for how heterogeneous quantum computing can be used to solve difficult optimization problems in any field.

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.

From quantum foundations to applications and back.

PubMed

Gisin, Nicolas; Fröwis, Florian

2018-07-13

Quantum non-locality has been an extremely fruitful subject of research, leading the scientific revolution towards quantum information science, in particular, to device-independent quantum information processing. We argue that the time is ripe to work on another basic problem in the foundations of quantum physics, the quantum measurement problem, which should produce good physics in theoretical, mathematical, experimental and applied physics. We briefly review how quantum non-locality contributed to physics (including some outstanding open problems) and suggest ways in which questions around macroscopic quantumness could equally contribute to all aspects of physics.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Observational exclusion of a consistent loop quantum cosmology scenario

NASA Astrophysics Data System (ADS)

Bolliet, Boris; Barrau, Aurélien; Grain, Julien; Schander, Susanne

2016-06-01

It is often argued that inflation erases all the information about what took place before it started. Quantum gravity, relevant in the Planck era, seems therefore mostly impossible to probe with cosmological observations. In general, only very ad hoc scenarios or hyper fine-tuned initial conditions can lead to observationally testable theories. Here we consider a well-defined and well-motivated candidate quantum cosmology model that predicts inflation. Using the most recent observational constraints on the cosmic microwave background B-modes, we show that the model is excluded for all its parameter space, without any tuning. Some important consequences are drawn for the deformed algebra approach to loop quantum cosmology. We emphasize that neither loop quantum cosmology in general nor loop quantum gravity are disfavored by this study but their falsifiability is established.

A quantum annealing approach for fault detection and diagnosis of graph-based systems

NASA Astrophysics Data System (ADS)

Perdomo-Ortiz, A.; Fluegemann, J.; Narasimhan, S.; Biswas, R.; Smelyanskiy, V. N.

2015-02-01

Diagnosing the minimal set of faults capable of explaining a set of given observations, e.g., from sensor readouts, is a hard combinatorial optimization problem usually tackled with artificial intelligence techniques. We present the mapping of this combinatorial problem to quadratic unconstrained binary optimization (QUBO), and the experimental results of instances embedded onto a quantum annealing device with 509 quantum bits. Besides being the first time a quantum approach has been proposed for problems in the advanced diagnostics community, to the best of our knowledge this work is also the first research utilizing the route Problem → QUBO → Direct embedding into quantum hardware, where we are able to implement and tackle problem instances with sizes that go beyond previously reported toy-model proof-of-principle quantum annealing implementations; this is a significant leap in the solution of problems via direct-embedding adiabatic quantum optimization. We discuss some of the programmability challenges in the current generation of the quantum device as well as a few possible ways to extend this work to more complex arbitrary network graphs.

Deformed Palmprint Matching Based on Stable Regions.

PubMed

Wu, Xiangqian; Zhao, Qiushi

2015-12-01

Palmprint recognition (PR) is an effective technology for personal recognition. A main problem, which deteriorates the performance of PR, is the deformations of palmprint images. This problem becomes more severe on contactless occasions, in which images are acquired without any guiding mechanisms, and hence critically limits the applications of PR. To solve the deformation problems, in this paper, a model for non-linearly deformed palmprint matching is derived by approximating non-linear deformed palmprint images with piecewise-linear deformed stable regions. Based on this model, a novel approach for deformed palmprint matching, named key point-based block growing (KPBG), is proposed. In KPBG, an iterative M-estimator sample consensus algorithm based on scale invariant feature transform features is devised to compute piecewise-linear transformations to approximate the non-linear deformations of palmprints, and then, the stable regions complying with the linear transformations are decided using a block growing algorithm. Palmprint feature extraction and matching are performed over these stable regions to compute matching scores for decision. Experiments on several public palmprint databases show that the proposed models and the KPBG approach can effectively solve the deformation problem in palmprint verification and outperform the state-of-the-art methods.

Categorization of Quantum Mechanics Problems by Professors and Students

ERIC Educational Resources Information Center

Lin, Shih-Yin; Singh, Chandralekha

2010-01-01

We discuss the categorization of 20 quantum mechanics problems by physics professors and undergraduate students from two honours-level quantum mechanics courses. Professors and students were asked to categorize the problems based upon similarity of solution. We also had individual discussions with professors who categorized the problems. Faculty…

Deformation of the Engle-Livine-Pereira-Rovelli spin foam model by a cosmological constant

NASA Astrophysics Data System (ADS)

Bahr, Benjamin; Rabuffo, Giovanni

2018-04-01

In this article, we consider an ad hoc deformation of the Engle-Livine-Pereira-Rovelli model for quantum gravity by a cosmological constant term. This sort of deformation was first introduced by Han for the case of the 4-simplex. In this article, we generalize the deformation to the case of arbitrary vertices, and compute its large-j asymptotics. We show that, if the boundary data correspond to a four-dimensional polyhedron P , then the asymptotic formula gives the usual Regge action plus a cosmological constant term. We pay particular attention to the determinant of the Hessian matrix, and show that it can be related to that of the undeformed vertex.

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.

Heterogeneous quantum computing for satellite constellation optimization: solving the weighted k-clique problem

NASA Astrophysics Data System (ADS)

Bass, Gideon; Tomlin, Casey; Kumar, Vaibhaw; Rihaczek, Pete; Dulny, Joseph, III

2018-04-01

NP-hard optimization problems scale very rapidly with problem size, becoming unsolvable with brute force methods, even with supercomputing resources. Typically, such problems have been approximated with heuristics. However, these methods still take a long time and are not guaranteed to find an optimal solution. Quantum computing offers the possibility of producing significant speed-up and improved solution quality. Current quantum annealing (QA) devices are designed to solve difficult optimization problems, but they are limited by hardware size and qubit connectivity restrictions. We present a novel heterogeneous computing stack that combines QA and classical machine learning, allowing the use of QA on problems larger than the hardware limits of the quantum device. These results represent experiments on a real-world problem represented by the weighted k-clique problem. Through this experiment, we provide insight into the state of quantum machine learning.

Towards topological quantum computer

NASA Astrophysics Data System (ADS)

Melnikov, D.; Mironov, A.; Mironov, S.; Morozov, A.; Morozov, An.

2018-01-01

Quantum R-matrices, the entangling deformations of non-entangling (classical) permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates) for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern-Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.

A review on economic emission dispatch problems using quantum computational intelligence

NASA Astrophysics Data System (ADS)

Mahdi, Fahad Parvez; Vasant, Pandian; Kallimani, Vish; Abdullah-Al-Wadud, M.

2016-11-01

Economic emission dispatch (EED) problems are one of the most crucial problems in power systems. Growing energy demand, limitation of natural resources and global warming make this topic into the center of discussion and research. This paper reviews the use of Quantum Computational Intelligence (QCI) in solving Economic Emission Dispatch problems. QCI techniques like Quantum Genetic Algorithm (QGA) and Quantum Particle Swarm Optimization (QPSO) algorithm are discussed here. This paper will encourage the researcher to use more QCI based algorithm to get better optimal result for solving EED problems.

Deformed supersymmetric quantum mechanics with spin variables

NASA Astrophysics Data System (ADS)

Fedoruk, Sergey; Ivanov, Evgeny; Sidorov, Stepan

2018-01-01

We quantize the one-particle model of the SU(2|1) supersymmetric multiparticle mechanics with the additional semi-dynamical spin degrees of freedom. We find the relevant energy spectrum and the full set of physical states as functions of the mass-dimension deformation parameter m and SU(2) spin q\\in (Z_{>0,}1/2+Z_{≥0}) . It is found that the states at the fixed energy level form irreducible multiplets of the supergroup SU(2|1). Also, the hidden superconformal symmetry OSp(4|2) of the model is revealed in the classical and quantum cases. We calculate the OSp(4|2) Casimir operators and demonstrate that the full set of the physical states belonging to different energy levels at fixed q are unified into an irreducible OSp(4|2) multiplet.

Completing the physical representation of quantum algorithms provides a retrocausal explanation of the speedup

NASA Astrophysics Data System (ADS)

Castagnoli, Giuseppe

2017-05-01

The usual representation of quantum algorithms, limited to the process of solving the problem, is physically incomplete as it lacks the initial measurement. We extend it to the process of setting the problem. An initial measurement selects a problem setting at random, and a unitary transformation sends it into the desired setting. The extended representation must be with respect to Bob, the problem setter, and any external observer. It cannot be with respect to Alice, the problem solver. It would tell her the problem setting and thus the solution of the problem implicit in it. In the representation to Alice, the projection of the quantum state due to the initial measurement should be postponed until the end of the quantum algorithm. In either representation, there is a unitary transformation between the initial and final measurement outcomes. As a consequence, the final measurement of any ℛ-th part of the solution could select back in time a corresponding part of the random outcome of the initial measurement; the associated projection of the quantum state should be advanced by the inverse of that unitary transformation. This, in the representation to Alice, would tell her, before she begins her problem solving action, that part of the solution. The quantum algorithm should be seen as a sum over classical histories in each of which Alice knows in advance one of the possible ℛ-th parts of the solution and performs the oracle queries still needed to find it - this for the value of ℛ that explains the algorithm's speedup. We have a relation between retrocausality ℛ and the number of oracle queries needed to solve an oracle problem quantumly. All the oracle problems examined can be solved with any value of ℛ up to an upper bound attained by the optimal quantum algorithm. This bound is always in the vicinity of 1/2 . Moreover, ℛ =1/2 always provides the order of magnitude of the number of queries needed to solve the problem in an optimal quantum way. If this were true for any oracle problem, as plausible, it would solve the quantum query complexity problem.

A strategy for quantum algorithm design assisted by machine learning

NASA Astrophysics Data System (ADS)

Bang, Jeongho; Ryu, Junghee; Yoo, Seokwon; Pawłowski, Marcin; Lee, Jinhyoung

2014-07-01

We propose a method for quantum algorithm design assisted by machine learning. The method uses a quantum-classical hybrid simulator, where a ‘quantum student’ is being taught by a ‘classical teacher’. In other words, in our method, the learning system is supposed to evolve into a quantum algorithm for a given problem, assisted by a classical main-feedback system. Our method is applicable for designing quantum oracle-based algorithms. We chose, as a case study, an oracle decision problem, called a Deutsch-Jozsa problem. We showed by using Monte Carlo simulations that our simulator can faithfully learn a quantum algorithm for solving the problem for a given oracle. Remarkably, the learning time is proportional to the square root of the total number of parameters, rather than showing the exponential dependence found in the classical machine learning-based method.

Spin Glass a Bridge Between Quantum Computation and Statistical Mechanics

NASA Astrophysics Data System (ADS)

Ohzeki, Masayuki

2013-09-01

In this chapter, we show two fascinating topics lying between quantum information processing and statistical mechanics. First, we introduce an elaborated technique, the surface code, to prepare the particular quantum state with robustness against decoherence. Interestingly, the theoretical limitation of the surface code, accuracy threshold, to restore the quantum state has a close connection with the problem on the phase transition in a special model known as spin glasses, which is one of the most active researches in statistical mechanics. The phase transition in spin glasses is an intractable problem, since we must strive many-body system with complicated interactions with change of their signs depending on the distance between spins. Fortunately, recent progress in spin-glass theory enables us to predict the precise location of the critical point, at which the phase transition occurs. It means that statistical mechanics is available for revealing one of the most interesting parts in quantum information processing. We show how to import the special tool in statistical mechanics into the problem on the accuracy threshold in quantum computation. Second, we show another interesting technique to employ quantum nature, quantum annealing. The purpose of quantum annealing is to search for the most favored solution of a multivariable function, namely optimization problem. The most typical instance is the traveling salesman problem to find the minimum tour while visiting all the cities. In quantum annealing, we introduce quantum fluctuation to drive a particular system with the artificial Hamiltonian, in which the ground state represents the optimal solution of the specific problem we desire to solve. Induction of the quantum fluctuation gives rise to the quantum tunneling effect, which allows nontrivial hopping from state to state. We then sketch a strategy to control the quantum fluctuation efficiently reaching the ground state. Such a generic framework is called quantum annealing. The most typical instance is quantum adiabatic computation based on the adiabatic theorem. The quantum adiabatic computation as discussed in the other chapter, unfortunately, has a crucial bottleneck for a part of the optimization problems. We here introduce several recent trials to overcome such a weakpoint by use of developments in statistical mechanics. Through both of the topics, we would shed light on the birth of the interdisciplinary field between quantum mechanics and statistical mechanics.

Efficiency of quantum vs. classical annealing in nonconvex learning problems

PubMed Central

Zecchina, Riccardo

2018-01-01

Quantum annealers aim at solving nonconvex optimization problems by exploiting cooperative tunneling effects to escape local minima. The underlying idea consists of designing a classical energy function whose ground states are the sought optimal solutions of the original optimization problem and add a controllable quantum transverse field to generate tunneling processes. A key challenge is to identify classes of nonconvex optimization problems for which quantum annealing remains efficient while thermal annealing fails. We show that this happens for a wide class of problems which are central to machine learning. Their energy landscapes are dominated by local minima that cause exponential slowdown of classical thermal annealers while simulated quantum annealing converges efficiently to rare dense regions of optimal solutions. PMID:29382764

Problems, acceptance and social inequality: a study of the deformed leprosy patients and their families.

PubMed

Kopparty, S N

1995-09-01

Though the impact of social inequality on health conditions is widely known, its impact on the chronic and stigmatized disease, leprosy, has received little attention. Deformity sometimes leads to disabilities and to handicaps causing problems to the patient and his family. In this paper an attempt has been made to understand the impact of social inequality, prevalent in the form of the caste system in India on the deformed leprosy patients and on their families. This impact was examined in terms of the problems faced by the patients. A sample of 150 deformed patients and their families, drawn from two districts in Tamil Nadu, was selected for the study. About 57% of the deformed patients experienced their deformity as a handicap which caused social and economic problems while the rest did not. Of the three caste groups, the Lower Caste group experienced more severe economic problems while the Upper Caste group faced more social problems. The extent of acceptance of deformed patients in their family varied significantly among those facing and not facing problems due to their deformity. The deformed patients without any handicap were accepted in a large majority of their families (82%) regardless of their caste status. In contrast the deformed but handicapped patients were accepted differentially among the three caste groups with the Upper group accepting them in most of their families (80%) while in the Lower group much less number of families (54%) did. All the families of the deformed but not handicapped patients desired to keep their patients till their death irrespective of their caste status. On the contrary, while all the families in the Upper Caste group expressed their willingness to keep their handicapped patients in the family till their death, 10% in the Middle and 22% in the Lower Caste groups did not want to do so. This suggests the gradual marginalization, rejection and dehabilitation of the affected. Thus, one's caste status can be a broad indicator of the nature and the extent of handicaps and acceptance in the family. This factor needs to be appropriately taken care of for rehabilitation and disability management in leprosy control programmes.

Fedosov Deformation Quantization as a BRST Theory

NASA Astrophysics Data System (ADS)

Grigoriev, M. A.; Lyakhovich, S. L.

The relationship is established between the Fedosov deformation quantization of a general symplectic manifold and the BFV-BRST quantization of constrained dynamical systems. The original symplectic manifold M is presented as a second class constrained surface in the fibre bundle ?*ρM which is a certain modification of a usual cotangent bundle equipped with a natural symplectic structure. The second class system is converted into the first class one by continuation of the constraints into the extended manifold, being a direct sum of ?*ρM and the tangent bundle TM. This extended manifold is equipped with a nontrivial Poisson bracket which naturally involves two basic ingredients of Fedosov geometry: the symplectic structure and the symplectic connection. The constructed first class constrained theory, being equivalent to the original symplectic manifold, is quantized through the BFV-BRST procedure. The existence theorem is proven for the quantum BRST charge and the quantum BRST invariant observables. The adjoint action of the quantum BRST charge is identified with the Abelian Fedosov connection while any observable, being proven to be a unique BRST invariant continuation for the values defined in the original symplectic manifold, is identified with the Fedosov flat section of the Weyl bundle. The Fedosov fibrewise star multiplication is thus recognized as a conventional product of the quantum BRST invariant observables.

A subgradient approach for constrained binary optimization via quantum adiabatic evolution

NASA Astrophysics Data System (ADS)

Karimi, Sahar; Ronagh, Pooya

2017-08-01

Outer approximation method has been proposed for solving the Lagrangian dual of a constrained binary quadratic programming problem via quantum adiabatic evolution in the literature. This should be an efficient prescription for solving the Lagrangian dual problem in the presence of an ideally noise-free quantum adiabatic system. However, current implementations of quantum annealing systems demand methods that are efficient at handling possible sources of noise. In this paper, we consider a subgradient method for finding an optimal primal-dual pair for the Lagrangian dual of a constrained binary polynomial programming problem. We then study the quadratic stable set (QSS) problem as a case study. We see that this method applied to the QSS problem can be viewed as an instance-dependent penalty-term approach that avoids large penalty coefficients. Finally, we report our experimental results of using the D-Wave 2X quantum annealer and conclude that our approach helps this quantum processor to succeed more often in solving these problems compared to the usual penalty-term approaches.

Performance of Quantum Annealers on Hard Scheduling Problems

NASA Astrophysics Data System (ADS)

Pokharel, Bibek; Venturelli, Davide; Rieffel, Eleanor

Quantum annealers have been employed to attack a variety of optimization problems. We compared the performance of the current D-Wave 2X quantum annealer to that of the previous generation D-Wave Two quantum annealer on scheduling-type planning problems. Further, we compared the effect of different anneal times, embeddings of the logical problem, and different settings of the ferromagnetic coupling JF across the logical vertex-model on the performance of the D-Wave 2X quantum annealer. Our results show that at the best settings, the scaling of expected anneal time to solution for D-WAVE 2X is better than that of the DWave Two, but still inferior to that of state of the art classical solvers on these problems. We discuss the implication of our results for the design and programming of future quantum annealers. Supported by NASA Ames Research Center.

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.

Constraining the loop quantum gravity parameter space from phenomenology

NASA Astrophysics Data System (ADS)

Brahma, Suddhasattwa; Ronco, Michele

2018-03-01

Development of quantum gravity theories rarely takes inputs from experimental physics. In this letter, we take a small step towards correcting this by establishing a paradigm for incorporating putative quantum corrections, arising from canonical quantum gravity (QG) theories, in deriving falsifiable modified dispersion relations (MDRs) for particles on a deformed Minkowski space-time. This allows us to differentiate and, hopefully, pick between several quantization choices via testable, state-of-the-art phenomenological predictions. Although a few explicit examples from loop quantum gravity (LQG) (such as the regularization scheme used or the representation of the gauge group) are shown here to establish the claim, our framework is more general and is capable of addressing other quantization ambiguities within LQG and also those arising from other similar QG approaches.

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.

Demonstration of essentiality of entanglement in a Deutsch-like quantum algorithm

NASA Astrophysics Data System (ADS)

Huang, He-Liang; Goswami, Ashutosh K.; Bao, Wan-Su; Panigrahi, Prasanta K.

2018-06-01

Quantum algorithms can be used to efficiently solve certain classically intractable problems by exploiting quantum parallelism. However, the effectiveness of quantum entanglement in quantum computing remains a question of debate. This study presents a new quantum algorithm that shows entanglement could provide advantages over both classical algorithms and quantum algo- rithms without entanglement. Experiments are implemented to demonstrate the proposed algorithm using superconducting qubits. Results show the viability of the algorithm and suggest that entanglement is essential in obtaining quantum speedup for certain problems in quantum computing. The study provides reliable and clear guidance for developing useful quantum algorithms.

Complexity of the Quantum Adiabatic Algorithm

NASA Astrophysics Data System (ADS)

Hen, Itay

2013-03-01

The Quantum Adiabatic Algorithm (QAA) has been proposed as a mechanism for efficiently solving optimization problems on a quantum computer. Since adiabatic computation is analog in nature and does not require the design and use of quantum gates, it can be thought of as a simpler and perhaps more profound method for performing quantum computations that might also be easier to implement experimentally. While these features have generated substantial research in QAA, to date there is still a lack of solid evidence that the algorithm can outperform classical optimization algorihms. Here, we discuss several aspects of the quantum adiabatic algorithm: We analyze the efficiency of the algorithm on several ``hard'' (NP) computational problems. Studying the size dependence of the typical minimum energy gap of the Hamiltonians of these problems using quantum Monte Carlo methods, we find that while for most problems the minimum gap decreases exponentially with the size of the problem, indicating that the QAA is not more efficient than existing classical search algorithms, for other problems there is evidence to suggest that the gap may be polynomial near the phase transition. We also discuss applications of the QAA to ``real life'' problems and how they can be implemented on currently available (albeit prototypical) quantum hardware such as ``D-Wave One'', that impose serious restrictions as to which type of problems may be tested. Finally, we discuss different approaches to find improved implementations of the algorithm such as local adiabatic evolution, adaptive methods, local search in Hamiltonian space and others.

Quantum chi-squared and goodness of fit testing

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

Temme, Kristan; Verstraete, Frank

2015-01-15

A quantum mechanical hypothesis test is presented for the hypothesis that a certain setup produces a given quantum state. Although the classical and the quantum problems are very much related to each other, the quantum problem is much richer due to the additional optimization over the measurement basis. A goodness of fit test for i.i.d quantum states is developed and a max-min characterization for the optimal measurement is introduced. We find the quantum measurement which leads both to the maximal Pitman and Bahadur efficiencies, and determine the associated divergence rates. We discuss the relationship of the quantum goodness of fitmore » test to the problem of estimating multiple parameters from a density matrix. These problems are found to be closely related and we show that the largest error of an optimal strategy, determined by the smallest eigenvalue of the Fisher information matrix, is given by the divergence rate of the goodness of fit test.« less

Quantum computation with coherent spin states and the close Hadamard problem

NASA Astrophysics Data System (ADS)

Adcock, Mark R. A.; Høyer, Peter; Sanders, Barry C.

2016-04-01

We study a model of quantum computation based on the continuously parameterized yet finite-dimensional Hilbert space of a spin system. We explore the computational powers of this model by analyzing a pilot problem we refer to as the close Hadamard problem. We prove that the close Hadamard problem can be solved in the spin system model with arbitrarily small error probability in a constant number of oracle queries. We conclude that this model of quantum computation is suitable for solving certain types of problems. The model is effective for problems where symmetries between the structure of the information associated with the problem and the structure of the unitary operators employed in the quantum algorithm can be exploited.

Radiation of quantum black holes and modified uncertainty relation

NASA Astrophysics Data System (ADS)

Kamali, A. D.; Pedram, P.

In this paper, using a deformed algebra [X,P] = iℏ/(1 ‑ λ2P2) which is originated from various theories of gravity, we study thermodynamical properties of quantum black holes (BHs) in canonical ensembles. We exactly calculate the modified internal energy, entropy and heat capacity. Moreover, we investigate a tunneling mechanism of massless particle in phase space. In this regard, the tunneling radiation of BH receives new corrections and the exact radiant spectrum is no longer precisely thermal. In addition, we show that our results are compatible with other quantum gravity (QG) approaches.

Modern Quantum Field Theory II - Proceeeings of the International Colloquium

NASA Astrophysics Data System (ADS)

Das, S. R.; Mandal, G.; Mukhi, S.; Wadia, S. R.

1995-08-01

The Table of Contents for the book is as follows: * Foreword * 1. Black Holes and Quantum Gravity * Quantum Black Holes and the Problem of Time * Black Hole Entropy and the Semiclassical Approximation * Entropy and Information Loss in Two Dimensions * Strings on a Cone and Black Hole Entropy (Abstract) * Boundary Dynamics, Black Holes and Spacetime Fluctuations in Dilation Gravity (Abstract) * Pair Creation of Black Holes (Abstract) * A Brief View of 2-Dim. String Theory and Black Holes (Abstract) * 2. String Theory * Non-Abelian Duality in WZW Models * Operators and Correlation Functions in c ≤ 1 String Theory * New Symmetries in String Theory * A Look at the Discretized Superstring Using Random Matrices * The Nested BRST Structure of Wn-Symmetries * Landau-Ginzburg Model for a Critical Topological String (Abstract) * On the Geometry of Wn Gravity (Abstract) * O(d, d) Tranformations, Marginal Deformations and the Coset Construction in WZNW Models (Abstract) * Nonperturbative Effects and Multicritical Behaviour of c = 1 Matrix Model (Abstract) * Singular Limits and String Solutions (Abstract) * BV Algebra on the Moduli Spaces of Riemann Surfaces and String Field Theory (Abstract) * 3. Condensed Matter and Statistical Mechanics * Stochastic Dynamics in a Deposition-Evaporation Model on a Line * Models with Inverse-Square Interactions: Conjectured Dynamical Correlation Functions of the Calogero-Sutherland Model at Rational Couplings * Turbulence and Generic Scale Invariance * Singular Perturbation Approach to Phase Ordering Dynamics * Kinetics of Diffusion-Controlled and Ballistically-Controlled Reactions * Field Theory of a Frustrated Heisenberg Spin Chain * FQHE Physics in Relativistic Field Theories * Importance of Initial Conditions in Determining the Dynamical Class of Cellular Automata (Abstract) * Do Hard-Core Bosons Exhibit Quantum Hall Effect? (Abstract) * Hysteresis in Ferromagnets * 4. Fundamental Aspects of Quantum Mechanics and Quantum Field Theory * Finite Quantum Physics and Noncommutative Geometry * Higgs as Gauge Field and the Standard Model * Canonical Quantisation of an Off-Conformal Theory * Deterministic Quantum Mechanics in One Dimension * Spin-Statistics Relations for Topological Geons in 2+1 Quantum Gravity * Generalized Fock Spaces * Geometrical Expression for Short Distance Singularities in Field Theory * 5. Mathematics and Quantum Field Theory * Knot Invariants from Quantum Field Theories * Infinite Grassmannians and Moduli Spaces of G-Bundles * A Review of an Algebraic Geometry Approach to a Model Quantum Field Theory on a Curve (Abstract) * 6. Integrable Models * Spectral Representation of Correlation Functions in Two-Dimensional Quantum Field Theories * On Various Avatars of the Pasquier Algebra * Supersymmetric Integrable Field Theories and Eight Vertex Free Fermion Models (Abstract) * 7. Lattice Field Theory * From Kondo Model and Strong Coupling Lattice QCD to the Isgur-Wise Function * Effective Confinement from a Logarithmically Running Coupling (Abstract)

Effect of local minima on adiabatic quantum optimization.

PubMed

Amin, M H S

2008-04-04

We present a perturbative method to estimate the spectral gap for adiabatic quantum optimization, based on the structure of the energy levels in the problem Hamiltonian. We show that, for problems that have an exponentially large number of local minima close to the global minimum, the gap becomes exponentially small making the computation time exponentially long. The quantum advantage of adiabatic quantum computation may then be accessed only via the local adiabatic evolution, which requires phase coherence throughout the evolution and knowledge of the spectrum. Such problems, therefore, are not suitable for adiabatic quantum computation.

A device-oriented optimizer for solving ground state problems on an approximate quantum computer, Part II: Experiments for interacting spin and molecular systems

NASA Astrophysics Data System (ADS)

Kandala, Abhinav; Mezzacapo, Antonio; Temme, Kristan; Bravyi, Sergey; Takita, Maika; Chavez-Garcia, Jose; Córcoles, Antonio; Smolin, John; Chow, Jerry; Gambetta, Jay

Hybrid quantum-classical algorithms can be used to find variational solutions to generic quantum problems. Here, we present an experimental implementation of a device-oriented optimizer that uses superconducting quantum hardware. The experiment relies on feedback between the quantum device and classical optimization software which is robust to measurement noise. Our device-oriented approach uses naturally available interactions for the preparation of trial states. We demonstrate the application of this technique for solving interacting spin and molecular structure problems.

Students' Epistemological Framing in Quantum Mechanics Problem Solving

ERIC Educational Resources Information Center

Modir, Bahar; Thompson, John D.; Sayre, Eleanor C.

2017-01-01

Students' difficulties in quantum mechanics may be the result of unproductive framing and not a fundamental inability to solve the problems or misconceptions about physics content. We observed groups of students solving quantum mechanics problems in an upper-division physics course. Using the lens of epistemological framing, we investigated four…

Geometry of Quantum Computation with Qudits

PubMed Central

Luo, Ming-Xing; Chen, Xiu-Bo; Yang, Yi-Xian; Wang, Xiaojun

2014-01-01

The circuit complexity of quantum qubit system evolution as a primitive problem in quantum computation has been discussed widely. We investigate this problem in terms of qudit system. Using the Riemannian geometry the optimal quantum circuits are equivalent to the geodetic evolutions in specially curved parametrization of SU(dn). And the quantum circuit complexity is explicitly dependent of controllable approximation error bound. PMID:24509710

Unraveling Quantum Annealers using Classical Hardness

PubMed Central

Martin-Mayor, Victor; Hen, Itay

2015-01-01

Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealing optimizers that contain hundreds of quantum bits. These optimizers, commonly referred to as ‘D-Wave’ chips, promise to solve practical optimization problems potentially faster than conventional ‘classical’ computers. Attempts to quantify the quantum nature of these chips have been met with both excitement and skepticism but have also brought up numerous fundamental questions pertaining to the distinguishability of experimental quantum annealers from their classical thermal counterparts. Inspired by recent results in spin-glass theory that recognize ‘temperature chaos’ as the underlying mechanism responsible for the computational intractability of hard optimization problems, we devise a general method to quantify the performance of quantum annealers on optimization problems suffering from varying degrees of temperature chaos: A superior performance of quantum annealers over classical algorithms on these may allude to the role that quantum effects play in providing speedup. We utilize our method to experimentally study the D-Wave Two chip on different temperature-chaotic problems and find, surprisingly, that its performance scales unfavorably as compared to several analogous classical algorithms. We detect, quantify and discuss several purely classical effects that possibly mask the quantum behavior of the chip. PMID:26483257

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.

Planar dynamics of large-deformation rods under moving loads

NASA Astrophysics Data System (ADS)

Zhao, X. W.; van der Heijden, G. H. M.

2018-01-01

We formulate the problem of a slender structure (a rod) undergoing large deformation under the action of a moving mass or load motivated by inspection robots crawling along bridge cables or high-voltage power lines. The rod is described by means of geometrically exact Cosserat theory which allows for arbitrary planar flexural, extensional and shear deformations. The equations of motion are discretised using the generalised-α method. The formulation is shown to handle the discontinuities of the problem well. Application of the method to a cable and an arch problem reveals interesting nonlinear phenomena. For the cable problem we find that large deformations have a resonance detuning effect on cable dynamics. The problem also offers a compelling illustration of the Timoshenko paradox. For the arch problem we find a stabilising (delay) effect on the in-plane collapse of the arch, with failure suppressed entirely at sufficiently high speed.

Quantum walks, deformed relativity and Hopf algebra symmetries

PubMed Central

2016-01-01

We show how the Weyl quantum walk derived from principles in D'Ariano & Perinotti (D'Ariano & Perinotti 2014 Phys. Rev. A 90, 062106. (doi:10.1103/PhysRevA.90.062106)), enjoying a nonlinear Lorentz symmetry of dynamics, allows one to introduce Hopf algebras for position and momentum of the emerging particle. We focus on two special models of Hopf algebras–the usual Poincaré and the κ-Poincaré algebras. PMID:27091171

SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics

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

Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

1998-09-01

This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.

Some aspects of forecasting the post-mining substratum deformation for evaluation of its influence on constructions

NASA Astrophysics Data System (ADS)

Strzałkowski, Piotr; Ścigała, Roman; Szafulera, Katarzyna

2018-04-01

Some problems have been discussed, connected with performing predictions of post-mining terrain deformations. Especially problems occur with the summation of horizontal strain over long time intervals as well as predictions of linear discontinuous deformations. Of great importance in recent years is the problem of taking into account transient values of deformations associated with the development of extraction field. The exemplary analysis has been presented of planned extraction influences on two characteristic locations of building structure. The proposal has been shown of calculations with using transient deformation model allowing to describe the influence of extraction advance influence on the value of coefficient of extraction rate c (time factor), according to own original empirical formula.

Interpretations of Quantum Theory in the Light of Modern Cosmology

NASA Astrophysics Data System (ADS)

Castagnino, Mario; Fortin, Sebastian; Laura, Roberto; Sudarsky, Daniel

2017-11-01

The difficult issues related to the interpretation of quantum mechanics and, in particular, the "measurement problem" are revisited using as motivation the process of generation of structure from quantum fluctuations in inflationary cosmology. The unessential mathematical complexity of the particular problem is bypassed, facilitating the discussion of the conceptual issues, by considering, within the paradigm set up by the cosmological problem, another problem where symmetry serves as a focal point: a simplified version of Mott's problem.

Fundamental Study on Quantum Nanojets

DTIC Science & Technology

2004-08-01

Pergamon Press. Bell , J. S . 1966 On the problem of hidden variables in quantum mechanics. Rev. of Modern Phys., 38, 447. Berndl, K., Daumer, M...fluid dynamics based on two quantum mechanical perspectives; Schrödinger’s wave mechanics and quantum fluid dynamics based on Hamilton-Jacoby...References 8 2). Direct Problems a). Quantum fluid dynamics formalism based on Hamilton-Jacoby equation are adapted for the numerical

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.

Investigations of quantum heuristics for optimization

NASA Astrophysics Data System (ADS)

Rieffel, Eleanor; Hadfield, Stuart; Jiang, Zhang; Mandra, Salvatore; Venturelli, Davide; Wang, Zhihui

We explore the design of quantum heuristics for optimization, focusing on the quantum approximate optimization algorithm, a metaheuristic developed by Farhi, Goldstone, and Gutmann. We develop specific instantiations of the of quantum approximate optimization algorithm for a variety of challenging combinatorial optimization problems. Through theoretical analyses and numeric investigations of select problems, we provide insight into parameter setting and Hamiltonian design for quantum approximate optimization algorithms and related quantum heuristics, and into their implementation on hardware realizable in the near term.

RG flows for λ-deformed CFTs

NASA Astrophysics Data System (ADS)

Sagkrioti, E.; Sfetsos, K.; Siampos, K.

2018-05-01

We study the renormalization group equations of the fully anisotropic λ-deformed CFTs involving the direct product of two current algebras at different levels k1,2 for general semi-simple groups. The exact, in the deformation parameters, β-function is found via the effective action of the quantum fluctuations around a classical background as well as from gravitational techniques. Furthermore, agreement with known results for symmetric couplings and/or for equal levels, is demonstrated. We study in detail the two coupling case arising by splitting the group into a subgroup and the corresponding coset manifold which consistency requires to be either a symmetric-space one or a non-symmetric Einstein-space.

Three-Dimensional Coupled Dynamics of The Two-Fluid Model in Superfluid 4He: Deformed Velocity Profile of Normal Fluid in Thermal Counterflow

NASA Astrophysics Data System (ADS)

Yui, Satoshi; Tsubota, Makoto; Kobayashi, Hiromichi

2018-04-01

The coupled dynamics of the two-fluid model of superfluid 4He is numerically studied for quantum turbulence of the thermal counterflow in a square channel. We combine the vortex filament model of the superfluid and the Navier-Stokes equations of normal fluid. Simulations of the coupled dynamics show that the velocity profile of the normal fluid is deformed significantly by superfluid turbulence as the vortices become dense. This result is consistent with recently performed visualization experiments. We introduce a dimensionless parameter that characterizes the deformation of the velocity profile.

Large-Amplitude Deformation and Bond Breakage in Shock-Induced Reactions of Explosive Molecules

NASA Astrophysics Data System (ADS)

Kay, Jeffrey

The response of explosive molecules to large-amplitude mechanical deformation plays an important role in shock-induced reactions and the initiation of detonation in explosive materials. In this presentation, the response of a series of explosive molecules (nitromethane, 2,4,6-trinitrotoluene [TNT], and 2,4,6-triamino-1,3,5-trinitrobenzene [TATB]) to a variety of large-amplitude deformations are examined using ab initio quantum chemical calculations. Large-amplitude motions that result in bond breakage are described, and the insights these results provide into both previous experimental observations and previous theoretical predictions of shock-induced reactions are discussed.

Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance

PubMed Central

Li, Zhaokai; Yung, Man-Hong; Chen, Hongwei; Lu, Dawei; Whitfield, James D.; Peng, Xinhua; Aspuru-Guzik, Alán; Du, Jiangfeng

2011-01-01

Quantum ground-state problems are computationally hard problems for general many-body Hamiltonians; there is no classical or quantum algorithm known to be able to solve them efficiently. Nevertheless, if a trial wavefunction approximating the ground state is available, as often happens for many problems in physics and chemistry, a quantum computer could employ this trial wavefunction to project the ground state by means of the phase estimation algorithm (PEA). We performed an experimental realization of this idea by implementing a variational-wavefunction approach to solve the ground-state problem of the Heisenberg spin model with an NMR quantum simulator. Our iterative phase estimation procedure yields a high accuracy for the eigenenergies (to the 10−5 decimal digit). The ground-state fidelity was distilled to be more than 80%, and the singlet-to-triplet switching near the critical field is reliably captured. This result shows that quantum simulators can better leverage classical trial wave functions than classical computers PMID:22355607

Boosting quantum annealer performance via sample persistence

NASA Astrophysics Data System (ADS)

Karimi, Hamed; Rosenberg, Gili

2017-07-01

We propose a novel method for reducing the number of variables in quadratic unconstrained binary optimization problems, using a quantum annealer (or any sampler) to fix the value of a large portion of the variables to values that have a high probability of being optimal. The resulting problems are usually much easier for the quantum annealer to solve, due to their being smaller and consisting of disconnected components. This approach significantly increases the success rate and number of observations of the best known energy value in samples obtained from the quantum annealer, when compared with calling the quantum annealer without using it, even when using fewer annealing cycles. Use of the method results in a considerable improvement in success metrics even for problems with high-precision couplers and biases, which are more challenging for the quantum annealer to solve. The results are further enhanced by applying the method iteratively and combining it with classical pre-processing. We present results for both Chimera graph-structured problems and embedded problems from a real-world application.

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.

Quantum electronic stress: density-functional-theory formulation and physical manifestation.

PubMed

Hu, Hao; Liu, Miao; Wang, Z F; Zhu, Junyi; Wu, Dangxin; Ding, Hepeng; Liu, Zheng; Liu, Feng

2012-08-03

The concept of quantum electronic stress (QES) is introduced and formulated within density functional theory to elucidate extrinsic electronic effects on the stress state of solids and thin films in the absence of lattice strain. A formal expression of QES (σ(QE)) is derived in relation to deformation potential of electronic states (Ξ) and variation of electron density (Δn), σ(QE) = ΞΔn as a quantum analog of classical Hooke's law. Two distinct QES manifestations are demonstrated quantitatively by density functional theory calculations: (1) in the form of bulk stress induced by charge carriers and (2) in the form of surface stress induced by quantum confinement. Implications of QES in some physical phenomena are discussed to underlie its importance.

Dynamics of hot random quantum spin chains: from anyons to Heisenberg spins

NASA Astrophysics Data System (ADS)

Parameswaran, Siddharth; Potter, Andrew; Vasseur, Romain

2015-03-01

We argue that the dynamics of the random-bond Heisenberg spin chain are ergodic at infinite temperature, in contrast to the many-body localized behavior seen in its random-field counterpart. First, we show that excited-state real-space renormalization group (RSRG-X) techniques suffer from a fatal breakdown of perturbation theory due to the proliferation of large effective spins that grow without bound. We repair this problem by deforming the SU (2) symmetry of the Heisenberg chain to its `anyonic' version, SU(2)k , where the growth of effective spins is truncated at spin S = k / 2 . This enables us to construct a self-consistent RSRG-X scheme that is particularly simple at infinite temperature. Solving the flow equations, we compute the excited-state entanglement and show that it crosses over from volume-law to logarithmic scaling at a length scale ξk ~eαk3 . This reveals that (a) anyon chains have random-singlet-like excited states for any finite k; and (b) ergodicity is restored in the Heisenberg limit k --> ∞ . We acknowledge support from the Quantum Materials program of LBNL (RV), the Gordon and Betty Moore Foundation (ACP), and UC Irvine startup funds (SAP).

q-Poincaré supersymmetry in AdS5/CFT4

NASA Astrophysics Data System (ADS)

Borsato, Riccardo; Torrielli, Alessandro

2018-03-01

We consider the exact S-matrix governing the planar spectral problem for strings on AdS5 ×S5 and N = 4 super Yang-Mills, and we show that it is invariant under a novel "boost" symmetry, which acts as a differentiation with respect to the particle momentum. This generator leads us also to reinterpret the usual centrally extended psu (2 | 2) symmetry, and to conclude that the S-matrix is invariant under a q-Poincaré supersymmetry algebra, where the deformation parameter is related to the 't Hooft coupling. We determine the two-particle action (coproduct) that turns out to be non-local, and study the property of the new symmetry under crossing transformations. We look at both the strong-coupling (large tension in the string theory) and weak-coupling (spin-chain description of the gauge theory) limits; in the former regime we calculate the cobracket utilising the universal classical r-matrix of Beisert and Spill. In the eventuality that the boost has higher partners, we also construct a quantum affine version of 2D Poincaré symmetry, by contraction of the quantum affine algebra Uq (sl2 ˆ) in Drinfeld's second realisation.

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.

Gravity from entanglement and RG flow in a top-down approach

NASA Astrophysics Data System (ADS)

Kwon, O.-Kab; Jang, Dongmin; Kim, Yoonbai; Tolla, D. D.

2018-05-01

The duality between a d-dimensional conformal field theory with relevant deformation and a gravity theory on an asymptotically AdS d+1 geometry, has become a suitable tool in the investigation of the emergence of gravity from quantum entanglement in field theory. Recently, we have tested the duality between the mass-deformed ABJM theory and asymptotically AdS4 gravity theory, which is obtained from the KK reduction of the 11-dimensional supergravity on the LLM geometry. In this paper, we extend the KK reduction procedure beyond the linear order and establish non-trivial KK maps between 4-dimensional fields and 11-dimensional fluctuations. We rely on this gauge/gravity duality to calculate the entanglement entropy by using the Ryu-Takayanagi holographic formula and the path integral method developed by Faulkner. We show that the entanglement entropies obtained using these two methods agree when the asymptotically AdS4 metric satisfies the linearized Einstein equation with nonvanishing energy-momentum tensor for two scalar fields. These scalar fields encode the information of the relevant deformation of the ABJM theory. This confirms that the asymptotic limit of LLM geometry is the emergent gravity of the quantum entanglement in the mass-deformed ABJM theory with a small mass parameter. We also comment on the issue of the relative entropy and the Fisher information in our setup.

Quantum speedup of the traveling-salesman problem for bounded-degree graphs

NASA Astrophysics Data System (ADS)

Moylett, Dominic J.; Linden, Noah; Montanaro, Ashley

2017-03-01

The traveling-salesman problem is one of the most famous problems in graph theory. However, little is currently known about the extent to which quantum computers could speed up algorithms for the problem. In this paper, we prove a quadratic quantum speedup when the degree of each vertex is at most 3 by applying a quantum backtracking algorithm to a classical algorithm by Xiao and Nagamochi. We then use similar techniques to accelerate a classical algorithm for when the degree of each vertex is at most 4, before speeding up higher-degree graphs via reductions to these instances.

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.

Truth Values of Quantum Phenomena

NASA Astrophysics Data System (ADS)

Bolotin, Arkady

2018-04-01

In the paper, the idea of describing not-yet-verified properties of quantum objects with logical many-valuedness is scrutinized. As it is argued, to promote such an idea, the following two foundational problems of many-valued quantum logic must be decided: the problem of choosing a proper system of many-valued logic and the problem of the emergence of bivalence from logical many-valuedness. Difficulties accompanying solutions of these problems are discussed.

Energy spectrum inverse problem of q-deformed harmonic oscillator and entanglement of composite bosons

NASA Astrophysics Data System (ADS)

Sang, Nguyen Anh; Thu Thuy, Do Thi; Loan, Nguyen Thi Ha; Lan, Nguyen Tri; Viet, Nguyen Ai

2017-06-01

Using the simple deformed three-level model (D3L model) proposed in our early work, we study the entanglement problem of composite bosons. Consider three first energy levels are known, we can get two energy separations, and can define the level deformation parameter δ. Using connection between q-deformed harmonic oscillator and Morse-like anharmonic potential, the deform parameter q also can be derived explicitly. Like the Einstein’s theory of special relativity, we introduce the observer e˙ects: out side observer (looking from outside the studying system) and inside observer (looking inside the studying system). Corresponding to those observers, the outside entanglement entropy and inside entanglement entropy will be defined.. Like the case of Foucault pendulum in the problem of Earth rotation, our deformation energy level investigation might be useful in prediction the environment e˙ect outside a confined box.

Quantum cryptography as a retrodiction problem.

PubMed

Werner, A H; Franz, T; Werner, R F

2009-11-27

We propose a quantum key distribution protocol based on a quantum retrodiction protocol, known as the Mean King problem. The protocol uses a two way quantum channel. We show security against coherent attacks in a transmission-error free scenario, even if Eve is allowed to attack both transmissions. This establishes a connection between retrodiction and key distribution.

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.

Compiling quantum circuits to realistic hardware architectures using temporal planners

NASA Astrophysics Data System (ADS)

Venturelli, Davide; Do, Minh; Rieffel, Eleanor; Frank, Jeremy

2018-04-01

To run quantum algorithms on emerging gate-model quantum hardware, quantum circuits must be compiled to take into account constraints on the hardware. For near-term hardware, with only limited means to mitigate decoherence, it is critical to minimize the duration of the circuit. We investigate the application of temporal planners to the problem of compiling quantum circuits to newly emerging quantum hardware. While our approach is general, we focus on compiling to superconducting hardware architectures with nearest neighbor constraints. Our initial experiments focus on compiling Quantum Alternating Operator Ansatz (QAOA) circuits whose high number of commuting gates allow great flexibility in the order in which the gates can be applied. That freedom makes it more challenging to find optimal compilations but also means there is a greater potential win from more optimized compilation than for less flexible circuits. We map this quantum circuit compilation problem to a temporal planning problem, and generated a test suite of compilation problems for QAOA circuits of various sizes to a realistic hardware architecture. We report compilation results from several state-of-the-art temporal planners on this test set. This early empirical evaluation demonstrates that temporal planning is a viable approach to quantum circuit compilation.

Exploring the quantum speed limit with computer games

NASA Astrophysics Data System (ADS)

Sørensen, Jens Jakob W. H.; Pedersen, Mads Kock; Munch, Michael; Haikka, Pinja; Jensen, Jesper Halkjær; Planke, Tilo; Andreasen, Morten Ginnerup; Gajdacz, Miroslav; Mølmer, Klaus; Lieberoth, Andreas; Sherson, Jacob F.

2016-04-01

Humans routinely solve problems of immense computational complexity by intuitively forming simple, low-dimensional heuristic strategies. Citizen science (or crowd sourcing) is a way of exploiting this ability by presenting scientific research problems to non-experts. ‘Gamification’—the application of game elements in a non-game context—is an effective tool with which to enable citizen scientists to provide solutions to research problems. The citizen science games Foldit, EteRNA and EyeWire have been used successfully to study protein and RNA folding and neuron mapping, but so far gamification has not been applied to problems in quantum physics. Here we report on Quantum Moves, an online platform gamifying optimization problems in quantum physics. We show that human players are able to find solutions to difficult problems associated with the task of quantum computing. Players succeed where purely numerical optimization fails, and analyses of their solutions provide insights into the problem of optimization of a more profound and general nature. Using player strategies, we have thus developed a few-parameter heuristic optimization method that efficiently outperforms the most prominent established numerical methods. The numerical complexity associated with time-optimal solutions increases for shorter process durations. To understand this better, we produced a low-dimensional rendering of the optimization landscape. This rendering reveals why traditional optimization methods fail near the quantum speed limit (that is, the shortest process duration with perfect fidelity). Combined analyses of optimization landscapes and heuristic solution strategies may benefit wider classes of optimization problems in quantum physics and beyond.

Exploring the quantum speed limit with computer games.

PubMed

Sørensen, Jens Jakob W H; Pedersen, Mads Kock; Munch, Michael; Haikka, Pinja; Jensen, Jesper Halkjær; Planke, Tilo; Andreasen, Morten Ginnerup; Gajdacz, Miroslav; Mølmer, Klaus; Lieberoth, Andreas; Sherson, Jacob F

2016-04-14

Humans routinely solve problems of immense computational complexity by intuitively forming simple, low-dimensional heuristic strategies. Citizen science (or crowd sourcing) is a way of exploiting this ability by presenting scientific research problems to non-experts. 'Gamification'--the application of game elements in a non-game context--is an effective tool with which to enable citizen scientists to provide solutions to research problems. The citizen science games Foldit, EteRNA and EyeWire have been used successfully to study protein and RNA folding and neuron mapping, but so far gamification has not been applied to problems in quantum physics. Here we report on Quantum Moves, an online platform gamifying optimization problems in quantum physics. We show that human players are able to find solutions to difficult problems associated with the task of quantum computing. Players succeed where purely numerical optimization fails, and analyses of their solutions provide insights into the problem of optimization of a more profound and general nature. Using player strategies, we have thus developed a few-parameter heuristic optimization method that efficiently outperforms the most prominent established numerical methods. The numerical complexity associated with time-optimal solutions increases for shorter process durations. To understand this better, we produced a low-dimensional rendering of the optimization landscape. This rendering reveals why traditional optimization methods fail near the quantum speed limit (that is, the shortest process duration with perfect fidelity). Combined analyses of optimization landscapes and heuristic solution strategies may benefit wider classes of optimization problems in quantum physics and beyond.

The classical limit of minimal length uncertainty relation: revisit with the Hamilton-Jacobi method

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

Guo, Xiaobo; Wang, Peng; Yang, Haitang, E-mail: guoxiaobo@swust.edu.cn, E-mail: pengw@scu.edu.cn, E-mail: hyanga@scu.edu.cn

2016-05-01

The existence of a minimum measurable length could deform not only the standard quantum mechanics but also classical physics. The effects of the minimal length on classical orbits of particles in a gravitation field have been investigated before, using the deformed Poisson bracket or Schwarzschild metric. In this paper, we first use the Hamilton-Jacobi method to derive the deformed equations of motion in the context of Newtonian mechanics and general relativity. We then employ them to study the precession of planetary orbits, deflection of light, and time delay in radar propagation. We also set limits on the deformation parameter bymore » comparing our results with the observational measurements. Finally, comparison with results from previous papers is given at the end of this paper.« less

Quantum issues in optical communication. [noise reduction in signal reception

NASA Technical Reports Server (NTRS)

Kennedy, R. S.

1973-01-01

Various approaches to the problem of controlling quantum noise, the dominant noise in an optical communications system, are discussed. It is shown that, no matter which way the problem is approached, there always remain uncertainties. These uncertainties exist because, to date, only very few communication problems have been solved in their full quantum form.

Quantum adiabatic machine learning

NASA Astrophysics Data System (ADS)

Pudenz, Kristen L.; Lidar, Daniel A.

2013-05-01

We develop an approach to machine learning and anomaly detection via quantum adiabatic evolution. This approach consists of two quantum phases, with some amount of classical preprocessing to set up the quantum problems. In the training phase we identify an optimal set of weak classifiers, to form a single strong classifier. In the testing phase we adiabatically evolve one or more strong classifiers on a superposition of inputs in order to find certain anomalous elements in the classification space. Both the training and testing phases are executed via quantum adiabatic evolution. All quantum processing is strictly limited to two-qubit interactions so as to ensure physical feasibility. We apply and illustrate this approach in detail to the problem of software verification and validation, with a specific example of the learning phase applied to a problem of interest in flight control systems. Beyond this example, the algorithm can be used to attack a broad class of anomaly detection problems.

Experimental realization of a one-way quantum computer algorithm solving Simon's problem.

PubMed

Tame, M S; Bell, B A; Di Franco, C; Wadsworth, W J; Rarity, J G

2014-11-14

We report an experimental demonstration of a one-way implementation of a quantum algorithm solving Simon's problem-a black-box period-finding problem that has an exponential gap between the classical and quantum runtime. Using an all-optical setup and modifying the bases of single-qubit measurements on a five-qubit cluster state, key representative functions of the logical two-qubit version's black box can be queried and solved. To the best of our knowledge, this work represents the first experimental realization of the quantum algorithm solving Simon's problem. The experimental results are in excellent agreement with the theoretical model, demonstrating the successful performance of the algorithm. With a view to scaling up to larger numbers of qubits, we analyze the resource requirements for an n-qubit version. This work helps highlight how one-way quantum computing provides a practical route to experimentally investigating the quantum-classical gap in the query complexity model.

Demonstration of quantum advantage in machine learning

NASA Astrophysics Data System (ADS)

Ristè, Diego; da Silva, Marcus P.; Ryan, Colm A.; Cross, Andrew W.; Córcoles, Antonio D.; Smolin, John A.; Gambetta, Jay M.; Chow, Jerry M.; Johnson, Blake R.

2017-04-01

The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage involve the repeated use of a black box, or oracle, whose structure encodes the solution. One measure of the algorithmic performance is the query complexity, i.e., the scaling of the number of oracle calls needed to find the solution with a given probability. Few-qubit demonstrations of quantum algorithms, such as Deutsch-Jozsa and Grover, have been implemented across diverse physical systems such as nuclear magnetic resonance, trapped ions, optical systems, and superconducting circuits. However, at the small scale, these problems can already be solved classically with a few oracle queries, limiting the obtained advantage. Here we solve an oracle-based problem, known as learning parity with noise, on a five-qubit superconducting processor. Executing classical and quantum algorithms using the same oracle, we observe a large gap in query count in favor of quantum processing. We find that this gap grows by orders of magnitude as a function of the error rates and the problem size. This result demonstrates that, while complex fault-tolerant architectures will be required for universal quantum computing, a significant quantum advantage already emerges in existing noisy systems.

An implementation problem for boson fields and quantum Girsanov transform

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

Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr; Obata, Nobuaki, E-mail: obata@math.is.tohoku.ac.jp

2016-08-15

We study an implementation problem for quadratic functions of annihilation and creation operators on a boson field in terms of quantum white noise calculus. The implementation problem is shown to be equivalent to a linear differential equation for white noise operators containing quantum white noise derivatives. The solution is explicitly obtained and turns out to form a class of white noise operators including generalized Fourier–Gauss and Fourier–Mehler transforms, Bogoliubov transform, and a quantum extension of the Girsanov transform.

Portfolios of quantum algorithms.

PubMed

Maurer, S M; Hogg, T; Huberman, B A

2001-12-17

Quantum computation holds promise for the solution of many intractable problems. However, since many quantum algorithms are stochastic in nature they can find the solution of hard problems only probabilistically. Thus the efficiency of the algorithms has to be characterized by both the expected time to completion and the associated variance. In order to minimize both the running time and its uncertainty, we show that portfolios of quantum algorithms analogous to those of finance can outperform single algorithms when applied to the NP-complete problems such as 3-satisfiability.

Quantum learning of classical stochastic processes: The completely positive realization problem

NASA Astrophysics Data System (ADS)

Monràs, Alex; Winter, Andreas

2016-01-01

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651-664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece in the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [M. Guţă, Phys. Rev. A 83(6), 062324 (2011); M. Guţă and N. Yamamoto, e-print arXiv:1303.3771(2013)].

Quantum κ-deformed differential geometry and field theory

NASA Astrophysics Data System (ADS)

Mercati, Flavio

2016-03-01

I introduce in κ-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge-∗ and the metric. I show the relevance of these tools for field theory with an application to complex scalar field, for which I am able to identify a vector-valued four-form which generalizes the energy-momentum tensor. Its closedness is proved, expressing in a covariant form the conservation of energy-momentum.

Quantum walks, deformed relativity and Hopf algebra symmetries.

PubMed

Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo

2016-05-28

We show how the Weyl quantum walk derived from principles in D'Ariano & Perinotti (D'Ariano & Perinotti 2014Phys. Rev. A90, 062106. (doi:10.1103/PhysRevA.90.062106)), enjoying a nonlinear Lorentz symmetry of dynamics, allows one to introduce Hopf algebras for position and momentum of the emerging particle. We focus on two special models of Hopf algebras-the usual Poincaré and theκ-Poincaré algebras. © 2016 The Author(s).

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.

Quantum speedup in solving the maximal-clique problem

NASA Astrophysics Data System (ADS)

Chang, Weng-Long; Yu, Qi; Li, Zhaokai; Chen, Jiahui; Peng, Xinhua; Feng, Mang

2018-03-01

The maximal-clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry, and bioinformatics to social networks. Here we develop a quantum algorithm to solve the maximal-clique problem for any graph G with n vertices with quadratic speedup over its classical counterparts, where the time and spatial complexities are reduced to, respectively, O (√{2n}) and O (n2) . With respect to oracle-related quantum algorithms for the NP-complete problems, we identify our algorithm as optimal. To justify the feasibility of the proposed quantum algorithm, we successfully solve a typical clique problem for a graph G with two vertices and one edge by carrying out a nuclear magnetic resonance experiment involving four qubits.

Decoherence induced deformation of the ground state in adiabatic quantum computation.

PubMed

Deng, Qiang; Averin, Dmitri V; Amin, Mohammad H; Smith, Peter

2013-01-01

Despite more than a decade of research on adiabatic quantum computation (AQC), its decoherence properties are still poorly understood. Many theoretical works have suggested that AQC is more robust against decoherence, but a quantitative relation between its performance and the qubits' coherence properties, such as decoherence time, is still lacking. While the thermal excitations are known to be important sources of errors, they are predominantly dependent on temperature but rather insensitive to the qubits' coherence. Less understood is the role of virtual excitations, which can also reduce the ground state probability even at zero temperature. Here, we introduce normalized ground state fidelity as a measure of the decoherence-induced deformation of the ground state due to virtual transitions. We calculate the normalized fidelity perturbatively at finite temperatures and discuss its relation to the qubits' relaxation and dephasing times, as well as its projected scaling properties.

Decoherence induced deformation of the ground state in adiabatic quantum computation

PubMed Central

Deng, Qiang; Averin, Dmitri V.; Amin, Mohammad H.; Smith, Peter

2013-01-01

Despite more than a decade of research on adiabatic quantum computation (AQC), its decoherence properties are still poorly understood. Many theoretical works have suggested that AQC is more robust against decoherence, but a quantitative relation between its performance and the qubits' coherence properties, such as decoherence time, is still lacking. While the thermal excitations are known to be important sources of errors, they are predominantly dependent on temperature but rather insensitive to the qubits' coherence. Less understood is the role of virtual excitations, which can also reduce the ground state probability even at zero temperature. Here, we introduce normalized ground state fidelity as a measure of the decoherence-induced deformation of the ground state due to virtual transitions. We calculate the normalized fidelity perturbatively at finite temperatures and discuss its relation to the qubits' relaxation and dephasing times, as well as its projected scaling properties. PMID:23528821

Thermodynamics properties study of diatomic molecules with q-deformed modified Poschl-Teller plus Manning Rosen non-central potential in D dimensions using SUSYQM approach

NASA Astrophysics Data System (ADS)

Suparmi, A.; Cari, C.; Pratiwi, B. N.

2016-04-01

D-dimensional Dirac equation of q-deformed modified Poschl-Teller plus Manning Rosen non-central potential was solved using supersymmetric quantum mechanics (SUSY QM). The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial part of D dimensional Dirac equation and the angular quantum numbers were obtained from angular part of D dimensional Dirac equation. The SUSY operators was used to generate the D dimensional relativistic wave functions both for radial and angular parts. In the non-relativistic limit, the relativistic energy equation was reduced to the non-relativistic energy. In the classical limit, the partition function of vibrational, the specific heat of vibrational, and the mean energy of vibrational of some diatomic molecules were calculated from the equation of non-relativistic energy with the help of error function and Mat-lab 2011.

Quantum proofs can be verified using only single-qubit measurements

NASA Astrophysics Data System (ADS)

Morimae, Tomoyuki; Nagaj, Daniel; Schuch, Norbert

2016-02-01

Quantum Merlin Arthur (QMA) is the class of problems which, though potentially hard to solve, have a quantum solution that can be verified efficiently using a quantum computer. It thus forms a natural quantum version of the classical complexity class NP (and its probabilistic variant MA, Merlin-Arthur games), where the verifier has only classical computational resources. In this paper, we study what happens when we restrict the quantum resources of the verifier to the bare minimum: individual measurements on single qubits received as they come, one by one. We find that despite this grave restriction, it is still possible to soundly verify any problem in QMA for the verifier with the minimum quantum resources possible, without using any quantum memory or multiqubit operations. We provide two independent proofs of this fact, based on measurement-based quantum computation and the local Hamiltonian problem. The former construction also applies to QMA1, i.e., QMA with one-sided error.

Empirical p-n interactions, the synchronized filling of Nilsson orbitals, and emergent collectivity

NASA Astrophysics Data System (ADS)

Cakirli, R. B.

2014-09-01

The onset of collectivity and deformation, changes to the single particle energies and magic numbers and so on are strongly influenced by, for example, proton (p) and neutron (n) interactions inside atomic nuclei. Experimentally, using binding energies (or masses), one can extract an average p-n interaction between the last two protons and the last two neutrons, called δVpn. We have studied δVpn values using calculations of spatial overlaps between p and n Nilsson orbitals, considering different deformations, for the Z= 50-82, N= 82-126 shells, and comparison of these theoretical results with experimental δVpn values. Our results show that enhanced valence p-n interactions are closely correlated with the development of collectivity, shape changes, and the saturation of deformation in nuclei. We note that the difference of the Nilsson quantum numbers of the last filled Nilsson p and n orbitals, has a special relation, 0[110], in which they differ by only a single quantum in the z-direction, for those nuclei where δVpn is largest for each Z in medium mass and heavy nuclei. The synchronised filling of such orbital pairs correlates with the emergence of collectivity.

A synchronous game for binary constraint systems

NASA Astrophysics Data System (ADS)

Kim, Se-Jin; Paulsen, Vern; Schafhauser, Christopher

2018-03-01

Recently, Slofstra proved that the set of quantum correlations is not closed. We prove that the set of synchronous quantum correlations is not closed, which implies his result, by giving an example of a synchronous game that has a perfect quantum approximate strategy but no perfect quantum strategy. We also exhibit a graph for which the quantum independence number and the quantum approximate independence number are different. We prove new characterisations of synchronous quantum approximate correlations and synchronous quantum spatial correlations. We solve the synchronous approximation problem of Dykema and the second author, which yields a new equivalence of Connes' embedding problem in terms of synchronous correlations.

Instantons in Quantum Annealing: Thermally Assisted Tunneling Vs Quantum Monte Carlo Simulations

NASA Technical Reports Server (NTRS)

Jiang, Zhang; Smelyanskiy, Vadim N.; Boixo, Sergio; Isakov, Sergei V.; Neven, Hartmut; Mazzola, Guglielmo; Troyer, Matthias

2015-01-01

Recent numerical result (arXiv:1512.02206) from Google suggested that the D-Wave quantum annealer may have an asymptotic speed-up than simulated annealing, however, the asymptotic advantage disappears when it is compared to quantum Monte Carlo (a classical algorithm despite its name). We show analytically that the asymptotic scaling of quantum tunneling is exactly the same as the escape rate in quantum Monte Carlo for a class of problems. Thus, the Google result might be explained in our framework. We also found that the transition state in quantum Monte Carlo corresponds to the instanton solution in quantum tunneling problems, which is observed in numerical simulations.

The Quantum Logical Challenge: Peter Mittelstaedt's Contributions to Logic and Philosophy of Science

NASA Astrophysics Data System (ADS)

Beltrametti, E.; Dalla Chiara, M. L.; Giuntini, R.

2017-12-01

Peter Mittelstaedt's contributions to quantum logic and to the foundational problems of quantum theory have significantly realized the most authentic spirit of the International Quantum Structures Association: an original research about hard technical problems, which are often "entangled" with the emergence of important changes in our general world-conceptions. During a time where both the logical and the physical community often showed a skeptical attitude towards Birkhoff and von Neumann's quantum logic, Mittelstaedt brought into light the deeply innovating features of a quantum logical thinking that allows us to overcome some strong and unrealistic assumptions of classical logical arguments. Later on his intense research on the unsharp approach to quantum theory and to the measurement problem stimulated the increasing interest for unsharp forms of quantum logic, creating a fruitful interaction between the work of quantum logicians and of many-valued logicians. Mittelstaedt's general views about quantum logic and quantum theory seem to be inspired by a conjecture that is today more and more confirmed: there is something universal in the quantum theoretic formalism that goes beyond the limits of microphysics, giving rise to interesting applications to a number of different fields.

Programming and Tuning a Quantum Annealing Device to Solve Real World Problems

NASA Astrophysics Data System (ADS)

Perdomo-Ortiz, Alejandro; O'Gorman, Bryan; Fluegemann, Joseph; Smelyanskiy, Vadim

2015-03-01

Solving real-world applications with quantum algorithms requires overcoming several challenges, ranging from translating the computational problem at hand to the quantum-machine language to tuning parameters of the quantum algorithm that have a significant impact on the performance of the device. In this talk, we discuss these challenges, strategies developed to enhance performance, and also a more efficient implementation of several applications. Although we will focus on applications of interest to NASA's Quantum Artificial Intelligence Laboratory, the methods and concepts presented here apply to a broader family of hard discrete optimization problems, including those that occur in many machine-learning algorithms.

Experimental demonstration of a quantum annealing algorithm for the traveling salesman problem in a nuclear-magnetic-resonance quantum simulator

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

Chen Hongwei; High Magnetic Field Laboratory, Hefei Institutes of Physical Science, Chinese Academy of Sciences, Hefei 230031; Kong Xi

The method of quantum annealing (QA) is a promising way for solving many optimization problems in both classical and quantum information theory. The main advantage of this approach, compared with the gate model, is the robustness of the operations against errors originated from both external controls and the environment. In this work, we succeed in demonstrating experimentally an application of the method of QA to a simplified version of the traveling salesman problem by simulating the corresponding Schroedinger evolution with a NMR quantum simulator. The experimental results unambiguously yielded the optimal traveling route, in good agreement with the theoretical prediction.

Isometric deformations of planar quadrilaterals with constant index

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

Zaputryaeva, E S

We consider isometric deformations (motions) of polygons (so-called carpenter's rule problem) in the case of self-intersecting polygons with the additional condition that the index of the polygon is preserved by the motion. We provide general information about isometric deformations of planar polygons and give a complete solution of the carpenter's problem for quadrilaterals. Bibliography: 17 titles.

Exploring quantum computing application to satellite data assimilation

NASA Astrophysics Data System (ADS)

Cheung, S.; Zhang, S. Q.

2015-12-01

This is an exploring work on potential application of quantum computing to a scientific data optimization problem. On classical computational platforms, the physical domain of a satellite data assimilation problem is represented by a discrete variable transform, and classical minimization algorithms are employed to find optimal solution of the analysis cost function. The computation becomes intensive and time-consuming when the problem involves large number of variables and data. The new quantum computer opens a very different approach both in conceptual programming and in hardware architecture for solving optimization problem. In order to explore if we can utilize the quantum computing machine architecture, we formulate a satellite data assimilation experimental case in the form of quadratic programming optimization problem. We find a transformation of the problem to map it into Quadratic Unconstrained Binary Optimization (QUBO) framework. Binary Wavelet Transform (BWT) will be applied to the data assimilation variables for its invertible decomposition and all calculations in BWT are performed by Boolean operations. The transformed problem will be experimented as to solve for a solution of QUBO instances defined on Chimera graphs of the quantum computer.

Simultaneous two component squeezing in generalized q-coherent states

NASA Technical Reports Server (NTRS)

Mcdermott, Roger J.; Solomon, Allan I.

1994-01-01

Using a generalization of the q-commutation relations, we develop a formalism in which it is possible to define generalized q-bosonic operators. This formalism includes both types of the usual q-deformed bosons as special cases. The coherent states of these operators show interesting and novel noise reduction properties including simultaneous squeezing in both field components, unlike the conventional case in which squeezing is permitted in only one component. This also contrasts with the usual quantum group deformation which also only permits one component squeezing.

Anamorphic quasiperiodic universes in modified and Einstein gravity with loop quantum gravity corrections

NASA Astrophysics Data System (ADS)

Amaral, Marcelo M.; Aschheim, Raymond; Bubuianu, Laurenţiu; Irwin, Klee; Vacaru, Sergiu I.; Woolridge, Daniel

2017-09-01

The goal of this work is to elaborate on new geometric methods of constructing exact and parametric quasiperiodic solutions for anamorphic cosmology models in modified gravity theories, MGTs, and general relativity, GR. There exist previously studied generic off-diagonal and diagonalizable cosmological metrics encoding gravitational and matter fields with quasicrystal like structures, QC, and holonomy corrections from loop quantum gravity, LQG. We apply the anholonomic frame deformation method, AFDM, in order to decouple the (modified) gravitational and matter field equations in general form. This allows us to find integral varieties of cosmological solutions determined by generating functions, effective sources, integration functions and constants. The coefficients of metrics and connections for such cosmological configurations depend, in general, on all spacetime coordinates and can be chosen to generate observable (quasi)-periodic/aperiodic/fractal/stochastic/(super) cluster/filament/polymer like (continuous, stochastic, fractal and/or discrete structures) in MGTs and/or GR. In this work, we study new classes of solutions for anamorphic cosmology with LQG holonomy corrections. Such solutions are characterized by nonlinear symmetries of generating functions for generic off-diagonal cosmological metrics and generalized connections, with possible nonholonomic constraints to Levi-Civita configurations and diagonalizable metrics depending only on a time like coordinate. We argue that anamorphic quasiperiodic cosmological models integrate the concept of quantum discrete spacetime, with certain gravitational QC-like vacuum and nonvacuum structures. And, that of a contracting universe that homogenizes, isotropizes and flattens without introducing initial conditions or multiverse problems.

Quantum Machine Learning

NASA Technical Reports Server (NTRS)

Biswas, Rupak

2018-01-01

Quantum computing promises an unprecedented ability to solve intractable problems by harnessing quantum mechanical effects such as tunneling, superposition, and entanglement. The Quantum Artificial Intelligence Laboratory (QuAIL) at NASA Ames Research Center is the space agency's primary facility for conducting research and development in quantum information sciences. QuAIL conducts fundamental research in quantum physics but also explores how best to exploit and apply this disruptive technology to enable NASA missions in aeronautics, Earth and space sciences, and space exploration. At the same time, machine learning has become a major focus in computer science and captured the imagination of the public as a panacea to myriad big data problems. In this talk, we will discuss how classical machine learning can take advantage of quantum computing to significantly improve its effectiveness. Although we illustrate this concept on a quantum annealer, other quantum platforms could be used as well. If explored fully and implemented efficiently, quantum machine learning could greatly accelerate a wide range of tasks leading to new technologies and discoveries that will significantly change the way we solve real-world problems.

Coherent states for quantum compact groups

NASA Astrophysics Data System (ADS)

Jurĉo, B.; Ŝťovíĉek, P.

1996-12-01

Coherent states are introduced and their properties are discussed for simple quantum compact groups A l, Bl, Cl and D l. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R-matrix formulation (generalizing this way the q-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested.

Solving search problems by strongly simulating quantum circuits

PubMed Central

Johnson, T. H.; Biamonte, J. D.; Clark, S. R.; Jaksch, D.

2013-01-01

Simulating quantum circuits using classical computers lets us analyse the inner workings of quantum algorithms. The most complete type of simulation, strong simulation, is believed to be generally inefficient. Nevertheless, several efficient strong simulation techniques are known for restricted families of quantum circuits and we develop an additional technique in this article. Further, we show that strong simulation algorithms perform another fundamental task: solving search problems. Efficient strong simulation techniques allow solutions to a class of search problems to be counted and found efficiently. This enhances the utility of strong simulation methods, known or yet to be discovered, and extends the class of search problems known to be efficiently simulable. Relating strong simulation to search problems also bounds the computational power of efficiently strongly simulable circuits; if they could solve all problems in P this would imply that all problems in NP and #P could be solved in polynomial time. PMID:23390585

Enhancing quantum annealing performance for the molecular similarity problem

NASA Astrophysics Data System (ADS)

Hernandez, Maritza; Aramon, Maliheh

2017-05-01

Quantum annealing is a promising technique which leverages quantum mechanics to solve hard optimization problems. Considerable progress has been made in the development of a physical quantum annealer, motivating the study of methods to enhance the efficiency of such a solver. In this work, we present a quantum annealing approach to measure similarity among molecular structures. Implementing real-world problems on a quantum annealer is challenging due to hardware limitations such as sparse connectivity, intrinsic control error, and limited precision. In order to overcome the limited connectivity, a problem must be reformulated using minor-embedding techniques. Using a real data set, we investigate the performance of a quantum annealer in solving the molecular similarity problem. We provide experimental evidence that common practices for embedding can be replaced by new alternatives which mitigate some of the hardware limitations and enhance its performance. Common practices for embedding include minimizing either the number of qubits or the chain length and determining the strength of ferromagnetic couplers empirically. We show that current criteria for selecting an embedding do not improve the hardware's performance for the molecular similarity problem. Furthermore, we use a theoretical approach to determine the strength of ferromagnetic couplers. Such an approach removes the computational burden of the current empirical approaches and also results in hardware solutions that can benefit from simple local classical improvement. Although our results are limited to the problems considered here, they can be generalized to guide future benchmarking studies.

Probing for quantum speedup in spin-glass problems with planted solutions

NASA Astrophysics Data System (ADS)

Hen, Itay; Job, Joshua; Albash, Tameem; Rønnow, Troels F.; Troyer, Matthias; Lidar, Daniel A.

2015-10-01

The availability of quantum annealing devices with hundreds of qubits has made the experimental demonstration of a quantum speedup for optimization problems a coveted, albeit elusive goal. Going beyond earlier studies of random Ising problems, here we introduce a method to construct a set of frustrated Ising-model optimization problems with tunable hardness. We study the performance of a D-Wave Two device (DW2) with up to 503 qubits on these problems and compare it to a suite of classical algorithms, including a highly optimized algorithm designed to compete directly with the DW2. The problems are generated around predetermined ground-state configurations, called planted solutions, which makes them particularly suitable for benchmarking purposes. The problem set exhibits properties familiar from constraint satisfaction (SAT) problems, such as a peak in the typical hardness of the problems, determined by a tunable clause density parameter. We bound the hardness regime where the DW2 device either does not or might exhibit a quantum speedup for our problem set. While we do not find evidence for a speedup for the hardest and most frustrated problems in our problem set, we cannot rule out that a speedup might exist for some of the easier, less frustrated problems. Our empirical findings pertain to the specific D-Wave processor and problem set we studied and leave open the possibility that future processors might exhibit a quantum speedup on the same problem set.

Quantum Stress: Density Functional Theory Formulation and Physical Manifestation

NASA Astrophysics Data System (ADS)

Hu, Hao; Liu, Feng

2012-02-01

The concept of ``quantum stress (QS)'' is introduced and formulated within density functional theory (DFT), to underlie extrinsic electronic effects on the stress state of solids and thin films in the absence of lattice strain. An explicit expression of QS (σ^Q) is derived in relation to the deformation potential of electronic states (ξ) and the variation of electron density (δn), σ^Q=ξ(δn), as a quantum analog of classical Hook's law. Two distinct QS manifestations are demonstrated quantitatively by DFT calculations: (1) in the form of bulk stress induced by charge carriers; and (2) in the form of surface stress induced by quantum confinement. QS has broad implications in physical phenomena and technological applications that are based on coupling of electronic structure with lattice strain.

Possible form of vacuum deformation by heavy particles

NASA Technical Reports Server (NTRS)

Mackenzie, R.; Wilczek, F.; Zee, A.

1984-01-01

The possibility is discussed that the lowest-energy state for certain quantum numbers involves a Higgs field polarized into a skyrmion-type configuration. In some models a new type of vacuum instability arises. Phenomenological consequences are indicated schematically.

Probing noncommutative theories with quantum optical experiments

NASA Astrophysics Data System (ADS)

Dey, Sanjib; Bhat, Anha; Momeni, Davood; Faizal, Mir; Ali, Ahmed Farag; Dey, Tarun Kumar; Rehman, Atikur

2017-11-01

One of the major difficulties of modern science underlies at the unification of general relativity and quantum mechanics. Different approaches towards such theory have been proposed. Noncommutative theories serve as the root of almost all such approaches. However, the identification of the appropriate passage to quantum gravity is suffering from the inadequacy of experimental techniques. It is beyond our ability to test the effects of quantum gravity thorough the available scattering experiments, as it is unattainable to probe such high energy scale at which the effects of quantum gravity appear. Here we propose an elegant alternative scheme to test such theories by detecting the deformations emerging from the noncommutative structures. Our protocol relies on the novelty of an opto-mechanical experimental setup where the information of the noncommutative oscillator is exchanged via the interaction with an optical pulse inside an optical cavity. We also demonstrate that our proposal is within the reach of current technology and, thus, it could uncover a feasible route towards the realization of quantum gravitational phenomena thorough a simple table-top experiment.

Ultrafast adiabatic quantum algorithm for the NP-complete exact cover problem

PubMed Central

Wang, Hefeng; Wu, Lian-Ao

2016-01-01

An adiabatic quantum algorithm may lose quantumness such as quantum coherence entirely in its long runtime, and consequently the expected quantum speedup of the algorithm does not show up. Here we present a general ultrafast adiabatic quantum algorithm. We show that by applying a sequence of fast random or regular signals during evolution, the runtime can be reduced substantially, whereas advantages of the adiabatic algorithm remain intact. We also propose a randomized Trotter formula and show that the driving Hamiltonian and the proposed sequence of fast signals can be implemented simultaneously. We illustrate the algorithm by solving the NP-complete 3-bit exact cover problem (EC3), where NP stands for nondeterministic polynomial time, and put forward an approach to implementing the problem with trapped ions. PMID:26923834

Fidelity-Based Ant Colony Algorithm with Q-learning of Quantum System

NASA Astrophysics Data System (ADS)

Liao, Qin; Guo, Ying; Tu, Yifeng; Zhang, Hang

2018-03-01

Quantum ant colony algorithm (ACA) has potential applications in quantum information processing, such as solutions of traveling salesman problem, zero-one knapsack problem, robot route planning problem, and so on. To shorten the search time of the ACA, we suggest the fidelity-based ant colony algorithm (FACA) for the control of quantum system. Motivated by structure of the Q-learning algorithm, we demonstrate the combination of a FACA with the Q-learning algorithm and suggest the design of a fidelity-based ant colony algorithm with the Q-learning to improve the performance of the FACA in a spin-1/2 quantum system. The numeric simulation results show that the FACA with the Q-learning can efficiently avoid trapping into local optimal policies and increase the speed of convergence process of quantum system.

Fidelity-Based Ant Colony Algorithm with Q-learning of Quantum System

NASA Astrophysics Data System (ADS)

Liao, Qin; Guo, Ying; Tu, Yifeng; Zhang, Hang

2017-12-01

Quantum ant colony algorithm (ACA) has potential applications in quantum information processing, such as solutions of traveling salesman problem, zero-one knapsack problem, robot route planning problem, and so on. To shorten the search time of the ACA, we suggest the fidelity-based ant colony algorithm (FACA) for the control of quantum system. Motivated by structure of the Q-learning algorithm, we demonstrate the combination of a FACA with the Q-learning algorithm and suggest the design of a fidelity-based ant colony algorithm with the Q-learning to improve the performance of the FACA in a spin-1/2 quantum system. The numeric simulation results show that the FACA with the Q-learning can efficiently avoid trapping into local optimal policies and increase the speed of convergence process of quantum system.

Playing distributed two-party quantum games on quantum networks

NASA Astrophysics Data System (ADS)

Liu, Bo-Yang; Dai, Hong-Yi; Zhang, Ming

2017-12-01

This paper investigates quantum games between two remote players on quantum networks. We propose two schemes for distributed remote quantum games: the client-server scheme based on states transmission between nodes of the network and the peer-to-peer scheme devised upon remote quantum operations. Following these schemes, we construct two designs of the distributed prisoners' dilemma game on quantum entangling networks, where concrete methods are employed for teleportation and nonlocal two-qubits unitary gates, respectively. It seems to us that the requirement for playing distributed quantum games on networks is still an open problem. We explore this problem by comparing and characterizing the two schemes from the viewpoints of network structures, quantum and classical operations, experimental realization and simplification.

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.

Perfect quantum multiple-unicast network coding protocol

NASA Astrophysics Data System (ADS)

Li, Dan-Dan; Gao, Fei; Qin, Su-Juan; Wen, Qiao-Yan

2018-01-01

In order to realize long-distance and large-scale quantum communication, it is natural to utilize quantum repeater. For a general quantum multiple-unicast network, it is still puzzling how to complete communication tasks perfectly with less resources such as registers. In this paper, we solve this problem. By applying quantum repeaters to multiple-unicast communication problem, we give encoding-decoding schemes for source nodes, internal ones and target ones, respectively. Source-target nodes share EPR pairs by using our encoding-decoding schemes over quantum multiple-unicast network. Furthermore, quantum communication can be accomplished perfectly via teleportation. Compared with existed schemes, our schemes can reduce resource consumption and realize long-distance transmission of quantum information.

A quantum annealing architecture with all-to-all connectivity from local interactions.

PubMed

Lechner, Wolfgang; Hauke, Philipp; Zoller, Peter

2015-10-01

Quantum annealers are physical devices that aim at solving NP-complete optimization problems by exploiting quantum mechanics. The basic principle of quantum annealing is to encode the optimization problem in Ising interactions between quantum bits (qubits). A fundamental challenge in building a fully programmable quantum annealer is the competing requirements of full controllable all-to-all connectivity and the quasi-locality of the interactions between physical qubits. We present a scalable architecture with full connectivity, which can be implemented with local interactions only. The input of the optimization problem is encoded in local fields acting on an extended set of physical qubits. The output is-in the spirit of topological quantum memories-redundantly encoded in the physical qubits, resulting in an intrinsic fault tolerance. Our model can be understood as a lattice gauge theory, where long-range interactions are mediated by gauge constraints. The architecture can be realized on various platforms with local controllability, including superconducting qubits, NV-centers, quantum dots, and atomic systems.

A quantum annealing architecture with all-to-all connectivity from local interactions

PubMed Central

Lechner, Wolfgang; Hauke, Philipp; Zoller, Peter

2015-01-01

Quantum annealers are physical devices that aim at solving NP-complete optimization problems by exploiting quantum mechanics. The basic principle of quantum annealing is to encode the optimization problem in Ising interactions between quantum bits (qubits). A fundamental challenge in building a fully programmable quantum annealer is the competing requirements of full controllable all-to-all connectivity and the quasi-locality of the interactions between physical qubits. We present a scalable architecture with full connectivity, which can be implemented with local interactions only. The input of the optimization problem is encoded in local fields acting on an extended set of physical qubits. The output is—in the spirit of topological quantum memories—redundantly encoded in the physical qubits, resulting in an intrinsic fault tolerance. Our model can be understood as a lattice gauge theory, where long-range interactions are mediated by gauge constraints. The architecture can be realized on various platforms with local controllability, including superconducting qubits, NV-centers, quantum dots, and atomic systems. PMID:26601316

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

Bezák, Viktor, E-mail: bezak@fmph.uniba.sk

Quantum theory of the non-harmonic oscillator defined by the energy operator proposed by Yurke and Buks (2006) is presented. Although these authors considered a specific problem related to a model of transmission lines in a Kerr medium, our ambition is not to discuss the physical substantiation of their model. Instead, we consider the problem from an abstract, logically deductive, viewpoint. Using the Yurke–Buks energy operator, we focus attention on the imaginary-time propagator. We derive it as a functional of the Mehler kernel and, alternatively, as an exact series involving Hermite polynomials. For a statistical ensemble of identical oscillators defined bymore » the Yurke–Buks energy operator, we calculate the partition function, average energy, free energy and entropy. Using the diagonal element of the canonical density matrix of this ensemble in the coordinate representation, we define a probability density, which appears to be a deformed Gaussian distribution. A peculiarity of this probability density is that it may reveal, when plotted as a function of the position variable, a shape with two peaks located symmetrically with respect to the central point.« less

Quantum learning of classical stochastic processes: The completely positive realization problem

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

Monràs, Alex; Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543; Winter, Andreas

2016-01-15

Among several tasks in Machine Learning, a specially important one is the problem of inferring the latent variables of a system and their causal relations with the observed behavior. A paradigmatic instance of this is the task of inferring the hidden Markov model underlying a given stochastic process. This is known as the positive realization problem (PRP), [L. Benvenuti and L. Farina, IEEE Trans. Autom. Control 49(5), 651–664 (2004)] and constitutes a central problem in machine learning. The PRP and its solutions have far-reaching consequences in many areas of systems and control theory, and is nowadays an important piece inmore » the broad field of positive systems theory. We consider the scenario where the latent variables are quantum (i.e., quantum states of a finite-dimensional system) and the system dynamics is constrained only by physical transformations on the quantum system. The observable dynamics is then described by a quantum instrument, and the task is to determine which quantum instrument — if any — yields the process at hand by iterative application. We take as a starting point the theory of quasi-realizations, whence a description of the dynamics of the process is given in terms of linear maps on state vectors and probabilities are given by linear functionals on the state vectors. This description, despite its remarkable resemblance with the hidden Markov model, or the iterated quantum instrument, is however devoid of any stochastic or quantum mechanical interpretation, as said maps fail to satisfy any positivity conditions. The completely positive realization problem then consists in determining whether an equivalent quantum mechanical description of the same process exists. We generalize some key results of stochastic realization theory, and show that the problem has deep connections with operator systems theory, giving possible insight to the lifting problem in quotient operator systems. Our results have potential applications in quantum machine learning, device-independent characterization and reverse-engineering of stochastic processes and quantum processors, and more generally, of dynamical processes with quantum memory [M. Guţă, Phys. Rev. A 83(6), 062324 (2011); M. Guţă and N. Yamamoto, e-print http://arxiv.org/abs/1303.3771 (2013)].« less

The Role of Frame Force in Quantum Detection

DTIC Science & Technology

2007-01-01

42040) 10. C. H. Bennett, Quantum cryptography using any two nonorthogonal states, Phys. Rev. Lett. 68 (1992), no. 21, 3121–3124. MR 1 163 546 11. S ...SUBTITLE The Role of Frame Force in Quantum Detection 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR( S ) 5d. PROJECT...equivalent to a quantum detection problem from quantum mechanics. To this end we first reformulate Problem 1.2 in terms of orthonormal bases instead of 1

The q-harmonic oscillators, q-coherent states and the q-symplecton

NASA Technical Reports Server (NTRS)

Biedenharn, L. C.; Lohe, M. A.; Nomura, Masao

1993-01-01

The recently introduced notion of a quantum group is discussed conceptually and then related to deformed harmonic oscillators ('q-harmonic oscillators'). Two developments in applying q-harmonic oscillators are reviewed: q-coherent states and the q-symplecton.

Nuclear exoticism

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

Penionzhkevich, Yu. E., E-mail: pyuer@mail.ru

2016-07-15

Extreme states of nuclearmatter (such that feature high spins, large deformations, high density and temperature, or a large excess of neutrons and protons) play an important role in studying fundamental properties of nuclei and are helpful in solving the problem of constructing the equation of state for nuclear matter. The synthesis of neutron-rich nuclei near the nucleon drip lines and investigation of their properties permit drawing conclusions about the positions of these boundaries and deducing information about unusual states of such nuclei and about their decays. At the present time, experimental investigations along these lines can only be performed viamore » the cooperation of leading research centers that possess powerful heavy-ion accelerators, such as the Large Hadron Collider (LHC) at CERN and the heavy-ion cyclotrons at the Joint Institute for Nuclear Research (JINR, Dubna), where respective experiments are being conducted by physicists from about 20 JINR member countries. The present article gives a survey of the most recent results in the realms of super neutron-rich nuclei. Implications of the change in the structure of such nuclei near the nucleon drip lines are discussed. Information about the results obtained by measuring the masses (binding energies) of exotic nuclei, the nucleon-distribution radii (neutron halo) and momentum distributions in them, and their deformations and quantum properties is presented. It is shown that the properties of nuclei lying near the stability boundaries differ strongly from the properties of other nuclei. The problem of the stability of nuclei that is associated with the magic numbers of 20 and 28 is discussed along with the effect of new magic numbers.« less

Philosophical perspectives on quantum chaos: Models and interpretations

NASA Astrophysics Data System (ADS)

Bokulich, Alisa Nicole

2001-09-01

The problem of quantum chaos is a special case of the larger problem of understanding how the classical world emerges from quantum mechanics. While we have learned that chaos is pervasive in classical systems, it appears to be almost entirely absent in quantum systems. The aim of this dissertation is to determine what implications the interpretation of quantum mechanics has for attempts to explain the emergence of classical chaos. There are three interpretations of quantum mechanics that have set out programs for solving the problem of quantum chaos: the standard interpretation, the statistical interpretation, and the deBroglie-Bohm causal interpretation. One of the main conclusions of this dissertation is that an interpretation alone is insufficient for solving the problem of quantum chaos and that the phenomenon of decoherence must be taken into account. Although a completely satisfactory solution of the problem of quantum chaos is still outstanding, I argue that the deBroglie-Bohm interpretation with the help of decoherence outlines the most promising research program to pursue. In addition to making a contribution to the debate in the philosophy of physics concerning the interpretation of quantum mechanics, this dissertation reveals two important methodological lessons for the philosophy of science. First, issues of reductionism and intertheoretic relations cannot be divorced from questions concerning the interpretation of the theories involved. Not only is the exploration of intertheoretic relations a central part of the articulation and interpretation of an individual theory, but the very terms used to discuss intertheoretic relations, such as `state' and `classical limit', are themselves defined by particular interpretations of the theory. The second lesson that emerges is that, when it comes to characterizing the relationship between classical chaos and quantum mechanics, the traditional approaches to intertheoretic relations, namely reductionism and theoretical pluralism, are inadequate. The fruitful ways in which models have been used in quantum chaos research point to the need for a new framework for addressing intertheoretic relations that focuses on models rather than laws.

Quantum algorithm for solving some discrete mathematical problems by probing their energy spectra

NASA Astrophysics Data System (ADS)

Wang, Hefeng; Fan, Heng; Li, Fuli

2014-01-01

When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum algorithm for solving discrete mathematical problems based on the circuit model. Our algorithm has favorable scaling properties in solving some discrete mathematical problems.

A random walk approach to quantum algorithms.

PubMed

Kendon, Vivien M

2006-12-15

The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial; pure quantum dynamics is deterministic, so randomness only enters during the measurement phase, i.e. when converting the quantum information into classical information. The outcome of a quantum random walk is very different from the corresponding classical random walk owing to the interference between the different possible paths. The upshot is that quantum walkers find themselves further from their starting point than a classical walker on average, and this forms the basis of a quantum speed up, which can be exploited to solve problems faster. Surprisingly, the effect of making the walk slightly less than perfectly quantum can optimize the properties of the quantum walk for algorithmic applications. Looking to the future, even with a small quantum computer available, the development of quantum walk algorithms might proceed more rapidly than it has, especially for solving real problems.

Modeling of electrical and mesoscopic circuits at quantum nanoscale from heat momentum operator

NASA Astrophysics Data System (ADS)

El-Nabulsi, Rami Ahmad

2018-04-01

We develop a new method to study electrical circuits at quantum nanoscale by introducing a heat momentum operator which reproduces quantum effects similar to those obtained in Suykens's nonlocal-in-time kinetic energy approach for the case of reversible motion. The series expansion of the heat momentum operator is similar to the momentum operator obtained in the framework of minimal length phenomenologies characterized by the deformation of Heisenberg algebra. The quantization of both LC and mesoscopic circuits revealed a number of motivating features like the emergence of a generalized uncertainty relation and a minimal charge similar to those obtained in the framework of minimal length theories. Additional features were obtained and discussed accordingly.

Robust quantum optimizer with full connectivity.

PubMed

Nigg, Simon E; Lörch, Niels; Tiwari, Rakesh P

2017-04-01

Quantum phenomena have the potential to speed up the solution of hard optimization problems. For example, quantum annealing, based on the quantum tunneling effect, has recently been shown to scale exponentially better with system size than classical simulated annealing. However, current realizations of quantum annealers with superconducting qubits face two major challenges. First, the connectivity between the qubits is limited, excluding many optimization problems from a direct implementation. Second, decoherence degrades the success probability of the optimization. We address both of these shortcomings and propose an architecture in which the qubits are robustly encoded in continuous variable degrees of freedom. By leveraging the phenomenon of flux quantization, all-to-all connectivity with sufficient tunability to implement many relevant optimization problems is obtained without overhead. Furthermore, we demonstrate the robustness of this architecture by simulating the optimal solution of a small instance of the nondeterministic polynomial-time hard (NP-hard) and fully connected number partitioning problem in the presence of dissipation.

Fracture mechanics and parapsychology

NASA Astrophysics Data System (ADS)

Cherepanov, G. P.

2010-08-01

The problem of postcritical deformation of materials beyond the ultimate strength is considered a division of fracture mechanics. A simple example is used to show the relationship between this problem and parapsychology, which studies phenomena and processes where the causality principle fails. It is shown that the concept of postcritical deformation leads to problems with no solution

Students' Conceptual Difficulties in Quantum Mechanics: Potential Well Problems

ERIC Educational Resources Information Center

Ozcan, Ozgur; Didis, Nilufer; Tasar, Mehmet Fatih

2009-01-01

In this study, students' conceptual difficulties about some basic concepts in quantum mechanics like one-dimensional potential well problems and probability density of tunneling particles were identified. For this aim, a multiple choice instrument named Quantum Mechanics Conceptual Test has been developed by one of the researchers of this study…

Time-varying q-deformed dark energy interacts with dark matter

NASA Astrophysics Data System (ADS)

Dil, Emre; Kolay, Erdinç

We propose a new model for studying the dark constituents of the universe by regarding the dark energy as a q-deformed scalar field interacting with the dark matter, in the framework of standard general relativity. Here we assume that the number of particles in each mode of the q-deformed scalar field varies in time by the particle creation and annihilation. We first describe the q-deformed scalar field dark energy quantum-field theoretically, then construct the action and the dynamical structure of these interacting dark sectors, in order to study the dynamics of the model. We perform the phase space analysis of the model to confirm and interpret our proposal by searching the stable attractor solutions implying the late-time accelerating phase of the universe. We then obtain the result that when interaction and equation-of-state parameter of the dark matter evolve from the present day values into a particular value, the dark energy turns out to be a q-deformed scalar field.

Improved mapping of the travelling salesman problem for quantum annealing

NASA Astrophysics Data System (ADS)

Troyer, Matthias; Heim, Bettina; Brown, Ethan; Wecker, David

2015-03-01

We consider the quantum adiabatic algorithm as applied to the travelling salesman problem (TSP). We introduce a novel mapping of TSP to an Ising spin glass Hamiltonian and compare it to previous known mappings. Through direct perturbative analysis, unitary evolution, and simulated quantum annealing, we show this new mapping to be significantly superior. We discuss how this advantage can translate to actual physical implementations of TSP on quantum annealers.

Two Quantum Protocols for Oblivious Set-member Decision Problem

NASA Astrophysics Data System (ADS)

Shi, Run-Hua; Mu, Yi; Zhong, Hong; Cui, Jie; Zhang, Shun

2015-10-01

In this paper, we defined a new secure multi-party computation problem, called Oblivious Set-member Decision problem, which allows one party to decide whether a secret of another party belongs to his private set in an oblivious manner. There are lots of important applications of Oblivious Set-member Decision problem in fields of the multi-party collaborative computation of protecting the privacy of the users, such as private set intersection and union, anonymous authentication, electronic voting and electronic auction. Furthermore, we presented two quantum protocols to solve the Oblivious Set-member Decision problem. Protocol I takes advantage of powerful quantum oracle operations so that it needs lower costs in both communication and computation complexity; while Protocol II takes photons as quantum resources and only performs simple single-particle projective measurements, thus it is more feasible with the present technology.

Two Quantum Protocols for Oblivious Set-member Decision Problem

PubMed Central

Shi, Run-hua; Mu, Yi; Zhong, Hong; Cui, Jie; Zhang, Shun

2015-01-01

In this paper, we defined a new secure multi-party computation problem, called Oblivious Set-member Decision problem, which allows one party to decide whether a secret of another party belongs to his private set in an oblivious manner. There are lots of important applications of Oblivious Set-member Decision problem in fields of the multi-party collaborative computation of protecting the privacy of the users, such as private set intersection and union, anonymous authentication, electronic voting and electronic auction. Furthermore, we presented two quantum protocols to solve the Oblivious Set-member Decision problem. Protocol I takes advantage of powerful quantum oracle operations so that it needs lower costs in both communication and computation complexity; while Protocol II takes photons as quantum resources and only performs simple single-particle projective measurements, thus it is more feasible with the present technology. PMID:26514668

Two Quantum Protocols for Oblivious Set-member Decision Problem.

PubMed

Shi, Run-Hua; Mu, Yi; Zhong, Hong; Cui, Jie; Zhang, Shun

2015-10-30

In this paper, we defined a new secure multi-party computation problem, called Oblivious Set-member Decision problem, which allows one party to decide whether a secret of another party belongs to his private set in an oblivious manner. There are lots of important applications of Oblivious Set-member Decision problem in fields of the multi-party collaborative computation of protecting the privacy of the users, such as private set intersection and union, anonymous authentication, electronic voting and electronic auction. Furthermore, we presented two quantum protocols to solve the Oblivious Set-member Decision problem. Protocol I takes advantage of powerful quantum oracle operations so that it needs lower costs in both communication and computation complexity; while Protocol II takes photons as quantum resources and only performs simple single-particle projective measurements, thus it is more feasible with the present technology.

Mesoscopic Elastic Distortions in GaAs Quantum Dot Heterostructures.

PubMed

Pateras, Anastasios; Park, Joonkyu; Ahn, Youngjun; Tilka, Jack A; Holt, Martin V; Reichl, Christian; Wegscheider, Werner; Baart, Timothy A; Dehollain, Juan Pablo; Mukhopadhyay, Uditendu; Vandersypen, Lieven M K; Evans, Paul G

2018-05-09

Quantum devices formed in high-electron-mobility semiconductor heterostructures provide a route through which quantum mechanical effects can be exploited on length scales accessible to lithography and integrated electronics. The electrostatic definition of quantum dots in semiconductor heterostructure devices intrinsically involves the lithographic fabrication of intricate patterns of metallic electrodes. The formation of metal/semiconductor interfaces, growth processes associated with polycrystalline metallic layers, and differential thermal expansion produce elastic distortion in the active areas of quantum devices. Understanding and controlling these distortions present a significant challenge in quantum device development. We report synchrotron X-ray nanodiffraction measurements combined with dynamical X-ray diffraction modeling that reveal lattice tilts with a depth-averaged value up to 0.04° and strain on the order of 10 -4 in the two-dimensional electron gas (2DEG) in a GaAs/AlGaAs heterostructure. Elastic distortions in GaAs/AlGaAs heterostructures modify the potential energy landscape in the 2DEG due to the generation of a deformation potential and an electric field through the piezoelectric effect. The stress induced by metal electrodes directly impacts the ability to control the positions of the potential minima where quantum dots form and the coupling between neighboring quantum dots.

Universal adiabatic quantum computation via the space-time circuit-to-Hamiltonian construction.

PubMed

Gosset, David; Terhal, Barbara M; Vershynina, Anna

2015-04-10

We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic XXZ chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q-deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.

Generalized uncertainty principle and quantum gravity phenomenology

NASA Astrophysics Data System (ADS)

Bosso, Pasquale

The fundamental physical description of Nature is based on two mutually incompatible theories: Quantum Mechanics and General Relativity. Their unification in a theory of Quantum Gravity (QG) remains one of the main challenges of theoretical physics. Quantum Gravity Phenomenology (QGP) studies QG effects in low-energy systems. The basis of one such phenomenological model is the Generalized Uncertainty Principle (GUP), which is a modified Heisenberg uncertainty relation and predicts a deformed canonical commutator. In this thesis, we compute Planck-scale corrections to angular momentum eigenvalues, the hydrogen atom spectrum, the Stern-Gerlach experiment, and the Clebsch-Gordan coefficients. We then rigorously analyze the GUP-perturbed harmonic oscillator and study new coherent and squeezed states. Furthermore, we introduce a scheme for increasing the sensitivity of optomechanical experiments for testing QG effects. Finally, we suggest future projects that may potentially test QG effects in the laboratory.

Application of Canonical Effective Methods to Background-Independent Theories

NASA Astrophysics Data System (ADS)

Buyukcam, Umut

Effective formalisms play an important role in analyzing phenomena above some given length scale when complete theories are not accessible. In diverse exotic but physically important cases, the usual path-integral techniques used in a standard Quantum Field Theory approach seldom serve as adequate tools. This thesis exposes a new effective method for quantum systems, called the Canonical Effective Method, which owns particularly wide applicability in backgroundindependent theories as in the case of gravitational phenomena. The central purpose of this work is to employ these techniques to obtain semi-classical dynamics from canonical quantum gravity theories. Application to non-associative quantum mechanics is developed and testable results are obtained. Types of non-associative algebras relevant for magnetic-monopole systems are discussed. Possible modifications of hypersurface deformation algebra and the emergence of effective space-times are presented. iii.

Universal Adiabatic Quantum Computation via the Space-Time Circuit-to-Hamiltonian Construction

NASA Astrophysics Data System (ADS)

Gosset, David; Terhal, Barbara M.; Vershynina, Anna

2015-04-01

We show how to perform universal adiabatic quantum computation using a Hamiltonian which describes a set of particles with local interactions on a two-dimensional grid. A single parameter in the Hamiltonian is adiabatically changed as a function of time to simulate the quantum circuit. We bound the eigenvalue gap above the unique ground state by mapping our model onto the ferromagnetic X X Z chain with kink boundary conditions; the gap of this spin chain was computed exactly by Koma and Nachtergaele using its q -deformed version of SU(2) symmetry. We also discuss a related time-independent Hamiltonian which was shown by Janzing to be capable of universal computation. We observe that in the limit of large system size, the time evolution is equivalent to the exactly solvable quantum walk on Young's lattice.

Modification of Schrödinger-Newton equation due to braneworld models with minimal length

NASA Astrophysics Data System (ADS)

Bhat, Anha; Dey, Sanjib; Faizal, Mir; Hou, Chenguang; Zhao, Qin

2017-07-01

We study the correction of the energy spectrum of a gravitational quantum well due to the combined effect of the braneworld model with infinite extra dimensions and generalized uncertainty principle. The correction terms arise from a natural deformation of a semiclassical theory of quantum gravity governed by the Schrödinger-Newton equation based on a minimal length framework. The two fold correction in the energy yields new values of the spectrum, which are closer to the values obtained in the GRANIT experiment. This raises the possibility that the combined theory of the semiclassical quantum gravity and the generalized uncertainty principle may provide an intermediate theory between the semiclassical and the full theory of quantum gravity. We also prepare a schematic experimental set-up which may guide to the understanding of the phenomena in the laboratory.

Real-time deformation of human soft tissues: A radial basis meshless 3D model based on Marquardt's algorithm.

PubMed

Zhou, Jianyong; Luo, Zu; Li, Chunquan; Deng, Mi

2018-01-01

When the meshless method is used to establish the mathematical-mechanical model of human soft tissues, it is necessary to define the space occupied by human tissues as the problem domain and the boundary of the domain as the surface of those tissues. Nodes should be distributed in both the problem domain and on the boundaries. Under external force, the displacement of the node is computed by the meshless method to represent the deformation of biological soft tissues. However, computation by the meshless method consumes too much time, which will affect the simulation of real-time deformation of human tissues in virtual surgery. In this article, the Marquardt's Algorithm is proposed to fit the nodal displacement at the problem domain's boundary and obtain the relationship between surface deformation and force. When different external forces are applied, the deformation of soft tissues can be quickly obtained based on this relationship. The analysis and discussion show that the improved model equations with Marquardt's Algorithm not only can simulate the deformation in real-time but also preserve the authenticity of the deformation model's physical properties. Copyright © 2017 Elsevier B.V. All rights reserved.

Quantum biological channel modeling and capacity calculation.

PubMed

Djordjevic, Ivan B

2012-12-10

Quantum mechanics has an important role in photosynthesis, magnetoreception, and evolution. There were many attempts in an effort to explain the structure of genetic code and transfer of information from DNA to protein by using the concepts of quantum mechanics. The existing biological quantum channel models are not sufficiently general to incorporate all relevant contributions responsible for imperfect protein synthesis. Moreover, the problem of determination of quantum biological channel capacity is still an open problem. To solve these problems, we construct the operator-sum representation of biological channel based on codon basekets (basis vectors), and determine the quantum channel model suitable for study of the quantum biological channel capacity and beyond. The transcription process, DNA point mutations, insertions, deletions, and translation are interpreted as the quantum noise processes. The various types of quantum errors are classified into several broad categories: (i) storage errors that occur in DNA itself as it represents an imperfect storage of genetic information, (ii) replication errors introduced during DNA replication process, (iii) transcription errors introduced during DNA to mRNA transcription, and (iv) translation errors introduced during the translation process. By using this model, we determine the biological quantum channel capacity and compare it against corresponding classical biological channel capacity. We demonstrate that the quantum biological channel capacity is higher than the classical one, for a coherent quantum channel model, suggesting that quantum effects have an important role in biological systems. The proposed model is of crucial importance towards future study of quantum DNA error correction, developing quantum mechanical model of aging, developing the quantum mechanical models for tumors/cancer, and study of intracellular dynamics in general.

Quantization of set theory and generalization of the fermion algebra

NASA Astrophysics Data System (ADS)

Arik, M.; Tekin, S. C.

2002-05-01

The quantum states of a d-dimensional fermion algebra are in one to one correspondence with the subsets of a d-element universal set. In this paper we use this set theoretical motivation to construct a one-parameter deformation of the fermion algebra and extend it to a d-dimensional generalization which is invariant under the group U(d). This discrete fermionic oscillator system is extended to the continuous case. We also show that the q-deformation of these systems is related to supercovariant q-oscillators.

Quantum superintegrable system with a novel chain structure of quadratic algebras

NASA Astrophysics Data System (ADS)

Liao, Yidong; Marquette, Ian; Zhang, Yao-Zhong

2018-06-01

We analyse the n-dimensional superintegrable Kepler–Coulomb system with non-central terms. We find a novel underlying chain structure of quadratic algebras formed by the integrals of motion. We identify the elements for each sub-structure and obtain the algebra relations satisfied by them and the corresponding Casimir operators. These quadratic sub-algebras are realized in terms of a chain of deformed oscillators with factorized structure functions. We construct the finite-dimensional unitary representations of the deformed oscillators, and give an algebraic derivation of the energy spectrum of the superintegrable system.

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

Quantum digital-to-analog conversion algorithm using decoherence

NASA Astrophysics Data System (ADS)

SaiToh, Akira

2015-08-01

We consider the problem of mapping digital data encoded on a quantum register to analog amplitudes in parallel. It is shown to be unlikely that a fully unitary polynomial-time quantum algorithm exists for this problem; NP becomes a subset of BQP if it exists. In the practical point of view, we propose a nonunitary linear-time algorithm using quantum decoherence. It tacitly uses an exponentially large physical resource, which is typically a huge number of identical molecules. Quantumness of correlation appearing in the process of the algorithm is also discussed.

Device-Independent Tests of Classical and Quantum Dimensions

NASA Astrophysics Data System (ADS)

Gallego, Rodrigo; Brunner, Nicolas; Hadley, Christopher; Acín, Antonio

2010-12-01

We address the problem of testing the dimensionality of classical and quantum systems in a “black-box” scenario. We develop a general formalism for tackling this problem. This allows us to derive lower bounds on the classical dimension necessary to reproduce given measurement data. Furthermore, we generalize the concept of quantum dimension witnesses to arbitrary quantum systems, allowing one to place a lower bound on the Hilbert space dimension necessary to reproduce certain data. Illustrating these ideas, we provide simple examples of classical and quantum dimension witnesses.

N = 2 → 0 super no-scale models and moduli quantum stability

NASA Astrophysics Data System (ADS)

Kounnas, Costas; Partouche, Hervé

2017-06-01

We consider a class of heterotic N = 2 → 0 super no-scale Z2-orbifold models. An appropriate stringy Scherk-Schwarz supersymmetry breaking induces tree level masses to all massless bosons of the twisted hypermultiplets and therefore stabilizes all twisted moduli. At high supersymmetry breaking scale, the tachyons that occur in the N = 4 → 0 parent theories are projected out, and no Hagedorn-like instability takes place in the N = 2 → 0 models (for small enough marginal deformations). At low supersymmetry breaking scale, the stability of the untwisted moduli is studied at the quantum level by taking into account both untwisted and twisted contributions to the 1-loop effective potential. The latter depends on the specific branch of the gauge theory along which the background can be deformed. We derive its expression in terms of all classical marginal deformations in the pure Coulomb phase, and in some mixed Coulomb/Higgs phases. In this class of models, the super no-scale condition requires having at the massless level equal numbers of untwisted bosonic and twisted fermionic degrees of freedom. Finally, we show that N = 1 → 0 super no-scale models are obtained by implementing a second Z2 orbifold twist on N = 2 → 0 super no-scale Z2-orbifold models.

The classical Taub-Nut system: factorization, spectrum generating algebra and solution to the equations of motion

NASA Astrophysics Data System (ADS)

Latini, Danilo; Ragnisco, Orlando

2015-05-01

The formalism of SUperSYmmetric quantum mechanics (SUSYQM) is properly modified in such a way to be suitable for the description and the solution of a classical maximally superintegrable Hamiltonian system, the so-called Taub-Nut system, associated with the Hamiltonian: In full agreement with the results recently derived by Ballesteros et al for the quantum case, we show that the classical Taub-Nut system shares a number of essential features with the Kepler system, that is just its Euclidean version arising in the limit η \\to 0, and for which a ‘SUSYQM’ approach has been recently introduced by Kuru and Negro. In particular, for positive η and negative energy the motion is always periodic; it turns out that the period depends upon η and goes to the Euclidean value as η \\to 0. Moreover, the maximal superintegrability is preserved by the η-deformation, due to the existence of a larger symmetry group related to an η-deformed Runge-Lenz vector, which ensures that in {{{R}}3} closed orbits are again ellipses. In this context, a deformed version of the third Kepler’s law is also recovered. The closing section is devoted to a discussion of the η \\lt 0 case, where new and partly unexpected features arise.

Calculating the mounting parameters for Taylor Spatial Frame correction using computed tomography.

PubMed

Kucukkaya, Metin; Karakoyun, Ozgur; Armagan, Raffi; Kuzgun, Unal

2011-07-01

The Taylor Spatial Frame uses a computer program-based six-axis deformity analysis. However, there is often a residual deformity after the initial correction, especially in deformities with a rotational component. This problem can be resolved by recalculating the parameters and inputting all new deformity and mounting parameters. However, this may necessitate repeated x-rays and delay treatment. We believe that error in the mounting parameters is the main reason for most residual deformities. To prevent these problems, we describe a new calculation technique for determining the mounting parameters that uses computed tomography. This technique is especially advantageous for deformities with a rotational component. Using this technique, exact calculation of the mounting parameters is possible and the residual deformity and number of repeated x-rays can be minimized. This new technique is an alternative method to accurately calculating the mounting parameters.

Corrections to the geometrical interpretation of bosonization

NASA Astrophysics Data System (ADS)

Steiner, Manfred; Marston, Brad

2012-02-01

Bosonization is a powerful approach for understanding certain strongly-correlated fermion systems, especially in one spatial dimension but also in higher dimensionsootnotetextA.Houghton, H.-J. Kwon and J. B. Marston, Adv. in Phys. 49, 141 (2000).. The method may be interpreted geometrically in terms of deformations of the Fermi surface, and the quantum operator that effects the deformations may be expressed in terms of a bilinear combination of fermion creation and annihilation operators. Alternatively the deformation operator has an approximate representation in terms of coherent states of bosonic fieldsootnotetextA. H. Castro Neto and E. Fradkin, Phys. Rev. B 49, 10877 (1994).. Calculation of the inner product of deformed Fermi surfaces within the two representations reveals corrections to the bosonic picture both in one and higher spatial dimensions. We discuss the implications of the corrections for efforts to improve the usefulness of multidimensional bosonization.

Deformed photon-added entangled squeezed vacuum and one-photon states: Entanglement, polarization, and nonclassical properties

NASA Astrophysics Data System (ADS)

A, Karimi; M, K. Tavassoly

2016-04-01

In this paper, after a brief review on the entangled squeezed states, we produce a new class of the continuous-variable-type entangled states, namely, deformed photon-added entangled squeezed states. These states are obtained via the iterated action of the f-deformed creation operator A = f (n)a † on the entangled squeezed states. In the continuation, by studying the criteria such as the degree of entanglement, quantum polarization as well as sub-Poissonian photon statistics, the two-mode correlation function, one-mode and two-mode squeezing, we investigate the nonclassical behaviors of the introduced states in detail by choosing a particular f-deformation function. It is revealed that the above-mentioned physical properties can be affected and so may be tuned by justifying the excitation number, after choosing a nonlinearity function. Finally, to generate the introduced states, we propose a theoretical scheme using the nonlinear Jaynes-Cummings model.

Effective field theory of emergent symmetry breaking in deformed atomic nuclei

DOE PAGES

Papenbrock, Thomas F.; Weidenmüller, H. A.

2015-09-03

Spontaneous symmetry breaking in non-relativistic quantum systems has previously been addressed in the framework of effective field theory. Low-lying excitations are constructed from Nambu–Goldstone modes using symmetry arguments only. In this study, we extend that approach to finite systems. The approach is very general. To be specific, however, we consider atomic nuclei with intrinsically deformed ground states. The emergent symmetry breaking in such systems requires the introduction of additional degrees of freedom on top of the Nambu–Goldstone modes. Symmetry arguments suffice to construct the low-lying states of the system. Lastly, in deformed nuclei these are vibrational modes each of whichmore » serves as band head of a rotational band.« less

A different Deutsch-Jozsa

NASA Astrophysics Data System (ADS)

Bera, Debajyoti

2015-06-01

One of the early achievements of quantum computing was demonstrated by Deutsch and Jozsa (Proc R Soc Lond A Math Phys Sci 439(1907):553, 1992) regarding classification of a particular type of Boolean functions. Their solution demonstrated an exponential speedup compared to classical approaches to the same problem; however, their solution was the only known quantum algorithm for that specific problem so far. This paper demonstrates another quantum algorithm for the same problem, with the same exponential advantage compared to classical algorithms. The novelty of this algorithm is the use of quantum amplitude amplification, a technique that is the key component of another celebrated quantum algorithm developed by Grover (Proceedings of the twenty-eighth annual ACM symposium on theory of computing, ACM Press, New York, 1996). A lower bound for randomized (classical) algorithms is also presented which establishes a sound gap between the effectiveness of our quantum algorithm and that of any randomized algorithm with similar efficiency.

Quantum Sensors for the Generating Functional of Interacting Quantum Field Theories

NASA Astrophysics Data System (ADS)

Bermudez, A.; Aarts, G.; Müller, M.

2017-10-01

Difficult problems described in terms of interacting quantum fields evolving in real time or out of equilibrium abound in condensed-matter and high-energy physics. Addressing such problems via controlled experiments in atomic, molecular, and optical physics would be a breakthrough in the field of quantum simulations. In this work, we present a quantum-sensing protocol to measure the generating functional of an interacting quantum field theory and, with it, all the relevant information about its in- or out-of-equilibrium phenomena. Our protocol can be understood as a collective interferometric scheme based on a generalization of the notion of Schwinger sources in quantum field theories, which make it possible to probe the generating functional. We show that our scheme can be realized in crystals of trapped ions acting as analog quantum simulators of self-interacting scalar quantum field theories.

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.

String theory, quantum phase transitions, and the emergent Fermi liquid.

PubMed

Cubrović, Mihailo; Zaanen, Jan; Schalm, Koenraad

2009-07-24

A central problem in quantum condensed matter physics is the critical theory governing the zero-temperature quantum phase transition between strongly renormalized Fermi liquids as found in heavy fermion intermetallics and possibly in high-critical temperature superconductors. We found that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the anti-de Sitter/conformal field theory correspondence to relate fermionic quantum critical fields to a gravitational problem, we computed the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi liquid.

Optimal quantum cloning based on the maximin principle by using a priori information

NASA Astrophysics Data System (ADS)

Kang, Peng; Dai, Hong-Yi; Wei, Jia-Hua; Zhang, Ming

2016-10-01

We propose an optimal 1 →2 quantum cloning method based on the maximin principle by making full use of a priori information of amplitude and phase about the general cloned qubit input set, which is a simply connected region enclosed by a "longitude-latitude grid" on the Bloch sphere. Theoretically, the fidelity of the optimal quantum cloning machine derived from this method is the largest in terms of the maximin principle compared with that of any other machine. The problem solving is an optimization process that involves six unknown complex variables, six vectors in an uncertain-dimensional complex vector space, and four equality constraints. Moreover, by restricting the structure of the quantum cloning machine, the optimization problem is simplified as a three-real-parameter suboptimization problem with only one equality constraint. We obtain the explicit formula for a suboptimal quantum cloning machine. Additionally, the fidelity of our suboptimal quantum cloning machine is higher than or at least equal to that of universal quantum cloning machines and phase-covariant quantum cloning machines. It is also underlined that the suboptimal cloning machine outperforms the "belt quantum cloning machine" for some cases.

Quantum Metropolis sampling.

PubMed

Temme, K; Osborne, T J; Vollbrecht, K G; Poulin, D; Verstraete, F

2011-03-03

The original motivation to build a quantum computer came from Feynman, who imagined a machine capable of simulating generic quantum mechanical systems--a task that is believed to be intractable for classical computers. Such a machine could have far-reaching applications in the simulation of many-body quantum physics in condensed-matter, chemical and high-energy systems. Part of Feynman's challenge was met by Lloyd, who showed how to approximately decompose the time evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer. However, this left open the problem of how to simulate the equilibrium and static properties of quantum systems. This requires the preparation of ground and Gibbs states on a quantum computer. For classical systems, this problem is solved by the ubiquitous Metropolis algorithm, a method that has basically acquired a monopoly on the simulation of interacting particles. Here we demonstrate how to implement a quantum version of the Metropolis algorithm. This algorithm permits sampling directly from the eigenstates of the Hamiltonian, and thus evades the sign problem present in classical simulations. A small-scale implementation of this algorithm should be achievable with today's technology.

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.

Review of the inverse scattering problem at fixed energy in quantum mechanics

NASA Technical Reports Server (NTRS)

Sabatier, P. C.

1972-01-01

Methods of solution of the inverse scattering problem at fixed energy in quantum mechanics are presented. Scattering experiments of a beam of particles at a nonrelativisitic energy by a target made up of particles are analyzed. The Schroedinger equation is used to develop the quantum mechanical description of the system and one of several functions depending on the relative distance of the particles. The inverse problem is the construction of the potentials from experimental measurements.

Quantum mechanics and hidden superconformal symmetry

NASA Astrophysics Data System (ADS)

Bonezzi, R.; Corradini, O.; Latini, E.; Waldron, A.

2017-12-01

Solvability of the ubiquitous quantum harmonic oscillator relies on a spectrum generating osp (1 |2 ) superconformal symmetry. We study the problem of constructing all quantum mechanical models with a hidden osp (1 |2 ) symmetry on a given space of states. This problem stems from interacting higher spin models coupled to gravity. In one dimension, we show that the solution to this problem is the Vasiliev-Plyushchay family of quantum mechanical models with hidden superconformal symmetry obtained by viewing the harmonic oscillator as a one dimensional Dirac system, so that Grassmann parity equals wave function parity. These models—both oscillator and particlelike—realize all possible unitary irreducible representations of osp (1 |2 ).

Faster than classical quantum algorithm for dense formulas of exact satisfiability and occupation problems

NASA Astrophysics Data System (ADS)

Mandrà, Salvatore; Giacomo Guerreschi, Gian; Aspuru-Guzik, Alán

2016-07-01

We present an exact quantum algorithm for solving the Exact Satisfiability problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts: the first step consists in the identification and efficient characterization of a restricted subspace that contains all the valid assignments of the Exact Satisfiability; while the second part performs a quantum search in such restricted subspace. The quantum algorithm can be used either to find a valid assignment (or to certify that no solution exists) or to count the total number of valid assignments. The query complexities for the worst-case are respectively bounded by O(\\sqrt{{2}n-{M\\prime }}) and O({2}n-{M\\prime }), where n is the number of variables and {M}\\prime the number of linearly independent clauses. Remarkably, the proposed quantum algorithm results to be faster than any known exact classical algorithm to solve dense formulas of Exact Satisfiability. As a concrete application, we provide the worst-case complexity for the Hamiltonian cycle problem obtained after mapping it to a suitable Occupation problem. Specifically, we show that the time complexity for the proposed quantum algorithm is bounded by O({2}n/4) for 3-regular undirected graphs, where n is the number of nodes. The same worst-case complexity holds for (3,3)-regular bipartite graphs. As a reference, the current best classical algorithm has a (worst-case) running time bounded by O({2}31n/96). Finally, when compared to heuristic techniques for Exact Satisfiability problems, the proposed quantum algorithm is faster than the classical WalkSAT and Adiabatic Quantum Optimization for random instances with a density of constraints close to the satisfiability threshold, the regime in which instances are typically the hardest to solve. The proposed quantum algorithm can be straightforwardly extended to the generalized version of the Exact Satisfiability known as Occupation problem. The general version of the algorithm is presented and analyzed.

Ubiquity of quantum zero-point fluctuations in dislocation glide

NASA Astrophysics Data System (ADS)

Landeiro Dos Reis, Marie; Choudhury, Anshuman; Proville, Laurent

2017-03-01

Modeling the dislocation glide through atomic scale simulations in Al, Cu, and Ni and in solid solution alloys Al(Mg) and Cu(Ag), we show that in the course of the plastic deformation the variation of the crystal zero-point energy (ZPE) and the dislocation potential energy barriers are of opposite sign. The multiplicity of situations where we have observed the same trend allows us to conclude that quantum fluctuations, giving rise to the crystal ZPE, make easier the dislocation glide in most materials, even those constituted of atoms heavier than H and He.

Magnetostriction and magnetoelastic quantum oscillations in P-type lead telluride

NASA Technical Reports Server (NTRS)

Thompson, T. E.; Aron, P. R.; Chandrasekhar, B. S.; Langenberg, D. N.

1972-01-01

A detailed experimental and theoretical study of quantum oscillations in the magnetostriction and Young's modulus of p-PbTe is presented. The valance band of PbTe is approximated by a spheroidal, nonparabolic model in which the effects of strain on the valance band parameters are described by a deformation potential model. Using appropriate thermodynamic derivatives of the modified Lifshitz-Kosevich expression for the oscillatory parts of the electronic free energy, it is shown that both types of oscillations arise mainly from relative shifts of the valance band maxima due to shear strains, accompanied by intervalley charge transfer. Band parameters derived from the periods, phases, and spin splitting of the oscillations are in generally good agreement with values reported by other workers. A detailed comparison is made of the experimentally observed oscillation amplitudes with those predicted by theory, and satisfactory agreement is found. The ratio of the amplitudes of the two effects yields a value of the valance band deformation potential in good agreement with a value found from piezoresistance experiments by Burke.

On the asymptotic states and the quantum S matrix of the η-deformed AdS 5 × S 5 superstring

DOE PAGES

Engelund, Oluf Tang; Roiban, Radu

2015-03-31

We investigate the worldsheet S matrix of string theory in η-deformed AdS 5 × S 5. By computing the six-point tree-level S matrix we explicitly show that there is no particle production at this level, as required by the classical integrability of the theory. At one and two loops we show that integrability requires that the classical two-particle states be redefined in a non-local and η-dependent way. This is a significant departure from the undeformed theory which is probably related to the quantum group symmetry of the worldsheet theory. We use generalized unitarity to carry out the loop calculations andmore » identify a set of integrals that allow us to give a two-loop Feynman integral representation of the logarithmic terms of the two-loop S matrix. We finally also discuss aspects of the calculation of the two-loop rational terms.« less

Quantum annealing correction with minor embedding

NASA Astrophysics Data System (ADS)

Vinci, Walter; Albash, Tameem; Paz-Silva, Gerardo; Hen, Itay; Lidar, Daniel A.

2015-10-01

Quantum annealing provides a promising route for the development of quantum optimization devices, but the usefulness of such devices will be limited in part by the range of implementable problems as dictated by hardware constraints. To overcome constraints imposed by restricted connectivity between qubits, a larger set of interactions can be approximated using minor embedding techniques whereby several physical qubits are used to represent a single logical qubit. However, minor embedding introduces new types of errors due to its approximate nature. We introduce and study quantum annealing correction schemes designed to improve the performance of quantum annealers in conjunction with minor embedding, thus leading to a hybrid scheme defined over an encoded graph. We argue that this scheme can be efficiently decoded using an energy minimization technique provided the density of errors does not exceed the per-site percolation threshold of the encoded graph. We test the hybrid scheme using a D-Wave Two processor on problems for which the encoded graph is a two-level grid and the Ising model is known to be NP-hard. The problems we consider are frustrated Ising model problem instances with "planted" (a priori known) solutions. Applied in conjunction with optimized energy penalties and decoding techniques, we find that this approach enables the quantum annealer to solve minor embedded instances with significantly higher success probability than it would without error correction. Our work demonstrates that quantum annealing correction can and should be used to improve the robustness of quantum annealing not only for natively embeddable problems but also when minor embedding is used to extend the connectivity of physical devices.

Quantum probability and Hilbert's sixth problem

NASA Astrophysics Data System (ADS)

Accardi, Luigi

2018-04-01

With the birth of quantum mechanics, the two disciplines that Hilbert proposed to axiomatize, probability and mechanics, became entangled and a new probabilistic model arose in addition to the classical one. Thus, to meet Hilbert's challenge, an axiomatization should account deductively for the basic features of all three disciplines. This goal was achieved within the framework of quantum probability. The present paper surveys the quantum probabilistic axiomatization. This article is part of the themed issue `Hilbert's sixth problem'.

Entanglement and the fermion sign problem in auxiliary field quantum Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Broecker, Peter; Trebst, Simon

2016-08-01

Quantum Monte Carlo simulations of fermions are hampered by the notorious sign problem whose most striking manifestation is an exponential growth of sampling errors with the number of particles. With the sign problem known to be an NP-hard problem and any generic solution thus highly elusive, the Monte Carlo sampling of interacting many-fermion systems is commonly thought to be restricted to a small class of model systems for which a sign-free basis has been identified. Here we demonstrate that entanglement measures, in particular the so-called Rényi entropies, can intrinsically exhibit a certain robustness against the sign problem in auxiliary-field quantum Monte Carlo approaches and possibly allow for the identification of global ground-state properties via their scaling behavior even in the presence of a strong sign problem. We corroborate these findings via numerical simulations of fermionic quantum phase transitions of spinless fermions on the honeycomb lattice at and below half filling.

A Generalization of the Simultaneous Diagonalization of Hermitian Matrices and its Relation to Quantum Estimation Theory

NASA Astrophysics Data System (ADS)

Nagaoka, Hiroshi

We study the problem of minimizing a quadratic quantity defined for given two Hermitian matrices X, Y and a positive-definite Hermitian matrix. This problem is reduced to the simultaneous diagonalization of X, Y when XY = YX. We derive a lower bound for the quantity, and in some special cases solve the problem by showing that the lower bound is achievable. This problem is closely related to a simultaneous measurement of quantum mechanical observables which are not commuting and has an application in the theory of quantum state estimation.

Quantum Zeno Effect in the Measurement Problem

NASA Technical Reports Server (NTRS)

Namiki, Mikio; Pasaczio, Saverio

1996-01-01

Critically analyzing the so-called quantum Zeno effect in the measurement problem, we show that observation of this effect does not necessarily mean experimental evidence for the naive notion of wave-function collapse by measurement (the simple projection rule). We also examine what kind of limitation the uncertainty relation and others impose on the observation of the quantum Zeno effect.

Car-Parrinello molecular dynamics study of the melting behaviors of n-atom (n = 6, 10) graphene quantum dots

NASA Astrophysics Data System (ADS)

Shekaari, Ashkan; Abolhassani, Mohammad Reza

2017-06-01

First-principles molecular dynamics has been applied to inquire into the melting behaviors of n-atom (n = 6, 10) graphene quantum dots (GQD6 and zigzag GQD10) within the temperature range of T = 0-500 K. The temperature dependence of the geometry of each quantum dot is thoroughly evaluated via calculating the related shape deformation parameters and the eigenvalues of the quadrupole tensors. Examining the variations of some phase-transition indicators such as root-mean-square bond length fluctuations and mean square displacements broadly proposes the value of Tm = 70 K for the melting point of GQD6 while a continuous, two-stage phase transition has been concluded for zigzag GQD10.

Spin-flip transitions in self-assembled quantum dots

NASA Astrophysics Data System (ADS)

Stavrou, V. N.

2017-12-01

Detailed realistic calculations of the spin-flip time (T 1) for an electron in a self-assembled quantum dot (SAQD) due to emission of an acoustic phonon, using only bulk properties with no fitting parameters, are presented. Ellipsoidal lens shaped Inx Ga1-x As quantum dots, with electronic states calculated using 8-band strain dependent {k \\cdot p} theory, are considered. The phonons are treated as bulk acoustic phonons coupled to the electron by both deformation potential and piezoelectric interactions. The dependence of T 1 on the geometry of SAQD, on the applied external magnetic field and on the lattice temperature is highlighted. The theoretical results are close to the experimental measurements on the spin-flip times for a single electron in QD.

Relativistic particle in a box: Klein-Gordon versus Dirac equations

NASA Astrophysics Data System (ADS)

Alberto, Pedro; Das, Saurya; Vagenas, Elias C.

2018-03-01

The problem of a particle in a box is probably the simplest problem in quantum mechanics which allows for significant insight into the nature of quantum systems and thus is a cornerstone in the teaching of quantum mechanics. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantised energy spectra. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one- and three-dimensional box using the Klein-Gordon equation in the Feshbach-Villars formalism. We compare the solutions and the energy spectra obtained with the corresponding ones from the Dirac equation for a spin one-half relativistic particle. We note the similarities and differences, in particular the spin effects in the relativistic energy spectrum. As expected, the non-relativistic limit is the same for both kinds of particles, since, for a particle in a box, the spin contribution to the energy is a relativistic effect.

Robust quantum optimizer with full connectivity

PubMed Central

Nigg, Simon E.; Lörch, Niels; Tiwari, Rakesh P.

2017-01-01

Quantum phenomena have the potential to speed up the solution of hard optimization problems. For example, quantum annealing, based on the quantum tunneling effect, has recently been shown to scale exponentially better with system size than classical simulated annealing. However, current realizations of quantum annealers with superconducting qubits face two major challenges. First, the connectivity between the qubits is limited, excluding many optimization problems from a direct implementation. Second, decoherence degrades the success probability of the optimization. We address both of these shortcomings and propose an architecture in which the qubits are robustly encoded in continuous variable degrees of freedom. By leveraging the phenomenon of flux quantization, all-to-all connectivity with sufficient tunability to implement many relevant optimization problems is obtained without overhead. Furthermore, we demonstrate the robustness of this architecture by simulating the optimal solution of a small instance of the nondeterministic polynomial-time hard (NP-hard) and fully connected number partitioning problem in the presence of dissipation. PMID:28435880

Experimental quantum annealing: case study involving the graph isomorphism problem.

PubMed

Zick, Kenneth M; Shehab, Omar; French, Matthew

2015-06-08

Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical pre- and post-processing; at this early stage, little is known about how to partition and optimize the processing. This article presents an experimental case study of quantum annealing and some of the factors involved in real-world solvers, using a 504-qubit D-Wave Two machine and the graph isomorphism problem. To illustrate the role of classical pre-processing, a compact Hamiltonian is presented that enables a reduced Ising model for each problem instance. On random N-vertex graphs, the median number of variables is reduced from N(2) to fewer than N log2 N and solvable graph sizes increase from N = 5 to N = 13. Additionally, error correction via classical post-processing majority voting is evaluated. While the solution times are not competitive with classical approaches to graph isomorphism, the enhanced solver ultimately classified correctly every problem that was mapped to the processor and demonstrated clear advantages over the baseline approach. The results shed some light on the nature of real-world quantum annealing and the associated hybrid classical-quantum solvers.

Experimental quantum annealing: case study involving the graph isomorphism problem

PubMed Central

Zick, Kenneth M.; Shehab, Omar; French, Matthew

2015-01-01

Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical pre- and post-processing; at this early stage, little is known about how to partition and optimize the processing. This article presents an experimental case study of quantum annealing and some of the factors involved in real-world solvers, using a 504-qubit D-Wave Two machine and the graph isomorphism problem. To illustrate the role of classical pre-processing, a compact Hamiltonian is presented that enables a reduced Ising model for each problem instance. On random N-vertex graphs, the median number of variables is reduced from N2 to fewer than N log2 N and solvable graph sizes increase from N = 5 to N = 13. Additionally, error correction via classical post-processing majority voting is evaluated. While the solution times are not competitive with classical approaches to graph isomorphism, the enhanced solver ultimately classified correctly every problem that was mapped to the processor and demonstrated clear advantages over the baseline approach. The results shed some light on the nature of real-world quantum annealing and the associated hybrid classical-quantum solvers. PMID:26053973

Quantum-enhanced reinforcement learning for finite-episode games with discrete state spaces

NASA Astrophysics Data System (ADS)

Neukart, Florian; Von Dollen, David; Seidel, Christian; Compostella, Gabriele

2017-12-01

Quantum annealing algorithms belong to the class of metaheuristic tools, applicable for solving binary optimization problems. Hardware implementations of quantum annealing, such as the quantum annealing machines produced by D-Wave Systems, have been subject to multiple analyses in research, with the aim of characterizing the technology's usefulness for optimization and sampling tasks. Here, we present a way to partially embed both Monte Carlo policy iteration for finding an optimal policy on random observations, as well as how to embed n sub-optimal state-value functions for approximating an improved state-value function given a policy for finite horizon games with discrete state spaces on a D-Wave 2000Q quantum processing unit (QPU). We explain how both problems can be expressed as a quadratic unconstrained binary optimization (QUBO) problem, and show that quantum-enhanced Monte Carlo policy evaluation allows for finding equivalent or better state-value functions for a given policy with the same number episodes compared to a purely classical Monte Carlo algorithm. Additionally, we describe a quantum-classical policy learning algorithm. Our first and foremost aim is to explain how to represent and solve parts of these problems with the help of the QPU, and not to prove supremacy over every existing classical policy evaluation algorithm.

Zero-index structures as an alternative platform for quantum optics

PubMed Central

Liberal, Iñigo

2017-01-01

Vacuum fluctuations are one of the most distinctive aspects of quantum optics, being the trigger of multiple nonclassical phenomena. Thus, platforms like resonant cavities and photonic crystals that enable the inhibition and manipulation of vacuum fluctuations have been key to our ability to control light–matter interactions (e.g., the decay of quantum emitters). Here, we theoretically demonstrate that vacuum fluctuations may be naturally inhibited within bodies immersed in epsilon-and-mu-near-zero (EMNZ) media, while they can also be selectively excited via bound eigenmodes. Therefore, zero-index structures are proposed as an alternative platform to manipulate the decay of quantum emitters, possibly leading to the exploration of qualitatively different dynamics. For example, a direct modulation of the vacuum Rabi frequency is obtained by deforming the EMNZ region without detuning a bound eigenmode. Ideas for the possible implementation of these concepts using synthetic implementations based on structural dispersion are also proposed. PMID:28096367

Zero-index structures as an alternative platform for quantum optics.

PubMed

Liberal, Iñigo; Engheta, Nader

2017-01-31

Vacuum fluctuations are one of the most distinctive aspects of quantum optics, being the trigger of multiple nonclassical phenomena. Thus, platforms like resonant cavities and photonic crystals that enable the inhibition and manipulation of vacuum fluctuations have been key to our ability to control light-matter interactions (e.g., the decay of quantum emitters). Here, we theoretically demonstrate that vacuum fluctuations may be naturally inhibited within bodies immersed in epsilon-and-mu-near-zero (EMNZ) media, while they can also be selectively excited via bound eigenmodes. Therefore, zero-index structures are proposed as an alternative platform to manipulate the decay of quantum emitters, possibly leading to the exploration of qualitatively different dynamics. For example, a direct modulation of the vacuum Rabi frequency is obtained by deforming the EMNZ region without detuning a bound eigenmode. Ideas for the possible implementation of these concepts using synthetic implementations based on structural dispersion are also proposed.

LETTER TO THE EDITOR: The quantum Knizhnik Zamolodchikov equation, generalized Razumov Stroganov sum rules and extended Joseph polynomials

NASA Astrophysics Data System (ADS)

Di Francesco, P.; Zinn-Justin, P.

2005-12-01

We prove higher rank analogues of the Razumov Stroganov sum rule for the ground state of the O(1) loop model on a semi-infinite cylinder: we show that a weighted sum of components of the ground state of the Ak-1 IRF model yields integers that generalize the numbers of alternating sign matrices. This is done by constructing minimal polynomial solutions of the level 1 U_q(\\widehat{\\frak{sl}(k)}) quantum Knizhnik Zamolodchikov equations, which may also be interpreted as quantum incompressible q-deformations of quantum Hall effect wavefunctions at filling fraction ν = k. In addition to the generalized Razumov Stroganov point q = -eiπ/k+1, another combinatorially interesting point is reached in the rational limit q → -1, where we identify the solution with extended Joseph polynomials associated with the geometry of upper triangular matrices with vanishing kth power.

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

An Introduction to Multi-player, Multi-choice Quantum Games: Quantum Minority Games & Kolkata Restaurant Problems

NASA Astrophysics Data System (ADS)

Sharif, Puya; Heydari, Hoshang

We give a self contained introduction to a few quantum game protocols, starting with the quantum version of the two-player two-choice game of Prisoners dilemma, followed by an n-player generalization trough the quantum minority games, and finishing with a contribution towards an n-player m-choice generalization with a quantum version of a three-player Kolkata restaurant problem. We have omitted some technical details accompanying these protocols, and instead laid the focus on presenting some general aspects of the field as a whole. This review contains an introduction to the formalism of quantum information theory, as well as to important game theoretical concepts, and is aimed to work as a review suiting economists and game theorists with limited knowledge of quantum physics as well as to physicists with limited knowledge of game theory.

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.

Computation of forces from deformed visco-elastic biological tissues

NASA Astrophysics Data System (ADS)

Muñoz, José J.; Amat, David; Conte, Vito

2018-04-01

We present a least-squares based inverse analysis of visco-elastic biological tissues. The proposed method computes the set of contractile forces (dipoles) at the cell boundaries that induce the observed and quantified deformations. We show that the computation of these forces requires the regularisation of the problem functional for some load configurations that we study here. The functional measures the error of the dynamic problem being discretised in time with a second-order implicit time-stepping and in space with standard finite elements. We analyse the uniqueness of the inverse problem and estimate the regularisation parameter by means of an L-curved criterion. We apply the methodology to a simple toy problem and to an in vivo set of morphogenetic deformations of the Drosophila embryo.

Performance of quantum annealing on random Ising problems implemented using the D-Wave Two

NASA Astrophysics Data System (ADS)

Wang, Zhihui; Job, Joshua; Rønnow, Troels F.; Troyer, Matthias; Lidar, Daniel A.; USC Collaboration; ETH Collaboration

2014-03-01

Detecting a possible speedup of quantum annealing compared to classical algorithms is a pressing task in experimental adiabatic quantum computing. In this talk, we discuss the performance of the D-Wave Two quantum annealing device on Ising spin glass problems. The expected time to solution for the device to solve random instances with up to 503 spins and with specified coupling ranges is evaluated while carefully addressing the issue of statistical errors. We perform a systematic comparison of the expected time to solution between the D-Wave Two and classical stochastic solvers, specifically simulated annealing, and simulated quantum annealing based on quantum Monte Carlo, and discuss the question of speedup.

Strange Bedfellows: Quantum Mechanics and Data Mining

NASA Astrophysics Data System (ADS)

Weinstein, Marvin

2010-02-01

Last year, in 2008, I gave a talk titled Quantum Calisthenics. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.

A numerical analysis of contact and limit-point behavior in a class of problems of finite elastic deformation

NASA Technical Reports Server (NTRS)

Endo, T.; Oden, J. T.; Becker, E. B.; Miller, T.

1984-01-01

Finite element methods for the analysis of bifurcations, limit-point behavior, and unilateral frictionless contact of elastic bodies undergoing finite deformation are presented. Particular attention is given to the development and application of Riks-type algorithms for the analysis of limit points and exterior penalty methods for handling the unilateral constraints. Applications focus on the problem of finite axisymmetric deformations, snap-through, and inflation of thick rubber spherical shells.

Optimum testing of multiple hypotheses in quantum detection theory

NASA Technical Reports Server (NTRS)

Yuen, H. P.; Kennedy, R. S.; Lax, M.

1975-01-01

The problem of specifying the optimum quantum detector in multiple hypotheses testing is considered for application to optical communications. The quantum digital detection problem is formulated as a linear programming problem on an infinite-dimensional space. A necessary and sufficient condition is derived by the application of a general duality theorem specifying the optimum detector in terms of a set of linear operator equations and inequalities. Existence of the optimum quantum detector is also established. The optimality of commuting detection operators is discussed in some examples. The structure and performance of the optimal receiver are derived for the quantum detection of narrow-band coherent orthogonal and simplex signals. It is shown that modal photon counting is asymptotically optimum in the limit of a large signaling alphabet and that the capacity goes to infinity in the absence of a bandwidth limitation.

Quantum-Enhanced Machine Learning

NASA Astrophysics Data System (ADS)

Dunjko, Vedran; Taylor, Jacob M.; Briegel, Hans J.

2016-09-01

The emerging field of quantum machine learning has the potential to substantially aid in the problems and scope of artificial intelligence. This is only enhanced by recent successes in the field of classical machine learning. In this work we propose an approach for the systematic treatment of machine learning, from the perspective of quantum information. Our approach is general and covers all three main branches of machine learning: supervised, unsupervised, and reinforcement learning. While quantum improvements in supervised and unsupervised learning have been reported, reinforcement learning has received much less attention. Within our approach, we tackle the problem of quantum enhancements in reinforcement learning as well, and propose a systematic scheme for providing improvements. As an example, we show that quadratic improvements in learning efficiency, and exponential improvements in performance over limited time periods, can be obtained for a broad class of learning problems.

Recall Performance for Content-Addressable Memory Using Adiabatic Quantum Optimization

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

Imam, Neena; Humble, Travis S.; McCaskey, Alex

A content-addressable memory (CAM) stores key-value associations such that the key is recalled by providing its associated value. While CAM recall is traditionally performed using recurrent neural network models, we show how to solve this problem using adiabatic quantum optimization. Our approach maps the recurrent neural network to a commercially available quantum processing unit by taking advantage of the common underlying Ising spin model. We then assess the accuracy of the quantum processor to store key-value associations by quantifying recall performance against an ensemble of problem sets. We observe that different learning rules from the neural network community influence recallmore » accuracy but performance appears to be limited by potential noise in the processor. The strong connection established between quantum processors and neural network problems supports the growing intersection of these two ideas.« less

Connes' embedding problem and winning strategies for quantum XOR games

NASA Astrophysics Data System (ADS)

Harris, Samuel J.

2017-12-01

We consider quantum XOR games, defined in the work of Regev and Vidick [ACM Trans. Comput. Theory 7, 43 (2015)], from the perspective of unitary correlations defined in the work of Harris and Paulsen [Integr. Equations Oper. Theory 89, 125 (2017)]. We show that the winning bias of a quantum XOR game in the tensor product model (respectively, the commuting model) is equal to the norm of its associated linear functional on the unitary correlation set from the appropriate model. We show that Connes' embedding problem has a positive answer if and only if every quantum XOR game has entanglement bias equal to the commuting bias. In particular, the embedding problem is equivalent to determining whether every quantum XOR game G with a winning strategy in the commuting model also has a winning strategy in the approximate finite-dimensional model.

Quantum-Inspired Maximizer

NASA Technical Reports Server (NTRS)

Zak, Michail

2008-01-01

A report discusses an algorithm for a new kind of dynamics based on a quantum- classical hybrid-quantum-inspired maximizer. The model is represented by a modified Madelung equation in which the quantum potential is replaced by different, specially chosen 'computational' potential. As a result, the dynamics attains both quantum and classical properties: it preserves superposition and entanglement of random solutions, while allowing one to measure its state variables, using classical methods. Such optimal combination of characteristics is a perfect match for quantum-inspired computing. As an application, an algorithm for global maximum of an arbitrary integrable function is proposed. The idea of the proposed algorithm is very simple: based upon the Quantum-inspired Maximizer (QIM), introduce a positive function to be maximized as the probability density to which the solution is attracted. Then the larger value of this function will have the higher probability to appear. Special attention is paid to simulation of integer programming and NP-complete problems. It is demonstrated that the problem of global maximum of an integrable function can be found in polynomial time by using the proposed quantum- classical hybrid. The result is extended to a constrained maximum with applications to integer programming and TSP (Traveling Salesman Problem).

Semiclassical approach to finite-temperature quantum annealing with trapped ions

NASA Astrophysics Data System (ADS)

Raventós, David; Graß, Tobias; Juliá-Díaz, Bruno; Lewenstein, Maciej

2018-05-01

Recently it has been demonstrated that an ensemble of trapped ions may serve as a quantum annealer for the number-partitioning problem [Nat. Commun. 7, 11524 (2016), 10.1038/ncomms11524]. This hard computational problem may be addressed by employing a tunable spin-glass architecture. Following the proposal of the trapped-ion annealer, we study here its robustness against thermal effects; that is, we investigate the role played by thermal phonons. For the efficient description of the system, we use a semiclassical approach, and benchmark it against the exact quantum evolution. The aim is to understand better and characterize how the quantum device approaches a solution of an otherwise difficult to solve NP-hard problem.

XY vs X Mixer in Quantum Alternating Operator Ansatz for Optimization Problems with Constraints

NASA Technical Reports Server (NTRS)

Wang, Zhihui; Rubin, Nicholas; Rieffel, Eleanor G.

2018-01-01

Quantum Approximate Optimization Algorithm, further generalized as Quantum Alternating Operator Ansatz (QAOA), is a family of algorithms for combinatorial optimization problems. It is a leading candidate to run on emerging universal quantum computers to gain insight into quantum heuristics. In constrained optimization, penalties are often introduced so that the ground state of the cost Hamiltonian encodes the solution (a standard practice in quantum annealing). An alternative is to choose a mixing Hamiltonian such that the constraint corresponds to a constant of motion and the quantum evolution stays in the feasible subspace. Better performance of the algorithm is speculated due to a much smaller search space. We consider problems with a constant Hamming weight as the constraint. We also compare different methods of generating the generalized W-state, which serves as a natural initial state for the Hamming-weight constraint. Using graph-coloring as an example, we compare the performance of using XY model as a mixer that preserves the Hamming weight with the performance of adding a penalty term in the cost Hamiltonian.

The Quantum Binding Problem in the Context of Associative Memory

PubMed Central

Wichert, Andreas

2016-01-01

We present a method to solve the binding problem by using a quantum algorithm for the retrieval of associations from associative memory during visual scene analysis. The problem is solved by mapping the information representing different objects into superposition by using entanglement and Grover’s amplification algorithm. PMID:27603782

Scalable effective-temperature reduction for quantum annealers via nested quantum annealing correction

NASA Astrophysics Data System (ADS)

Vinci, Walter; Lidar, Daniel A.

2018-02-01

Nested quantum annealing correction (NQAC) is an error-correcting scheme for quantum annealing that allows for the encoding of a logical qubit into an arbitrarily large number of physical qubits. The encoding replaces each logical qubit by a complete graph of degree C . The nesting level C represents the distance of the error-correcting code and controls the amount of protection against thermal and control errors. Theoretical mean-field analyses and empirical data obtained with a D-Wave Two quantum annealer (supporting up to 512 qubits) showed that NQAC has the potential to achieve a scalable effective-temperature reduction, Teff˜C-η , with 0 <η ≤2 . We confirm that this scaling is preserved when NQAC is tested on a D-Wave 2000Q device (supporting up to 2048 qubits). In addition, we show that NQAC can also be used in sampling problems to lower the effective-temperature of a quantum annealer. Such effective-temperature reduction is relevant for machine-learning applications. Since we demonstrate that NQAC achieves error correction via a reduction of the effective-temperature of the quantum annealing device, our results address the problem of the "temperature scaling law for quantum annealers," which requires the temperature of quantum annealers to be reduced as problems of larger sizes are attempted to be solved.

Thermalization and prethermalization in isolated quantum systems: a theoretical overview

NASA Astrophysics Data System (ADS)

Mori, Takashi; Ikeda, Tatsuhiko N.; Kaminishi, Eriko; Ueda, Masahito

2018-06-01

The approach to thermal equilibrium, or thermalization, in isolated quantum systems is among the most fundamental problems in statistical physics. Recent theoretical studies have revealed that thermalization in isolated quantum systems has several remarkable features, which emerge from quantum entanglement and are quite distinct from those in classical systems. Experimentally, well isolated and highly controllable ultracold quantum gases offer an ideal testbed to study the nonequilibrium dynamics in isolated quantum systems, promoting intensive recent theoretical endeavors on this fundamental subject. Besides thermalization, many isolated quantum systems show intriguing behavior in relaxation processes, especially prethermalization. Prethermalization occurs when there is a clear separation of relevant time scales and has several different physical origins depending on individual systems. In this review, we overview theoretical approaches to the problems of thermalization and prethermalization.

Protecting software agents from malicious hosts using quantum computing

NASA Astrophysics Data System (ADS)

Reisner, John; Donkor, Eric

2000-07-01

We evaluate how quantum computing can be applied to security problems for software agents. Agent-based computing, which merges technological advances in artificial intelligence and mobile computing, is a rapidly growing domain, especially in applications such as electronic commerce, network management, information retrieval, and mission planning. System security is one of the more eminent research areas in agent-based computing, and the specific problem of protecting a mobile agent from a potentially hostile host is one of the most difficult of these challenges. In this work, we describe our agent model, and discuss the capabilities and limitations of classical solutions to the malicious host problem. Quantum computing may be extremely helpful in addressing the limitations of classical solutions to this problem. This paper highlights some of the areas where quantum computing could be applied to agent security.

Electron spin relaxation in a transition-metal dichalcogenide quantum dot

NASA Astrophysics Data System (ADS)

Pearce, Alexander J.; Burkard, Guido

2017-06-01

We study the relaxation of a single electron spin in a circular quantum dot in a transition-metal dichalcogenide monolayer defined by electrostatic gating. Transition-metal dichalcogenides provide an interesting and promising arena for quantum dot nano-structures due to the combination of a band gap, spin-valley physics and strong spin-orbit coupling. First we will discuss which bound state solutions in different B-field regimes can be used as the basis for qubits states. We find that at low B-fields combined spin-valley Kramers qubits to be suitable, while at large magnetic fields pure spin or valley qubits can be envisioned. Then we present a discussion of the relaxation of a single electron spin mediated by electron-phonon interaction via various different relaxation channels. In the low B-field regime we consider the spin-valley Kramers qubits and include impurity mediated valley mixing which will arise in disordered quantum dots. Rashba spin-orbit admixture mechanisms allow for relaxation by in-plane phonons either via the deformation potential or by piezoelectric coupling, additionally direct spin-phonon mechanisms involving out-of-plane phonons give rise to relaxation. We find that the relaxation rates scale as \\propto B 6 for both in-plane phonons coupling via deformation potential and the piezoelectric effect, while relaxation due to the direct spin-phonon coupling scales independant to B-field to lowest order but depends strongly on device mechanical tension. We will also discuss the relaxation mechanisms for pure spin or valley qubits formed in the large B-field regime.

Incremental analysis of large elastic deformation of a rotating cylinder

NASA Technical Reports Server (NTRS)

Buchanan, G. R.

1976-01-01

The effect of finite deformation upon a rotating, orthotropic cylinder was investigated using a general incremental theory. The incremental equations of motion are developed using the variational principle. The governing equations are derived using the principle of virtual work for a body with initial stress. The governing equations are reduced to those for the title problem and a numerical solution is obtained using finite difference approximations. Since the problem is defined in terms of one independent space coordinate, the finite difference grid can be modified as the incremental deformation occurs without serious numerical difficulties. The nonlinear problem is solved incrementally by totaling a series of linear solutions.

Quantum simulation of the integer factorization problem: Bell states in a Penning trap

NASA Astrophysics Data System (ADS)

Rosales, Jose Luis; Martin, Vicente

2018-03-01

The arithmetic problem of factoring an integer N can be translated into the physics of a quantum device, a result that supports Pólya's and Hilbert's conjecture to demonstrate Riemann's hypothesis. The energies of this system, being univocally related to the factors of N , are the eigenvalues of a bounded Hamiltonian. Here we solve the quantum conditions and show that the histogram of the discrete energies, provided by the spectrum of the system, should be interpreted in number theory as the relative probability for a prime to be a factor candidate of N . This is equivalent to a quantum sieve that is shown to require only o (ln√{N}) 3 energy measurements to solve the problem, recovering Shor's complexity result. Hence the outcome can be seen as a probability map that a pair of primes solve the given factorization problem. Furthermore, we show that a possible embodiment of this quantum simulator corresponds to two entangled particles in a Penning trap. The possibility to build the simulator experimentally is studied in detail. The results show that factoring numbers, many orders of magnitude larger than those computed with experimentally available quantum computers, is achievable using typical parameters in Penning traps.

Controlling the thermoelectric effect by mechanical manipulation of the electron's quantum phase in atomic junctions.

PubMed

Aiba, Akira; Demir, Firuz; Kaneko, Satoshi; Fujii, Shintaro; Nishino, Tomoaki; Tsukagoshi, Kazuhito; Saffarzadeh, Alireza; Kirczenow, George; Kiguchi, Manabu

2017-08-11

The thermoelectric voltage developed across an atomic metal junction (i.e., a nanostructure in which one or a few atoms connect two metal electrodes) in response to a temperature difference between the electrodes, results from the quantum interference of electrons that pass through the junction multiple times after being scattered by the surrounding defects. Here we report successfully tuning this quantum interference and thus controlling the magnitude and sign of the thermoelectric voltage by applying a mechanical force that deforms the junction. The observed switching of the thermoelectric voltage is reversible and can be cycled many times. Our ab initio and semi-empirical calculations elucidate the detailed mechanism by which the quantum interference is tuned. We show that the applied strain alters the quantum phases of electrons passing through the narrowest part of the junction and hence modifies the electronic quantum interference in the device. Tuning the quantum interference causes the energies of electronic transport resonances to shift, which affects the thermoelectric voltage. These experimental and theoretical studies reveal that Au atomic junctions can be made to exhibit both positive and negative thermoelectric voltages on demand, and demonstrate the importance and tunability of the quantum interference effect in the atomic-scale metal nanostructures.

S-Duality, Deconstruction and Confinement for a Marginal Deformation of N=4 SUSY Yang-Mills

NASA Astrophysics Data System (ADS)

Dorey, Nick

2004-08-01

We study an exactly marginal deformation of Script N = 4 SUSY Yang-Mills with gauge group U(N) using field theory and string theory methods. The classical theory has a Higgs branch for rational values of the deformation parameter. We argue that the quantum theory also has an S-dual confining branch which cannot be seen classically. The low-energy effective theory on these branches is a six-dimensional non-commutative gauge theory with sixteen supercharges. Confinement of magnetic and electric charges, on the Higgs and confining branches respectively, occurs due to the formation of BPS-saturated strings in the low energy theory. The results also suggest a new way of deconstructing Little String Theory as a large-N limit of a confining gauge theory in four dimensions.

Energy and the Confused Student V: The Energy/Momentum Approach to Problems Involving Rotating and Deformable Systems

ERIC Educational Resources Information Center

Jewett, John W., Jr.

2008-01-01

Energy is a critical concept in physics problem-solving, but is often a major source of confusion for students if the presentation is not carefully crafted by the instructor or the textbook. A common approach to problems involving deformable or rotating systems that has been discussed in the literature is to employ the work-kinetic energy theorem…

Influence of gravity on deformation of blocks in Earth's crust

NASA Astrophysics Data System (ADS)

Tataurova, A. A.; Stefanov, Yu. P.; Bakeev, R. A.

2017-12-01

The article presents the results of numerical calculations of deformation using an Earth's crust model fragment under the influence of gravitational force. It is shown that plastic deformation in low-strength blocks changes the stress-strain state in the medium and produces a surface deflection which is hundred meters deep. The deflection is defined by the properties of the medium, its extent, and conditions at the lateral boundaries. The order of load application beyond the elastic limit affects the development of deformation, which should be taken into account when formulating problems and performing numerical simulations. The problem has been solved using a two-dimensional elastoplastic approach.

Discrete Surface Evolution and Mesh Deformation for Aircraft Icing Applications

NASA Technical Reports Server (NTRS)

Thompson, David; Tong, Xiaoling; Arnoldus, Qiuhan; Collins, Eric; McLaurin, David; Luke, Edward; Bidwell, Colin S.

2013-01-01

Robust, automated mesh generation for problems with deforming geometries, such as ice accreting on aerodynamic surfaces, remains a challenging problem. Here we describe a technique to deform a discrete surface as it evolves due to the accretion of ice. The surface evolution algorithm is based on a smoothed, face-offsetting approach. We also describe a fast algebraic technique to propagate the computed surface deformations into the surrounding volume mesh while maintaining geometric mesh quality. Preliminary results presented here demonstrate the ecacy of the approach for a sphere with a prescribed accretion rate, a rime ice accretion, and a more complex glaze ice accretion.

Quo vadis: Hydrologic inverse analyses using high-performance computing and a D-Wave quantum annealer

NASA Astrophysics Data System (ADS)

O'Malley, D.; Vesselinov, V. V.

2017-12-01

Classical microprocessors have had a dramatic impact on hydrology for decades, due largely to the exponential growth in computing power predicted by Moore's law. However, this growth is not expected to continue indefinitely and has already begun to slow. Quantum computing is an emerging alternative to classical microprocessors. Here, we demonstrated cutting edge inverse model analyses utilizing some of the best available resources in both worlds: high-performance classical computing and a D-Wave quantum annealer. The classical high-performance computing resources are utilized to build an advanced numerical model that assimilates data from O(10^5) observations, including water levels, drawdowns, and contaminant concentrations. The developed model accurately reproduces the hydrologic conditions at a Los Alamos National Laboratory contamination site, and can be leveraged to inform decision-making about site remediation. We demonstrate the use of a D-Wave 2X quantum annealer to solve hydrologic inverse problems. This work can be seen as an early step in quantum-computational hydrology. We compare and contrast our results with an early inverse approach in classical-computational hydrology that is comparable to the approach we use with quantum annealing. Our results show that quantum annealing can be useful for identifying regions of high and low permeability within an aquifer. While the problems we consider are small-scale compared to the problems that can be solved with modern classical computers, they are large compared to the problems that could be solved with early classical CPUs. Further, the binary nature of the high/low permeability problem makes it well-suited to quantum annealing, but challenging for classical computers.

Effective optimization using sample persistence: A case study on quantum annealers and various Monte Carlo optimization methods

NASA Astrophysics Data System (ADS)

Karimi, Hamed; Rosenberg, Gili; Katzgraber, Helmut G.

2017-10-01

We present and apply a general-purpose, multistart algorithm for improving the performance of low-energy samplers used for solving optimization problems. The algorithm iteratively fixes the value of a large portion of the variables to values that have a high probability of being optimal. The resulting problems are smaller and less connected, and samplers tend to give better low-energy samples for these problems. The algorithm is trivially parallelizable since each start in the multistart algorithm is independent, and could be applied to any heuristic solver that can be run multiple times to give a sample. We present results for several classes of hard problems solved using simulated annealing, path-integral quantum Monte Carlo, parallel tempering with isoenergetic cluster moves, and a quantum annealer, and show that the success metrics and the scaling are improved substantially. When combined with this algorithm, the quantum annealer's scaling was substantially improved for native Chimera graph problems. In addition, with this algorithm the scaling of the time to solution of the quantum annealer is comparable to the Hamze-de Freitas-Selby algorithm on the weak-strong cluster problems introduced by Boixo et al. Parallel tempering with isoenergetic cluster moves was able to consistently solve three-dimensional spin glass problems with 8000 variables when combined with our method, whereas without our method it could not solve any.

Quantum cryptography and applications in the optical fiber network

NASA Astrophysics Data System (ADS)

Luo, Yuhui

2005-09-01

Quantum cryptography, as part of quantum information and communications, can provide absolute security for information transmission because it is established on the fundamental laws of quantum theory, such as the principle of uncertainty, No-cloning theorem and quantum entanglement. In this thesis research, a novel scheme to implement quantum key distribution based on multiphoton entanglement with a new protocol is proposed. Its advantages are: a larger information capacity can be obtained with a longer transmission distance and the detection of multiple photons is easier than that of a single photon. The security and attacks pertaining to such a system are also studied. Next, a quantum key distribution over wavelength division multiplexed (WDM) optical fiber networks is realized. Quantum key distribution in networks is a long-standing problem for practical applications. Here we combine quantum cryptography and WDM to solve this problem because WDM technology is universally deployed in the current and next generation fiber networks. The ultimate target is to deploy quantum key distribution over commercial networks. The problems arising from the networks are also studied in this part. Then quantum key distribution in multi-access networks using wavelength routing technology is investigated in this research. For the first time, quantum cryptography for multiple individually targeted users has been successfully implemented in sharp contrast to that using the indiscriminating broadcasting structure. It overcomes the shortcoming that every user in the network can acquire the quantum key signals intended to be exchanged between only two users. Furthermore, a more efficient scheme of quantum key distribution is adopted, hence resulting in a higher key rate. Lastly, a quantum random number generator based on quantum optics has been experimentally demonstrated. This device is a key component for quantum key distribution as it can create truly random numbers, which is an essential requirement to perform quantum key distribution. This new generator is composed of a single optical fiber coupler with fiber pigtails, which can be easily used in optical fiber communications.

An Early Quantum Computing Proposal

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

Lee, Stephen Russell; Alexander, Francis Joseph; Barros, Kipton Marcos

The D-Wave 2X is the third generation of quantum processing created by D-Wave. NASA (with Google and USRA) and Lockheed Martin (with USC), both own D-Wave systems. Los Alamos National Laboratory (LANL) purchased a D-Wave 2X in November 2015. The D-Wave 2X processor contains (nominally) 1152 quantum bits (or qubits) and is designed to specifically perform quantum annealing, which is a well-known method for finding a global minimum of an optimization problem. This methodology is based on direct execution of a quantum evolution in experimental quantum hardware. While this can be a powerful method for solving particular kinds of problems,more » it also means that the D-Wave 2X processor is not a general computing processor and cannot be programmed to perform a wide variety of tasks. It is a highly specialized processor, well beyond what NNSA currently thinks of as an “advanced architecture.”A D-Wave is best described as a quantum optimizer. That is, it uses quantum superposition to find the lowest energy state of a system by repeated doses of power and settling stages. The D-Wave produces multiple solutions to any suitably formulated problem, one of which is the lowest energy state solution (global minimum). Mapping problems onto the D-Wave requires defining an objective function to be minimized and then encoding that function in the Hamiltonian of the D-Wave system. The quantum annealing method is then used to find the lowest energy configuration of the Hamiltonian using the current D-Wave Two, two-level, quantum processor. This is not always an easy thing to do, and the D-Wave Two has significant limitations that restrict problem sizes that can be run and algorithmic choices that can be made. Furthermore, as more people are exploring this technology, it has become clear that it is very difficult to come up with general approaches to optimization that can both utilize the D-Wave and that can do better than highly developed algorithms on conventional computers for specific applications. These are all fundamental challenges that must be overcome for the D-Wave, or similar, quantum computing technology to be broadly applicable.« less

Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning

NASA Technical Reports Server (NTRS)

Smelyanskiy, V. N.; Toussaint, U. V.; Timucin, D. A.

2002-01-01

We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum excitation gap. g min, = O(n 2(exp -n/2), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to 'the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.

Space and time in the quantum universe.

NASA Astrophysics Data System (ADS)

Smolin, L.

This paper is devoted to the problem of constructing a quantum theory that could describe a closed system - a quantum cosmology. The author argues that this problem is an aspect of a much older problem - that of how to eliminate from the physical theories "ideal elements", which are elements of the mathematical structure whose interpretation requires the existence of things outside the dynamical system described by the theory. This discussion is aimed at uncovering criteria that a theory of quantum cosmology must satisfy, if it is to give physically sensible predictions. The author proposes three such criteria and shows that conventional quantum cosmology can only satisfy them, if there is an intrinsic time coordinate on the phase space of the theory. It is shown that approaches based on correlations in the wave function, that do not use an inner product, cannot satisfy these criteria. As example, the author discusses the problem of quantizing a class of relational dynamical models invented by Barbour and Bertotti. The dynamical structure of these theories is closely analogous to general relativity, and the problem of their measurement theory is also similar. It is concluded that these theories can only be sensibly quantized if they contain an intrinsic time.

Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning

NASA Technical Reports Server (NTRS)

Smelyanskiy, Vadius; vonToussaint, Udo V.; Timucin, Dogan A.; Clancy, Daniel (Technical Monitor)

2002-01-01

We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum exitation gap, gmin = O(n2(sup -n/2)), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.

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

Stetsko, M. M., E-mail: mstetsko@gmail.com, E-mail: mykola@ktf.franko.lviv.ua

Three dimensional Dirac oscillator was considered in space with deformed commutation relations known as Snyder-de Sitter algebra. Snyder-de Sitter commutation relations give rise to appearance of minimal uncertainties in position as well as in momentum. To derive energy spectrum and wavefunctions of the Dirac oscillator, supersymmetric quantum mechanics and shape invariance technique were applied.

Semiclassical Origin of Superdeformed Shell Structure in the Spheroidal Cavity Model

NASA Astrophysics Data System (ADS)

Arita, K.; Sugita, A.; Matsuyanagi, K.

1998-12-01

Classical periodic orbits responsible for emergence of the superdeformed shell structures of single-particle motion in spheroidal cavities are identified and their relative contributions to the shell structures are evaluated. Both prolate and oblate superdeformations (axis ratio approximately 2:1) as well as prolate hyperdeformation (axis ratio approximately 3:1) are investigated. Fourier transforms of quantum spectra clearly show that three-dimensional periodic orbits born out of bifurcations of planar orbits in the equatorial plane become predominant at large prolate deformations, while butterfly-shaped planar orbits bifurcated from linear orbits along the minor axis are important at large oblate deformations.

Loop Quantum Gravity and Asymptotically Flat Spaces

NASA Astrophysics Data System (ADS)

Arnsdorf, Matthias

2002-12-01

Remarkable progress has been made in the field of non-perturbative (loop) quantum gravity in the last decade or so and it is now a rigorously defined kinematical theory (c.f. [5] for a review and references). We are now at the stage where physical applications of loop quantum gravity can be studied and used to provide checks for the consistency of the quantisation programme. Equally, old fundamental problems of canonical quantum gravity such as the problem of time or the interpretation of quantum cosmology need to be reevaluated seriously. These issues can be addressed most profitably in the asymptotically flat sector of quantum gravity. Indeed, it is likely that we should obtain a quantum theory for this special case even if it is not possible to quantise full general relativity. The purpose of this summary is to advertise the extension of loop quantum gravity to this sector that was developed in [1]...

Time-dependent perturbation of a two-state quantum mechanical system

NASA Technical Reports Server (NTRS)

Dion, D. R.

1974-01-01

A two- (nondegenerate) level quantum system interacting with a classical monochromatic radiation field is described. The existing work on this problem is reviewed and some novel aspects of the problems are presented.

Physics: Quantum problems solved through games

NASA Astrophysics Data System (ADS)

Maniscalco, Sabrina

2016-04-01

Humans are better than computers at performing certain tasks because of their intuition and superior visual processing. Video games are now being used to channel these abilities to solve problems in quantum physics. See Letter p.210

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.

Quantum dice rolling: a multi-outcome generalization of quantum coin flipping

NASA Astrophysics Data System (ADS)

Aharon, N.; Silman, J.

2010-03-01

The problem of quantum dice rolling (DR)—a generalization of the problem of quantum coin flipping (CF) to more than two outcomes and parties—is studied in both its weak and strong variants. We prove by construction that quantum mechanics allows for (i) weak N-sided DR admitting arbitrarily small bias for any N and (ii) two-party strong N-sided DR saturating Kitaev's bound for any N. To derive (ii) we also prove by construction that quantum mechanics allows for (iii) strong imbalanced CF saturating Kitaev's bound for any degree of imbalance. Furthermore, as a corollary of (ii) we introduce a family of optimal 2m-party strong nm-sided DR protocols for any pair m and n.

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.

The "Hard Problem" and the Quantum Physicists. Part 1: The First Generation

ERIC Educational Resources Information Center

Smith, C. U. M.

2006-01-01

All four of the most important figures in the early twentieth-century development of quantum physics--Niels Bohr, Erwin Schroedinger, Werner Heisenberg and Wolfgang Pauli--had strong interests in the traditional mind--brain, or "hard," problem. This paper reviews their approach to this problem, showing the influence of Bohr's complementarity…

Replicating the benefits of Deutschian closed timelike curves without breaking causality

NASA Astrophysics Data System (ADS)

Yuan, Xiao; Assad, Syed M.; Thompson, Jayne; Haw, Jing Yan; Vedral, Vlatko; Ralph, Timothy C.; Lam, Ping Koy; Weedbrook, Christian; Gu, Mile

2015-11-01

In general relativity, closed timelike curves can break causality with remarkable and unsettling consequences. At the classical level, they induce causal paradoxes disturbing enough to motivate conjectures that explicitly prevent their existence. At the quantum level such problems can be resolved through the Deutschian formalism, however this induces radical benefits—from cloning unknown quantum states to solving problems intractable to quantum computers. Instinctively, one expects these benefits to vanish if causality is respected. Here we show that in harnessing entanglement, we can efficiently solve NP-complete problems and clone arbitrary quantum states—even when all time-travelling systems are completely isolated from the past. Thus, the many defining benefits of Deutschian closed timelike curves can still be harnessed, even when causality is preserved. Our results unveil a subtle interplay between entanglement and general relativity, and significantly improve the potential of probing the radical effects that may exist at the interface between relativity and quantum theory.

Quantum annealing for the number-partitioning problem using a tunable spin glass of ions

PubMed Central

Graß, Tobias; Raventós, David; Juliá-Díaz, Bruno; Gogolin, Christian; Lewenstein, Maciej

2016-01-01

Exploiting quantum properties to outperform classical ways of information processing is an outstanding goal of modern physics. A promising route is quantum simulation, which aims at implementing relevant and computationally hard problems in controllable quantum systems. Here we demonstrate that in a trapped ion setup, with present day technology, it is possible to realize a spin model of the Mattis-type that exhibits spin glass phases. Our method produces the glassy behaviour without the need for any disorder potential, just by controlling the detuning of the spin-phonon coupling. Applying a transverse field, the system can be used to benchmark quantum annealing strategies which aim at reaching the ground state of the spin glass starting from the paramagnetic phase. In the vicinity of a phonon resonance, the problem maps onto number partitioning, and instances which are difficult to address classically can be implemented. PMID:27230802

Probing for quantum speedup on D-Wave Two

NASA Astrophysics Data System (ADS)

Rønnow, Troels F.; Wang, Zhihui; Job, Joshua; Isakov, Sergei V.; Boixo, Sergio; Lidar, Daniel; Martinis, John; Troyer, Matthias

2014-03-01

Quantum speedup refers to the advantage quantum devices can have over classical ones in solving classes of computational problems. In this talk we show how to correctly define and measure quantum speedup in experimental devices. We show how to avoid issues that might mask or fake quantum speedup.

EDITORIAL: Focus on Quantum Information and Many-Body Theory

NASA Astrophysics Data System (ADS)

Eisert, Jens; Plenio, Martin B.

2010-02-01

Quantum many-body models describing natural systems or materials and physical systems assembled piece by piece in the laboratory for the purpose of realizing quantum information processing share an important feature: intricate correlations that originate from the coherent interaction between a large number of constituents. In recent years it has become manifest that the cross-fertilization between research devoted to quantum information science and to quantum many-body physics leads to new ideas, methods, tools, and insights in both fields. Issues of criticality, quantum phase transitions, quantum order and magnetism that play a role in one field find relations to the classical simulation of quantum systems, to error correction and fault tolerance thresholds, to channel capacities and to topological quantum computation, to name but a few. The structural similarities of typical problems in both fields and the potential for pooling of ideas then become manifest. Notably, methods and ideas from quantum information have provided fresh approaches to long-standing problems in strongly correlated systems in the condensed matter context, including both numerical methods and conceptual insights. Focus on quantum information and many-body theory Contents TENSOR NETWORKS Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems M Rizzi, S Montangero, P Silvi, V Giovannetti and Rosario Fazio Concatenated tensor network states R Hübener, V Nebendahl and W Dür Entanglement renormalization in free bosonic systems: real-space versus momentum-space renormalization group transforms G Evenbly and G Vidal Finite-size geometric entanglement from tensor network algorithms Qian-Qian Shi, Román Orús, John Ove Fjærestad and Huan-Qiang Zhou Characterizing symmetries in a projected entangled pair state D Pérez-García, M Sanz, C E González-Guillén, M M Wolf and J I Cirac Matrix product operator representations B Pirvu, V Murg, J I Cirac and F Verstraete SIMULATION AND DYNAMICS A quantum differentiation of k-SAT instances B Tamir and G Ortiz Classical Ising model test for quantum circuits Joseph Geraci and Daniel A Lidar Exact matrix product solutions in the Heisenberg picture of an open quantum spin chain S R Clark, J Prior, M J Hartmann, D Jaksch and M B Plenio Exact solution of Markovian master equations for quadratic Fermi systems: thermal baths, open XY spin chains and non-equilibrium phase transition Tomaž Prosen and Bojan Žunkovič Quantum kinetic Ising models R Augusiak, F M Cucchietti, F Haake and M Lewenstein ENTANGLEMENT AND SPECTRAL PROPERTIES Ground states of unfrustrated spin Hamiltonians satisfy an area law Niel de Beaudrap, Tobias J Osborne and Jens Eisert Correlation density matrices for one-dimensional quantum chains based on the density matrix renormalization group W Münder, A Weichselbaum, A Holzner, Jan von Delft and C L Henley The invariant-comb approach and its relation to the balancedness of multipartite entangled states Andreas Osterloh and Jens Siewert Entanglement scaling of fractional quantum Hall states through geometric deformations Andreas M Läuchli, Emil J Bergholtz and Masudul Haque Entanglement versus gap for one-dimensional spin systems Daniel Gottesman and M B Hastings Entanglement spectra of critical and near-critical systems in one dimension F Pollmann and J E Moore Macroscopic bound entanglement in thermal graph states D Cavalcanti, L Aolita, A Ferraro, A García-Saez and A Acín Entanglement at the quantum phase transition in a harmonic lattice Elisabeth Rieper, Janet Anders and Vlatko Vedral Multipartite entanglement and frustration P Facchi, G Florio, U Marzolino, G Parisi and S Pascazio Entropic uncertainty relations—a survey Stephanie Wehner and Andreas Winter Entanglement in a spin system with inverse square statistical interaction D Giuliano, A Sindona, G Falcone, F Plastina and L Amico APPLICATIONS Time-dependent currents of one-dimensional bosons in an optical lattice J Schachenmayer, G Pupillo and A J Daley Implementing quantum gates using the ferromagnetic spin-J XXZ chain with kink boundary conditions Tom Michoel, Jaideep Mulherkar and Bruno Nachtergaele Long-distance entanglement in many-body atomic and optical systems Salvatore M Giampaolo and Fabrizio Illuminati QUANTUM MEMORIES AND TOPOLOGICAL ORDER Thermodynamic stability criteria for a quantum memory based on stabilizer and subsystem codes Stefano Chesi, Daniel Loss, Sergey Bravyi and Barbara M Terhal Topological color codes and two-body quantum lattice Hamiltonians M Kargarian, H Bombin and M A Martin-Delgado RENORMALIZATION Local renormalization method for random systems O Gittsovich, R Hübener, E Rico and H J Briegel

Composition in the Quantum World

NASA Astrophysics Data System (ADS)

Hall, Edward Jonathan

This thesis presents a problem for the foundations of quantum mechanics. It arises from the way that theory describes the composition of larger systems in terms of smaller ones, and renders untenable a wide range of interpretations of quantum mechanics. That quantum mechanics is difficult to interpret is old news, given the well-known Measurement Problem. But the problem I raise is quite different, and in important respects more fundamental. In brief: The physical world exhibits mereological structure: physical objects have parts, which in turn have parts, and so on. A natural way to try to represent this structure is by means of a particle theory, according to which the physical world consists entirely enduring physical objects which themselves have no proper parts, but aggregates of which are, or compose, all physical objects. Elementary, non-relativistic quantum mechanics can be cast in this mold--at least, according to the usual expositions of that theory. But herein lies the problem: the standard attempt to give a systematic particle interpretation to elementary quantum mechanics results in nonsense, thanks to the well-established principle of Permutation Invariance, which constrains the quantum -mechanical description of systems containing identical particles. Specifically, it follows from the most minimal principles of a particle interpretation (much weaker than those needed to generate the Measurement Problem), together with Permutation Invariance, that systems identical in composition must have the same physical state. In other words, systems which merely have the same numbers of the same types of particles are therefore, at all times, perfect physical duplicates. This conclusion is absurd: e.g., it is quite plausible that some of those particles which compose my body make up a system identical in composition to some pepperoni pizza. Yet no part of me is a qualitative physical duplicate of any pepperoni pizza. Perhaps "you are what you eat" --but not in this sense! In what follows I develop the principles needed to explore this problem, contrast it with the Measurement Problem, and consider, finally, how it should influence our judgments of the relative merits of the many extant interpretations of quantum mechanics.

Semiclassical transport in nearly symmetric quantum dots. I. Symmetry breaking in the dot.

PubMed

Whitney, Robert S; Schomerus, Henning; Kopp, Marten

2009-11-01

We apply the semiclassical theory of transport to quantum dots with exact and approximate spatial symmetries; left-right mirror symmetry, up-down mirror symmetry, inversion symmetry, or fourfold symmetry. In this work-the first of a pair of articles-we consider (a) perfectly symmetric dots and (b) nearly symmetric dots in which the symmetry is broken by the dot's internal dynamics. The second article addresses symmetry-breaking by displacement of the leads. Using semiclassics, we identify the origin of the symmetry-induced interference effects that contribute to weak localization corrections and universal conductance fluctuations. For perfect spatial symmetry, we recover results previously found using the random-matrix theory conjecture. We then go on to show how the results are affected by asymmetries in the dot, magnetic fields, and decoherence. In particular, the symmetry-asymmetry crossover is found to be described by a universal dependence on an asymmetry parameter gamma_{asym} . However, the form of this parameter is very different depending on how the dot is deformed away from spatial symmetry. Symmetry-induced interference effects are completely destroyed when the dot's boundary is globally deformed by less than an electron wavelength. In contrast, these effects are only reduced by a finite amount when a part of the dot's boundary smaller than a lead-width is deformed an arbitrarily large distance.

Preface of the special issue quantum foundations: information approach

PubMed Central

2016-01-01

This special issue is based on the contributions of a group of top experts in quantum foundations and quantum information and probability. It enlightens a number of interpretational, mathematical and experimental problems of quantum theory. PMID:27091161

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.

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

Donnelly, William; Freidel, Laurent

We consider the problem of defining localized subsystems in gauge theory and gravity. Such systems are associated to spacelike hypersurfaces with boundaries and provide the natural setting for studying entanglement entropy of regions of space. We present a general formalism to associate a gauge-invariant classical phase space to a spatial slice with boundary by introducing new degrees of freedom on the boundary. In Yang-Mills theory the new degrees of freedom are a choice of gauge on the boundary, transformations of which are generated by the normal component of the nonabelian electric field. In general relativity the new degrees of freedommore » are the location of a codimension-2 surface and a choice of conformal normal frame. These degrees of freedom transform under a group of surface symmetries, consisting of diffeomorphisms of the codimension-2 boundary, and position-dependent linear deformations of its normal plane. We find the observables which generate these symmetries, consisting of the conformal normal metric and curvature of the normal connection. We discuss the implications for the problem of defining entanglement entropy in quantum gravity. Finally, our work suggests that the Bekenstein-Hawking entropy may arise from the different ways of gluing together two partial Cauchy surfaces at a cross-section of the horizon.« less

Area-Preserving Diffeomorphisms, W∞ and { U}q [sl(2)] in Chern-Simons Theory and the Quantum Hall System

NASA Astrophysics Data System (ADS)

Kogan, Ian I.

We discuss a quantum { U}q [sl(2)] symmetry in the Landau problem, which naturally arises due to the relation between { U}q [sl(2)] and the group of magnetic translations. The latter is connected with W∞ and area-preserving (symplectic) diffeomorphisms which are the canonical transformations in the two-dimensional phase space. We shall discuss the hidden quantum symmetry in a 2 + 1 gauge theory with the Chern-Simons term and in a quantum Hall system, which are both connected with the Landau problem.

Semi-quantum communication: protocols for key agreement, controlled secure direct communication and dialogue

NASA Astrophysics Data System (ADS)

Shukla, Chitra; Thapliyal, Kishore; Pathak, Anirban

2017-12-01

Semi-quantum protocols that allow some of the users to remain classical are proposed for a large class of problems associated with secure communication and secure multiparty computation. Specifically, first-time semi-quantum protocols are proposed for key agreement, controlled deterministic secure communication and dialogue, and it is shown that the semi-quantum protocols for controlled deterministic secure communication and dialogue can be reduced to semi-quantum protocols for e-commerce and private comparison (socialist millionaire problem), respectively. Complementing with the earlier proposed semi-quantum schemes for key distribution, secret sharing and deterministic secure communication, set of schemes proposed here and subsequent discussions have established that almost every secure communication and computation tasks that can be performed using fully quantum protocols can also be performed in semi-quantum manner. Some of the proposed schemes are completely orthogonal-state-based, and thus, fundamentally different from the existing semi-quantum schemes that are conjugate coding-based. Security, efficiency and applicability of the proposed schemes have been discussed with appropriate importance.

Quantum self-gravitating collapsing matter in a quantum geometry

NASA Astrophysics Data System (ADS)

Campiglia, Miguel; Gambini, Rodolfo; Olmedo, Javier; Pullin, Jorge

2016-09-01

The problem of how space-time responds to gravitating quantum matter in full quantum gravity has been one of the main questions that any program of quantization of gravity should address. Here we analyze this issue by considering the quantization of a collapsing null shell coupled to spherically symmetric loop quantum gravity. We show that the constraint algebra of canonical gravity is Abelian both classically and when quantized using loop quantum gravity techniques. The Hamiltonian constraint is well defined and suitable Dirac observables characterizing the problem were identified at the quantum level. We can write the metric as a parameterized Dirac observable at the quantum level and study the physics of the collapsing shell and black hole formation. We show how the singularity inside the black hole is eliminated by loop quantum gravity and how the shell can traverse it. The construction is compatible with a scenario in which the shell tunnels into a baby universe inside the black hole or one in which it could emerge through a white hole.

Quantum geodesy

NASA Astrophysics Data System (ADS)

Jitrik, Oliverio; Lanzagorta, Marco; Uhlmann, Jeffrey; Venegas-Andraca, Salvador E.

2017-05-01

The study of plate tectonic motion is important to generate theoretical models of the structure and dynamics of the Earth. In turn, understanding tectonic motion provides insight to develop sophisticated models that can be used for earthquake early warning systems and for nuclear forensics. Tectonic geodesy uses the position of a network of points on the surface of earth to determine the motion of tectonic plates and the deformation of the earths crust. GPS and interferometric synthetic aperture radar are commonly used techniques used in tectonic geodesy. In this paper we will describe the feasibility of interferometric synthetic aperture quantum radar and its theoretical performance for tectonic geodesy.

Towards an emergent model of solitonic particles from non-trivial vacuum structure

NASA Astrophysics Data System (ADS)

Gillard, Adam B.; Gresnigt, Niels G.

2017-12-01

We motivate and introduce what we refer to as the principles of Lie-stability and Hopf-stability and see what the physical theories must look like. Lie-stability is needed on the classical side and Hopf-stability is needed on the quantum side. We implement these two principles together with Lie-deformations consistent with basic constraints on the classical kinematical variables to arrive at the form of a theory that identifies standard model fermions with quantum solitonic trefoil knotted flux tubes which emerge from a flux tube vacuum network. Moreover, twisted unknot fluxtubes form natural dark matter candidates

Atmospheric Quantum Channels with Weak and Strong Turbulence.

PubMed

Vasylyev, D; Semenov, A A; Vogel, W

2016-08-26

The free-space transfer of high-fidelity optical signals between remote locations has many applications, including both classical and quantum communication, precision navigation, clock synchronization, etc. The physical processes that contribute to signal fading and loss need to be carefully analyzed in the theory of light propagation through the atmospheric turbulence. Here we derive the probability distribution for the atmospheric transmittance including beam wandering, beam shape deformation, and beam-broadening effects. Our model, referred to as the elliptic beam approximation, applies to weak, weak-to-moderate, and strong turbulence and hence to the most important regimes in atmospheric communication scenarios.

Demonstration of analyzers for multimode photonic time-bin qubits

NASA Astrophysics Data System (ADS)

Jin, Jeongwan; Agne, Sascha; Bourgoin, Jean-Philippe; Zhang, Yanbao; Lütkenhaus, Norbert; Jennewein, Thomas

2018-04-01

We demonstrate two approaches for unbalanced interferometers as time-bin qubit analyzers for quantum communication, robust against mode distortions and polarization effects as expected from free-space quantum communication systems including wavefront deformations, path fluctuations, pointing errors, and optical elements. Despite strong spatial and temporal distortions of the optical mode of a time-bin qubit, entangled with a separate polarization qubit, we verify entanglement using the Negative Partial Transpose, with the measured visibility of up to 0.85 ±0.01 . The robustness of the analyzers is further demonstrated for various angles of incidence up to 0 .2∘ . The output of the interferometers is coupled into multimode fiber yielding a high system throughput of 0.74. Therefore, these analyzers are suitable and efficient for quantum communication over multimode optical channels.

Emerging interpretations of quantum mechanics and recent progress in quantum measurement

NASA Astrophysics Data System (ADS)

Clarke, M. L.

2014-01-01

The focus of this paper is to provide a brief discussion on the quantum measurement process, by reviewing select examples highlighting recent progress towards its understanding. The areas explored include an outline of the measurement problem, the standard interpretation of quantum mechanics, quantum to classical transition, types of measurement (including weak and projective measurements) and newly emerging interpretations of quantum mechanics (decoherence theory, objective reality, quantum Darwinism and quantum Bayesianism).

Detection of Biochemical Pathogens, Laser Stand-off Spectroscopy, Quantum Coherence, and Many Body Quantum Optics

DTIC Science & Technology

2012-02-24

AND SUBTITLE Detection of Biochemical Pathogens, Laser Stand-off Spectroscopy, Quantum Coherence, and Many Body Quantum Optics 6. AUTHORS Marian O...Maximum 200 words) Results of our earlier research in the realm of quantum optics were extended in order to solve the challenging technical problems of...efficient methods of generating UV light via quantum coherence. 14. SUBJECT TERMS Quantum coherence, quantum optics, lasers 15. NUMBER OF PAGES 15

A novel model-based evolutionary algorithm for multi-objective deformable image registration with content mismatch and large deformations: benchmarking efficiency and quality

NASA Astrophysics Data System (ADS)

Bouter, Anton; Alderliesten, Tanja; Bosman, Peter A. N.

2017-02-01

Taking a multi-objective optimization approach to deformable image registration has recently gained attention, because such an approach removes the requirement of manually tuning the weights of all the involved objectives. Especially for problems that require large complex deformations, this is a non-trivial task. From the resulting Pareto set of solutions one can then much more insightfully select a registration outcome that is most suitable for the problem at hand. To serve as an internal optimization engine, currently used multi-objective algorithms are competent, but rather inefficient. In this paper we largely improve upon this by introducing a multi-objective real-valued adaptation of the recently introduced Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) for discrete optimization. In this work, GOMEA is tailored specifically to the problem of deformable image registration to obtain substantially improved efficiency. This improvement is achieved by exploiting a key strength of GOMEA: iteratively improving small parts of solutions, allowing to faster exploit the impact of such updates on the objectives at hand through partial evaluations. We performed experiments on three registration problems. In particular, an artificial problem containing a disappearing structure, a pair of pre- and post-operative breast CT scans, and a pair of breast MRI scans acquired in prone and supine position were considered. Results show that compared to the previously used evolutionary algorithm, GOMEA obtains a speed-up of up to a factor of 1600 on the tested registration problems while achieving registration outcomes of similar quality.

Quantum communication and information processing

NASA Astrophysics Data System (ADS)

Beals, Travis Roland

Quantum computers enable dramatically more efficient algorithms for solving certain classes of computational problems, but, in doing so, they create new problems. In particular, Shor's Algorithm allows for efficient cryptanalysis of many public-key cryptosystems. As public key cryptography is a critical component of present-day electronic commerce, it is crucial that a working, secure replacement be found. Quantum key distribution (QKD), first developed by C.H. Bennett and G. Brassard, offers a partial solution, but many challenges remain, both in terms of hardware limitations and in designing cryptographic protocols for a viable large-scale quantum communication infrastructure. In Part I, I investigate optical lattice-based approaches to quantum information processing. I look at details of a proposal for an optical lattice-based quantum computer, which could potentially be used for both quantum communications and for more sophisticated quantum information processing. In Part III, I propose a method for converting and storing photonic quantum bits in the internal state of periodically-spaced neutral atoms by generating and manipulating a photonic band gap and associated defect states. In Part II, I present a cryptographic protocol which allows for the extension of present-day QKD networks over much longer distances without the development of new hardware. I also present a second, related protocol which effectively solves the authentication problem faced by a large QKD network, thus making QKD a viable, information-theoretic secure replacement for public key cryptosystems.

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.

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

A New Ontological View of the Quantum Measurement Problem

DTIC Science & Technology

2005-06-13

broader issues in the foundations of quantum mechanics as well. In this scenario, a quantum measurement is a nonequilibrium phase transition in a...the foundations of quantum mechan - ics as well. In this scenario a quantum measurement is a non-equilibrium phase transition in a “resonant cavity...ontology, and the probabilistic element is removed from the foundations of quantum mechanics , its apparent presence in the quantum measurement being solely

Infinitesimal deformations of Poisson bi-vectors using the Kontsevich graph calculus

NASA Astrophysics Data System (ADS)

Buring, Ricardo; Kiselev, Arthemy V.; Rutten, Nina

2018-02-01

Let \\mathscr{P} be a Poisson structure on a finite-dimensional affine real manifold. Can \\mathscr{P} be deformed in such a way that it stays Poisson? The language of Kontsevich graphs provides a universal approach - with respect to all affine Poisson manifolds - to finding a class of solutions to this deformation problem. For that reasoning, several types of graphs are needed. In this paper we outline the algorithms to generate those graphs. The graphs that encode deformations are classified by the number of internal vertices k; for k ≤ 4 we present all solutions of the deformation problem. For k ≥ 5, first reproducing the pentagon-wheel picture suggested at k = 6 by Kontsevich and Willwacher, we construct the heptagon-wheel cocycle that yields a new unique solution without 2-loops and tadpoles at k = 8.

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

Quantum snake walk on graphs

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

Rosmanis, Ansis

2011-02-15

I introduce a continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First, I analyze the quantum snake walk on the line, and I show that, even though most states stay localized throughout the evolution, there are specific states that most likely move on the line as wave packets with momentum inversely proportional to the length of the snake. Next, I discuss how an algorithm based on the quantum snake walk might potentially be able to solve an extended version of the glued trees problem, whichmore » asks to find a path connecting both roots of the glued trees graph. To the best of my knowledge, no efficient quantum algorithm solving this problem is known yet.« less

The Quantum Measurement Problem and Physical reality: A Computation Theoretic Perspective

NASA Astrophysics Data System (ADS)

Srikanth, R.

2006-11-01

Is the universe computable? If yes, is it computationally a polynomial place? In standard quantum mechanics, which permits infinite parallelism and the infinitely precise specification of states, a negative answer to both questions is not ruled out. On the other hand, empirical evidence suggests that NP-complete problems are intractable in the physical world. Likewise, computational problems known to be algorithmically uncomputable do not seem to be computable by any physical means. We suggest that this close correspondence between the efficiency and power of abstract algorithms on the one hand, and physical computers on the other, finds a natural explanation if the universe is assumed to be algorithmic; that is, that physical reality is the product of discrete sub-physical information processing equivalent to the actions of a probabilistic Turing machine. This assumption can be reconciled with the observed exponentiality of quantum systems at microscopic scales, and the consequent possibility of implementing Shor's quantum polynomial time algorithm at that scale, provided the degree of superposition is intrinsically, finitely upper-bounded. If this bound is associated with the quantum-classical divide (the Heisenberg cut), a natural resolution to the quantum measurement problem arises. From this viewpoint, macroscopic classicality is an evidence that the universe is in BPP, and both questions raised above receive affirmative answers. A recently proposed computational model of quantum measurement, which relates the Heisenberg cut to the discreteness of Hilbert space, is briefly discussed. A connection to quantum gravity is noted. Our results are compatible with the philosophy that mathematical truths are independent of the laws of physics.

Implementation of a three-qubit refined Deutsch Jozsa algorithm using SFG quantum logic gates

NASA Astrophysics Data System (ADS)

DelDuce, A.; Savory, S.; Bayvel, P.

2006-05-01

In this paper we present a quantum logic circuit which can be used for the experimental demonstration of a three-qubit solid state quantum computer based on a recent proposal of optically driven quantum logic gates. In these gates, the entanglement of randomly placed electron spin qubits is manipulated by optical excitation of control electrons. The circuit we describe solves the Deutsch problem with an improved algorithm called the refined Deutsch-Jozsa algorithm. We show that it is possible to select optical pulses that solve the Deutsch problem correctly, and do so without losing quantum information to the control electrons, even though the gate parameters vary substantially from one gate to another.

Strategies in a symmetric quantum Kolkata restaurant problem

NASA Astrophysics Data System (ADS)

Sharif, Puya; Heydari, Hoshang

2012-12-01

The Quantum Kolkata restaurant problem is a multiple-choice version of the quantum minority game, where a set of n non-communicating players have to chose between one of m choices. A payoff is granted to the players that make a unique choice. It has previously been shown that shared entanglement and quantum operations can aid the players to coordinate their actions and acquire higher payoffs than is possible with classical randomization. In this paper the initial quantum state is expanded to a family of GHZ-type states and strategies are discussed in terms of possible final outcomes. It is shown that the players individually seek outcomes that maximize the collective good.

Combinatorial quantization of the Hamiltonian Chern-Simons theory II

NASA Astrophysics Data System (ADS)

Alekseev, Anton Yu.; Grosse, Harald; Schomerus, Volker

1996-01-01

This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory advertised in [1]. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of quantum group gauge theory. This allows to discuss flatness of quantum connections so that we can give a mathematically rigorous definition of the algebra of observables A CS of the Chern Simons model. It is a *-algebra of “functions on the quantum moduli space of flat connections” and comes equipped with a positive functional ω (“integration”). We prove that this data does not depend on the particular choices which have been made in the construction. Following ideas of Fock and Rosly [2], the algebra A CS provides a deformation quantization of the algebra of functions on the moduli space along the natural Poisson bracket induced by the Chern Simons action. We evaluate a volume of the quantized moduli space and prove that it coincides with the Verlinde number. This answer is also interpreted as a partition partition function of the lattice Yang-Mills theory corresponding to a quantum gauge group.

NP-hardness of decoding quantum error-correction codes

NASA Astrophysics Data System (ADS)

Hsieh, Min-Hsiu; Le Gall, François

2011-05-01

Although the theory of quantum error correction is intimately related to classical coding theory and, in particular, one can construct quantum error-correction codes (QECCs) from classical codes with the dual-containing property, this does not necessarily imply that the computational complexity of decoding QECCs is the same as their classical counterparts. Instead, decoding QECCs can be very much different from decoding classical codes due to the degeneracy property. Intuitively, one expects degeneracy would simplify the decoding since two different errors might not and need not be distinguished in order to correct them. However, we show that general quantum decoding problem is NP-hard regardless of the quantum codes being degenerate or nondegenerate. This finding implies that no considerably fast decoding algorithm exists for the general quantum decoding problems and suggests the existence of a quantum cryptosystem based on the hardness of decoding QECCs.

A variational eigenvalue solver on a photonic quantum processor

PubMed Central

Peruzzo, Alberto; McClean, Jarrod; Shadbolt, Peter; Yung, Man-Hong; Zhou, Xiao-Qi; Love, Peter J.; Aspuru-Guzik, Alán; O’Brien, Jeremy L.

2014-01-01

Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the physical dimension grows exponentially, finding the eigenvalues of certain operators is one such intractable problem and remains a fundamental challenge. The quantum phase estimation algorithm efficiently finds the eigenvalue of a given eigenvector but requires fully coherent evolution. Here we present an alternative approach that greatly reduces the requirements for coherent evolution and combine this method with a new approach to state preparation based on ansätze and classical optimization. We implement the algorithm by combining a highly reconfigurable photonic quantum processor with a conventional computer. We experimentally demonstrate the feasibility of this approach with an example from quantum chemistry—calculating the ground-state molecular energy for He–H+. The proposed approach drastically reduces the coherence time requirements, enhancing the potential of quantum resources available today and in the near future. PMID:25055053

Quantum game application to spectrum scarcity problems

NASA Astrophysics Data System (ADS)

Zabaleta, O. G.; Barrangú, J. P.; Arizmendi, C. M.

2017-01-01

Recent spectrum-sharing research has produced a strategy to address spectrum scarcity problems. This novel idea, named cognitive radio, considers that secondary users can opportunistically exploit spectrum holes left temporarily unused by primary users. This presents a competitive scenario among cognitive users, making it suitable for game theory treatment. In this work, we show that the spectrum-sharing benefits of cognitive radio can be increased by designing a medium access control based on quantum game theory. In this context, we propose a model to manage spectrum fairly and effectively, based on a multiple-users multiple-choice quantum minority game. By taking advantage of quantum entanglement and quantum interference, it is possible to reduce the probability of collision problems commonly associated with classic algorithms. Collision avoidance is an essential property for classic and quantum communications systems. In our model, two different scenarios are considered, to meet the requirements of different user strategies. The first considers sensor networks where the rational use of energy is a cornerstone; the second focuses on installations where the quality of service of the entire network is a priority.

Schroedinger's immortal cat

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

Peres, A.

1988-01-01

The purpose of this paper is to review and clarify the quantum measurement problem. The latter originates in the ambivalent nature of the observer: Although the observer is not described by the Schroedinger equation, it should nevertheless be possible to quantize him and include him in the wave function if quantum theory is universally valid. The problem is to prove that no contradiction may arise in these two conflicting descriptions. The proof invokes the notion of irreversibility. The validity of the latter is questionable, because the standard rationale for classical irreversibility, namely mixing and coarse graining, does not apply tomore » quantum theory. There is no chaos in a closed, finite quantum system. However, when a system is large enough, it cannot be perfectly isolated from it environment, namely from external (or even internal) degrees of freedom which are not fully accounted for in the Hamiltonian of that system. As a consequence, the long-range evolution of such a quantum system is essentially unpredictable. It follows that the notion of irreversibility is a valid one in quantum theory and the measurement problem can be brought to a satisfactory solution.« less

Computational Role of Tunneling in a Programmable Quantum Annealer

NASA Technical Reports Server (NTRS)

Boixo, Sergio; Smelyanskiy, Vadim; Shabani, Alireza; Isakov, Sergei V.; Dykman, Mark; Amin, Mohammad; Mohseni, Masoud; Denchev, Vasil S.; Neven, Hartmut

2016-01-01

Quantum tunneling is a phenomenon in which a quantum state tunnels through energy barriers above the energy of the state itself. Tunneling has been hypothesized as an advantageous physical resource for optimization. Here we present the first experimental evidence of a computational role of multiqubit quantum tunneling in the evolution of a programmable quantum annealer. We developed a theoretical model based on a NIBA Quantum Master Equation to describe the multi-qubit dissipative cotunneling effects under the complex noise characteristics of such quantum devices.We start by considering a computational primitive, the simplest non-convex optimization problem consisting of just one global and one local minimum. The quantum evolutions enable tunneling to the global minimum while the corresponding classical paths are trapped in a false minimum. In our study the non-convex potentials are realized by frustrated networks of qubit clusters with strong intra-cluster coupling. We show that the collective effect of the quantum environment is suppressed in the critical phase during the evolution where quantum tunneling decides the right path to solution. In a later stage dissipation facilitates the multiqubit cotunneling leading to the solution state. The predictions of the model accurately describe the experimental data from the D-WaveII quantum annealer at NASA Ames. In our computational primitive the temperature dependence of the probability of success in the quantum model is opposite to that of the classical paths with thermal hopping. Specially, we provide an analysis of an optimization problem with sixteen qubits,demonstrating eight qubit cotunneling that increases success probabilities. Furthermore, we report results for larger problems with up to 200 qubits that contain the primitive as subproblems.

Solution to the satisfiability problem using a complete Grover search with trapped ions

NASA Astrophysics Data System (ADS)

Yang, Wan-Li; Wei, Hua; Zhou, Fei; Chang, Weng-Long; Feng, Mang

2009-07-01

The main idea in the original Grover search (1997 Phys. Rev. Lett. 79 325) is to single out a target state containing the solution to a search problem by amplifying the amplitude of the state, following the Oracle's job, i.e., a black box giving us information about the target state. We design quantum circuits to accomplish a complete Grover search involving both the Oracle's job and the amplification of the target state, which are employed to solve satisfiability (SAT) problems. We explore how to carry out the quantum circuits with currently available ion-trap quantum computing technology.

The quantum N-body problem in the mean-field and semiclassical regime

NASA Astrophysics Data System (ADS)

Golse, François

2018-04-01

The present work discusses the mean-field limit for the quantum N-body problem in the semiclassical regime. More precisely, we establish a convergence rate for the mean-field limit which is uniform as the ratio of Planck constant to the action of the typical single particle tends to zero. This convergence rate is formulated in terms of a quantum analogue of the quadratic Monge-Kantorovich or Wasserstein distance. This paper is an account of some recent collaboration with C. Mouhot, T. Paul and M. Pulvirenti. This article is part of the themed issue `Hilbert's sixth problem'.

Deformation of the free surface of a conducting fluid in the magnetic field of current-carrying linear conductors

NASA Astrophysics Data System (ADS)

Zubarev, N. M.; Zubareva, O. V.

2017-06-01

The magnetic shaping problem is studied for the situation where a cylindrical column of a perfectly conducting fluid is deformed by the magnetic field of a system of linear current-carrying conductors. Equilibrium is achieved due to the balance of capillary and magnetic pressures. Two two-parametric families of exact solutions of the problem are obtained with the help of conformal mapping technique. In accordance with them, the column essentially deforms in the cross section up to its disintegration.

Large-amplitude nuclear motion formulated in terms of dissipation of quantum fluctuations

NASA Astrophysics Data System (ADS)

Kuzyakin, R. A.; Sargsyan, V. V.; Adamian, G. G.; Antonenko, N. V.

2017-01-01

The potential-barrier penetrability and quasi-stationary thermal-decay rate of a metastable state are formulated in terms of microscopic quantum diffusion. Apart from linear coupling in momentum between the collective and internal subsystems, the formalism embraces the more general case of linear couplings in both the momentum and the coordinates. The developed formalism is then used for describing the process of projectile-nucleus capture by a target nucleus at incident energies near and below the Coulomb barrier. The capture partial probability, which determines the cross section for formation of a dinuclear system, is derived in analytical form. The total and partial capture cross sections, mean and root-mean-square angular momenta of the formed dinuclear system, astrophysical -factors, logarithmic derivatives, and barrier distributions are derived for various reactions. Also investigated are the effects of nuclear static deformation and neutron transfer between the interacting nuclei on the capture cross section and its isotopic dependence, and the entrance-channel effects on the capture process. The results of calculations for reactions involving both spherical and deformed nuclei are in good agreement with available experimental data.

Deformed oscillator algebra approach of some quantum superintegrable Lissajous systems on the sphere and of their rational extensions

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

Marquette, Ian, E-mail: i.marquette@uq.edu.au; Quesne, Christiane, E-mail: cquesne@ulb.ac.be

2015-06-15

We extend the construction of 2D superintegrable Hamiltonians with separation of variables in spherical coordinates using combinations of shift, ladder, and supercharge operators to models involving rational extensions of the two-parameter Lissajous systems on the sphere. These new families of superintegrable systems with integrals of arbitrary order are connected with Jacobi exceptional orthogonal polynomials of type I (or II) and supersymmetric quantum mechanics. Moreover, we present an algebraic derivation of the degenerate energy spectrum for the one- and two-parameter Lissajous systems and the rationally extended models. These results are based on finitely generated polynomial algebras, Casimir operators, realizations as deformedmore » oscillator algebras, and finite-dimensional unitary representations. Such results have only been established so far for 2D superintegrable systems separable in Cartesian coordinates, which are related to a class of polynomial algebras that display a simpler structure. We also point out how the structure function of these deformed oscillator algebras is directly related with the generalized Heisenberg algebras spanned by the nonpolynomial integrals.« less

Study of the total reaction cross section via QMD

NASA Astrophysics Data System (ADS)

Yang, Lin-Meng; Guo, Wen-Jun; Zhang, Fan; Ni, Sheng

2013-10-01

This paper presents a new empirical formula to calculate the average nucleon-nucleon (N-N) collision number for the total reaction cross sections (σR). Based on the initial average N-N collision number calculated by quantum molecular dynamics (QMD), quantum correction and Coulomb correction are taken into account within it. The average N-N collision number is calculated by this empirical formula. The total reaction cross sections are obtained within the framework of the Glauber theory. σR of 23Al+12C, 24Al+12C, 25 Al+12C, 26Al+12C and 27Al+12C are calculated in the range of low energy. We also calculate the σR of 27Al+12C with different incident energies. The calculated σR are compared with the experimental data and the results of Glauber theory including the σR of both spherical nuclear and deformed nuclear. It is seen that the calculated σR are larger than σR of spherical nuclear and smaller than σR of deformed nuclear, whereas the results agree well with the experimental data in low-energy range.

Linear solver performance in elastoplastic problem solution on GPU cluster

NASA Astrophysics Data System (ADS)

Khalevitsky, Yu. V.; Konovalov, A. V.; Burmasheva, N. V.; Partin, A. S.

2017-12-01

Applying the finite element method to severe plastic deformation problems involves solving linear equation systems. While the solution procedure is relatively hard to parallelize and computationally intensive by itself, a long series of large scale systems need to be solved for each problem. When dealing with fine computational meshes, such as in the simulations of three-dimensional metal matrix composite microvolume deformation, tens and hundreds of hours may be needed to complete the whole solution procedure, even using modern supercomputers. In general, one of the preconditioned Krylov subspace methods is used in a linear solver for such problems. The method convergence highly depends on the operator spectrum of a problem stiffness matrix. In order to choose the appropriate method, a series of computational experiments is used. Different methods may be preferable for different computational systems for the same problem. In this paper we present experimental data obtained by solving linear equation systems from an elastoplastic problem on a GPU cluster. The data can be used to substantiate the choice of the appropriate method for a linear solver to use in severe plastic deformation simulations.

Solution to the sign problem in a frustrated quantum impurity model

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

Hann, Connor T., E-mail: connor.hann@yale.edu; Huffman, Emilie; Chandrasekharan, Shailesh

2017-01-15

In this work we solve the sign problem of a frustrated quantum impurity model consisting of three quantum spin-half chains interacting through an anti-ferromagnetic Heisenberg interaction at one end. We first map the model into a repulsive Hubbard model of spin-half fermions hopping on three independent one dimensional chains that interact through a triangular hopping at one end. We then convert the fermion model into an inhomogeneous one dimensional model and express the partition function as a weighted sum over fermion worldline configurations. By imposing a pairing of fermion worldlines in half the space we show that all negative weightmore » configurations can be eliminated. This pairing naturally leads to the original frustrated quantum spin model at half filling and thus solves its sign problem.« less

N=2 supersymmetric a=4-Korteweg-de Vries hierarchy derived via Gardner's deformation of Kaup-Boussinesq equation

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

Hussin, V.; Kiselev, A. V.; Krutov, A. O.

2010-08-15

We consider the problem of constructing Gardner's deformations for the N=2 supersymmetric a=4-Korteweg-de Vries (SKdV) equation; such deformations yield recurrence relations between the super-Hamiltonians of the hierarchy. We prove the nonexistence of supersymmetry-invariant deformations that retract to Gardner's formulas for the Korteweg-de Vries (KdV) with equation under the component reduction. At the same time, we propose a two-step scheme for the recursive production of the integrals of motion for the N=2, a=4-SKdV. First, we find a new Gardner's deformation of the Kaup-Boussinesq equation, which is contained in the bosonic limit of the superhierarchy. This yields the recurrence relation between themore » Hamiltonians of the limit, whence we determine the bosonic super-Hamiltonians of the full N=2, a=4-SKdV hierarchy. Our method is applicable toward the solution of Gardner's deformation problems for other supersymmetric KdV-type systems.« less

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

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?

Quantum harmonic oscillator in a thermal bath

NASA Technical Reports Server (NTRS)

Zhang, Yuhong

1993-01-01

The influence functional path-integral treatment of quantum Brownian motion is briefly reviewed. A newly derived exact master equation of a quantum harmonic oscillator coupled to a general environment at arbitrary temperature is discussed. It is applied to the problem of loss of quantum coherence.

Problems in particle theory. Technical report - 1993--1994

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

Adler, S.L.; Wilczek, F.

This report is a progress report on the work of two principal investigators in the broad area of particle physics theory, covering their personal work, that of their coworkers, and their proposed work for the future. One author has worked in the past on various topics in field theory and particle physics, among them current algebras, the physics of neutrino induced reactions, quantum electrodynamics (including strong magnetic field processes), the theory of the axial-vector current anomaly, topics in quantum gravity, and nonlinear models for quark confinement. While much of his work has been analytical, all of the projects listed abovemore » (except for the work on gravity) had phases which required considerable computer work as well. Over the next several years, he proposes to continue or initiate research on the following problems: (1) Acceleration algorithms for the Monte Carlo analysis of lattice field and gauge theories, and more generally, new research in computational neuroscience and pattern recognition. (2) Construction of quaternionic generalizations of complex quantum mechanics and field theory, and their application to composite models of quarks and leptons, and to the problem of unifying quantum theories of matter with general relativity. One author has worked on problems in exotic quantum statistics and its applications to condensed matter systems. His work has also continued on the quantum theory of black holes. This has evolved toward understanding properties of quantum field theory and string theory in incomplete regions of flat space.« less

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.

Quantum Matching Theory (with new complexity-theoretic, combinatorial and topical insights on the nature of the quantum entanglement)

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

Gurvits, L.

2002-01-01

Classical matching theory can be defined in terms of matrices with nonnegative entries. The notion of Positive operator, central in Quantum Theory, is a natural generalization of matrices with non-negative entries. Based on this point of view, we introduce a definition of perfect Quantum (operator) matching. We show that the new notion inherits many 'classical' properties, but not all of them. This new notion goes somewhere beyound matroids. For separable bipartite quantum states this new notion coinsides with the full rank property of the intersection of two corresponding geometric matroids. In the classical situation, permanents are naturally associated with perfectsmore » matchings. We introduce an analog of permanents for positive operators, called Quantum Permanent and show how this generalization of the permanent is related to the Quantum Entanglement. Besides many other things, Quantum Permanents provide new rational inequalities necessary for the separability of bipartite quantum states. Using Quantum Permanents, we give deterministic poly-time algorithm to solve Hidden Matroids Intersection Problem and indicate some 'classical' complexity difficulties associated with the Quantum Entanglement. Finally, we prove that the weak membership problem for the convex set of separable bipartite density matrices is NP-HARD.« less

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

Weinstein, Marvin; /SLAC

Last year, in 2008, I gave a talk titled Quantum Calisthenics. This year I am going to tell you about how the work I described then has spun off into a most unlikely direction. What I am going to talk about is how one maps the problem of finding clusters in a given data set into a problem in quantum mechanics. I will then use the tricks I described to let quantum evolution lets the clusters come together on their own.

Quantum Resonance Approach to Combinatorial Optimization

NASA Technical Reports Server (NTRS)

Zak, Michail

1997-01-01

It is shown that quantum resonance can be used for combinatorial optimization. The advantage of the approach is in independence of the computing time upon the dimensionality of the problem. As an example, the solution to a constraint satisfaction problem of exponential complexity is demonstrated.

Degenerate quantum codes and the quantum Hamming bound

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

Sarvepalli, Pradeep; Klappenecker, Andreas

2010-03-15

The parameters of a nondegenerate quantum code must obey the Hamming bound. An important open problem in quantum coding theory is whether the parameters of a degenerate quantum code can violate this bound for nondegenerate quantum codes. In this article we show that Calderbank-Shor-Steane (CSS) codes, over a prime power alphabet q{>=}5, cannot beat the quantum Hamming bound. We prove a quantum version of the Griesmer bound for the CSS codes, which allows us to strengthen the Rains' bound that an [[n,k,d

About approximation of integer factorization problem by the combination fixed-point iteration method and Bayesian rounding for quantum cryptography

NASA Astrophysics Data System (ADS)

Ogorodnikov, Yuri; Khachay, Michael; Pljonkin, Anton

2018-04-01

We describe the possibility of employing the special case of the 3-SAT problem stemming from the well known integer factorization problem for the quantum cryptography. It is known, that for every instance of our 3-SAT setting the given 3-CNF is satisfiable by a unique truth assignment, and the goal is to find this assignment. Since the complexity status of the factorization problem is still undefined, development of approximation algorithms and heuristics adopts interest of numerous researchers. One of promising approaches to construction of approximation techniques is based on real-valued relaxation of the given 3-CNF followed by minimizing of the appropriate differentiable loss function, and subsequent rounding of the fractional minimizer obtained. Actually, algorithms developed this way differ by the rounding scheme applied on their final stage. We propose a new rounding scheme based on Bayesian learning. The article shows that the proposed method can be used to determine the security in quantum key distribution systems. In the quantum distribution the Shannon rules is applied and the factorization problem is paramount when decrypting secret keys.

Introduction to quantized LIE groups and algebras

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

Tjin, T.

1992-10-10

In this paper, the authors give a self-contained introduction to the theory of quantum groups according to Drinfeld, highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representation theory. Introductions to Hopf algebras, Poisson structures and deformation quantization are also provided. After defining Poisson Lie groups the authors study their relation to Lie bialgebras and the classical Yang-Baxter equation. Then the authors explain in detail the concept of quantization for them. As an example the quantization of sl[sub 2] is explicitly carried out. Next, the authors show how quantum groups are related to the Yang-Baxtermore » equation and how they can be used to solve it. Using the quantum double construction, the authors explicitly construct the universal R matrix for the quantum sl[sub 2] algebra. In the last section, the authors deduce all finite-dimensional irreducible representations for q a root of unity. The authors also give their tensor product decomposition (fusion rules), which is relevant to conformal field theory.« less

Engineering the quantum anomalous Hall effect in graphene with uniaxial strains

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

Diniz, G. S., E-mail: ginetom@gmail.com; Guassi, M. R.; Qu, F.

2013-12-28

We theoretically investigate the manipulation of the quantum anomalous Hall effect (QAHE) in graphene by means of the uniaxial strain. The values of Chern number and Hall conductance demonstrate that the strained graphene in presence of Rashba spin-orbit coupling and exchange field, for vanishing intrinsic spin-orbit coupling, possesses non-trivial topological phase, which is robust against the direction and modulus of the strain. Besides, we also find that the interplay between Rashba and intrinsic spin-orbit couplings results in a topological phase transition in the strained graphene. Remarkably, as the strain strength is increased beyond approximately 7%, the critical parameters of themore » exchange field for triggering the quantum anomalous Hall phase transition show distinct behaviors—decrease (increase) for strains along zigzag (armchair) direction. Our findings open up a new platform for manipulation of the QAHE by an experimentally accessible strain deformation of the graphene structure, with promising application on novel quantum electronic devices with high efficiency.« less

Solution of elastic-plastic stress analysis problems by the p-version of the finite element method

NASA Technical Reports Server (NTRS)

Szabo, Barna A.; Actis, Ricardo L.; Holzer, Stefan M.

1993-01-01

The solution of small strain elastic-plastic stress analysis problems by the p-version of the finite element method is discussed. The formulation is based on the deformation theory of plasticity and the displacement method. Practical realization of controlling discretization errors for elastic-plastic problems is the main focus. Numerical examples which include comparisons between the deformation and incremental theories of plasticity under tight control of discretization errors are presented.

Quantum histories without contrary inferences

NASA Astrophysics Data System (ADS)

Losada, Marcelo; Laura, Roberto

2014-12-01

In the consistent histories formulation of quantum theory it was shown that it is possible to retrodict contrary properties. We show that this problem do not appear in our formalism of generalized contexts for quantum histories.

REVIEWS OF TOPICAL PROBLEMS: Concept of consciousness in the context of quantum mechanics

NASA Astrophysics Data System (ADS)

Menskii, Mikhail B.

2005-04-01

Conceptual problems of the quantum theory of measurement are considered, which are embodied in well-known paradoxes and in Bell's inequalities. Arguments are advanced in favor of the viewpoint that these problems may hardly be solved without direct inclusion of the observer's consciousness in the theoretical description of a quantum measurement. Discussed in this connection is the so-called many-worlds interpretation of quantum mechanics proposed by Everett, as is the extension of Everett's concept, which consists in the assumption that separating the quantum state components corresponding to alternative measurements is not only associated with the observer's consciousness but is completely identified with it. This approach is shown to open up qualitatively new avenues for the unification of physics and psychology and, more broadly, of the sciences and the humanities. This may lead to an extension of the theory of consciousness and shed light on significant and previously misunderstood phenomena in the sphere of consciousness.

Test-state approach to the quantum search problem

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

Sehrawat, Arun; Nguyen, Le Huy; Graduate School for Integrative Sciences and Engineering, National University of Singapore, Singapore 117597

2011-05-15

The search for 'a quantum needle in a quantum haystack' is a metaphor for the problem of finding out which one of a permissible set of unitary mappings - the oracles - is implemented by a given black box. Grover's algorithm solves this problem with quadratic speedup as compared with the analogous search for 'a classical needle in a classical haystack'. Since the outcome of Grover's algorithm is probabilistic - it gives the correct answer with high probability, not with certainty - the answer requires verification. For this purpose we introduce specific test states, one for each oracle. These testmore » states can also be used to realize 'a classical search for the quantum needle' which is deterministic - it always gives a definite answer after a finite number of steps - and 3.41 times as fast as the purely classical search. Since the test-state search and Grover's algorithm look for the same quantum needle, the average number of oracle queries of the test-state search is the classical benchmark for Grover's algorithm.« less

SU-E-J-108: Solving the Chinese Postman Problem for Effective Contour Deformation

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

Yang, J; Zhang, L; Balter, P

2015-06-15

Purpose: To develop a practical approach for accurate contour deformation when deformable image registration (DIR) is used for atlas-based segmentation or contour propagation in image-guided radiotherapy. Methods: A contour deformation approach was developed on the basis of 3D mesh operations. The 2D contours represented by a series of points in each slice were first converted to a 3D triangular mesh, which was deformed by the deformation vectors resulting from DIR. A set of parallel 2D planes then cut through the deformed 3D mesh, generating unordered points and line segments, which should be reorganized into a set of 2D contour points.more » It was realized that the reorganization problem was equivalent to solving the Chinese Postman Problem (CPP) by traversing a graph built from the unordered points with the least cost. Alternatively, deformation could be applied to a binary mask converted from the original contours. The deformed binary mask was then converted back into contours at the CT slice locations. We performed a qualitative comparison to validate the mesh-based approach against the image-based approach. Results: The DIR could considerably change the 3D mesh, making complicated 2D contour representations after deformation. CPP was able to effectively reorganize the points in 2D planes no matter how complicated the 2D contours were. The mesh-based approach did not require a post-processing of the contour, thus accurately showing the actual deformation in DIR. The mesh-based approach could keep some fine details and resulted in smoother contours than the image-based approach did, especially for the lung structure. Image-based approach appeared to over-process contours and suffered from image resolution limits. The mesh-based approach was integrated into in-house DIR software for use in routine clinic and research. Conclusion: We developed a practical approach for accurate contour deformation. The efficiency of this approach was demonstrated in both clinic and research applications. This work was partially supported by Cancer Prevention & Research Institute of Texas (CPRIT) RP110562.« less

Symmetric quantum fully homomorphic encryption with perfect security

NASA Astrophysics Data System (ADS)

Liang, Min

2013-12-01

Suppose some data have been encrypted, can you compute with the data without decrypting them? This problem has been studied as homomorphic encryption and blind computing. We consider this problem in the context of quantum information processing, and present the definitions of quantum homomorphic encryption (QHE) and quantum fully homomorphic encryption (QFHE). Then, based on quantum one-time pad (QOTP), we construct a symmetric QFHE scheme, where the evaluate algorithm depends on the secret key. This scheme permits any unitary transformation on any -qubit state that has been encrypted. Compared with classical homomorphic encryption, the QFHE scheme has perfect security. Finally, we also construct a QOTP-based symmetric QHE scheme, where the evaluate algorithm is independent of the secret key.

Nonlinear dynamics and quantum entanglement in optomechanical systems.

PubMed

Wang, Guanglei; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso

2014-03-21

To search for and exploit quantum manifestations of classical nonlinear dynamics is one of the most fundamental problems in physics. Using optomechanical systems as a paradigm, we address this problem from the perspective of quantum entanglement. We uncover strong fingerprints in the quantum entanglement of two common types of classical nonlinear dynamical behaviors: periodic oscillations and quasiperiodic motion. There is a transition from the former to the latter as an experimentally adjustable parameter is changed through a critical value. Accompanying this process, except for a small region about the critical value, the degree of quantum entanglement shows a trend of continuous increase. The time evolution of the entanglement measure, e.g., logarithmic negativity, exhibits a strong dependence on the nature of classical nonlinear dynamics, constituting its signature.

Quantum Optics in Phase Space

NASA Astrophysics Data System (ADS)

Schleich, Wolfgang P.

2001-04-01

Quantum Optics in Phase Space provides a concise introduction to the rapidly moving field of quantum optics from the point of view of phase space. Modern in style and didactically skillful, Quantum Optics in Phase Space prepares students for their own research by presenting detailed derivations, many illustrations and a large set of workable problems at the end of each chapter. Often, the theoretical treatments are accompanied by the corresponding experiments. An exhaustive list of references provides a guide to the literature. Quantum Optics in Phase Space also serves advanced researchers as a comprehensive reference book. Starting with an extensive review of the experiments that define quantum optics and a brief summary of the foundations of quantum mechanics the author Wolfgang P. Schleich illustrates the properties of quantum states with the help of the Wigner phase space distribution function. His description of waves ala WKB connects semi-classical phase space with the Berry phase. These semi-classical techniques provide deeper insight into the timely topics of wave packet dynamics, fractional revivals and the Talbot effect. Whereas the first half of the book deals with mechanical oscillators such as ions in a trap or atoms in a standing wave the second half addresses problems where the quantization of the radiation field is of importance. Such topics extensively discussed include optical interferometry, the atom-field interaction, quantum state preparation and measurement, entanglement, decoherence, the one-atom maser and atom optics in quantized light fields. Quantum Optics in Phase Space presents the subject of quantum optics as transparently as possible. Giving wide-ranging references, it enables students to study and solve problems with modern scientific literature. The result is a remarkably concise yet comprehensive and accessible text- and reference book - an inspiring source of information and insight for students, teachers and researchers alike.

Renormalized vacuum polarization of rotating black holes

NASA Astrophysics Data System (ADS)

Ferreira, Hugo R. C.

2015-04-01

Quantum field theory on rotating black hole spacetimes is plagued with technical difficulties. Here, we describe a general method to renormalize and compute the vacuum polarization of a quantum field in the Hartle-Hawking state on rotating black holes. We exemplify the technique with a massive scalar field on the warped AdS3 black hole solution to topologically massive gravity, a deformation of (2 + 1)-dimensional Einstein gravity. We use a "quasi-Euclidean" technique, which generalizes the Euclidean techniques used for static spacetimes, and we subtract the divergences by matching to a sum over mode solutions on Minkowski spacetime. This allows us, for the first time, to have a general method to compute the renormalized vacuum polarization, for a given quantum state, on a rotating black hole, such as the physically relevant case of the Kerr black hole in four dimensions.

Electronic Structure and Properties of Deformed Carbon Nanotubes

NASA Technical Reports Server (NTRS)

Yang, Liu; Arnold, Jim (Technical Monitor)

2001-01-01

A theoretical framework based on Huckel tight-binding model has been formulated to analyze the electronic structure of carbon nanotubes under uniform deformation. The model successfully quantifies the dispersion relation, density of states and bandgap change of nanotubes under uniform stretching, compression, torsion and bending. Our analysis shows that the shifting of the Fermi point away from the Brillouin zone vertices is the key reason for these changes. As a result of this shifting, the electronic structure of deformed carbon nanotubes varies dramatically depending on their chirality and deformation mode. Treating the Fermi point as a function of strain and tube chirality, the analytical solution preserves the concise form of undeformed carbon nanotubes. It predicts the shifting, merging and splitting of the Van Hove singularities in the density of states and the zigzag pattern of bandgap change under strains. Four orbital tight-binding simulations of carbon nanotubes under uniform stretching, compression, torsion and bending have been performed to verify the analytical solution. Extension to more complex systems are being performed to relate this analytical solution to the spectroscopic characterization, device performance and proposed quantum structures induced by the deformation. The limitations of this model will also be discussed.

Quantum neurophysics: From non-living matter to quantum neurobiology and psychopathology.

PubMed

Tarlacı, Sultan; Pregnolato, Massimo

2016-05-01

The concepts of quantum brain, quantum mind and quantum consciousness have been increasingly gaining currency in recent years, both in scientific papers and in the popular press. In fact, the concept of the quantum brain is a general framework. Included in it are basically four main sub-headings. These are often incorrectly used interchangeably. The first of these and the one which started the quantum mind/consciousness debate was the place of consciousness in the problem of measurement in quantum mechanics. Debate on the problem of quantum measurement and about the place of the conscious observer has lasted almost a century. One solution to this problem is that the participation of a conscious observer in the experiment will radically change our understanding of the universe and our relationship with the outside world. The second topic is that of quantum biology. This topic has become a popular field of research, especially in the last decade. It concerns whether or not the rules of quantum physics operate in biological structures. It has been shown in the latest research on photosynthesis, the sense of smell and magnetic direction finding in animals that the laws of quantum physics may operate in warm-wet-noisy biological structures. The third sub-heading is quantum neurobiology. This topic has not yet gained wide acceptance and is still in its early stages. Its primary purpose is directed to understand whether the laws of quantum physics are effective in the biology of the nervous system or not. A further step in brain neurobiology, toward the understanding of consciousness formation, is the research of quantum laws effects upon neural network functions. The fourth and final topic is quantum psychopathology. This topic takes its basis and its support from quantum neurobiology. It comes from the idea that if quantum physics is involved in the normal working of the brain, diseased conditions of the brain such as depression, anxiety, dementia, schizophrenia and hallucinations can be explained by quantum physical pathology. In this article, these topics will be reviewed in a general framework, and for the first time a general classification will be made for the quantum brain theory. Copyright © 2016 Elsevier B.V. All rights reserved.

Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators

DOE PAGES

Claassen, Martin; Lee, Ching-Hua; Thomale, Ronny; ...

2015-06-11

We develop a first quantization description of fractional Chern insulators that is the dual of the conventional fractional quantum Hall (FQH) problem, with the roles of position and momentum interchanged. In this picture, FQH states are described by anisotropic FQH liquids forming in momentum-space Landau levels in a fluctuating magnetic field. The fundamental quantum geometry of the problem emerges from the interplay of single-body and interaction metrics, both of which act as momentum-space duals of the geometrical picture of the anisotropic FQH effect. We then present a novel broad class of ideal Chern insulator lattice models that act as dualsmore » of the isotropic FQH effect. The interacting problem is well-captured by Haldane pseudopotentials and affords a detailed microscopic understanding of the interplay of interactions and non-trivial quantum geometry.« less

Infinite variance in fermion quantum Monte Carlo calculations.

PubMed

Shi, Hao; Zhang, Shiwei

2016-03-01

For important classes of many-fermion problems, quantum Monte Carlo (QMC) methods allow exact calculations of ground-state and finite-temperature properties without the sign problem. The list spans condensed matter, nuclear physics, and high-energy physics, including the half-filled repulsive Hubbard model, the spin-balanced atomic Fermi gas, and lattice quantum chromodynamics calculations at zero density with Wilson Fermions, and is growing rapidly as a number of problems have been discovered recently to be free of the sign problem. In these situations, QMC calculations are relied on to provide definitive answers. Their results are instrumental to our ability to understand and compute properties in fundamental models important to multiple subareas in quantum physics. It is shown, however, that the most commonly employed algorithms in such situations have an infinite variance problem. A diverging variance causes the estimated Monte Carlo statistical error bar to be incorrect, which can render the results of the calculation unreliable or meaningless. We discuss how to identify the infinite variance problem. An approach is then proposed to solve the problem. The solution does not require major modifications to standard algorithms, adding a "bridge link" to the imaginary-time path integral. The general idea is applicable to a variety of situations where the infinite variance problem may be present. Illustrative results are presented for the ground state of the Hubbard model at half-filling.

Completing the Physical Representation of Quantum Algorithms Provides a Quantitative Explanation of Their Computational Speedup

NASA Astrophysics Data System (ADS)

Castagnoli, Giuseppe

2018-03-01

The usual representation of quantum algorithms, limited to the process of solving the problem, is physically incomplete. We complete it in three steps: (i) extending the representation to the process of setting the problem, (ii) relativizing the extended representation to the problem solver to whom the problem setting must be concealed, and (iii) symmetrizing the relativized representation for time reversal to represent the reversibility of the underlying physical process. The third steps projects the input state of the representation, where the problem solver is completely ignorant of the setting and thus the solution of the problem, on one where she knows half solution (half of the information specifying it when the solution is an unstructured bit string). Completing the physical representation shows that the number of computation steps (oracle queries) required to solve any oracle problem in an optimal quantum way should be that of a classical algorithm endowed with the advanced knowledge of half solution.

Quantum Mechanics From the Cradle?

ERIC Educational Resources Information Center

Martin, John L.

1974-01-01

States that the major problem in learning quantum mechanics is often the student's ignorance of classical mechanics and that one conceptual hurdle in quantum mechanics is its statistical nature, in contrast to the determinism of classical mechanics. (MLH)

Statistics of resonances for a class of billiards on the Poincaré half-plane

NASA Astrophysics Data System (ADS)

Howard, P. J.; Mota-Furtado, F.; O'Mahony, P. F.; Uski, V.

2005-12-01

The lower boundary of Artin's billiard on the Poincaré half-plane is continuously deformed to generate a class of billiards with classical dynamics varying from fully integrable to completely chaotic. The quantum scattering problem in these open billiards is described and the statistics of both real and imaginary parts of the resonant momenta are investigated. The evolution of the resonance positions is followed as the boundary is varied which leads to large changes in their distribution. The transition to arithmetic chaos in Artin's billiard, which is responsible for the Poissonian level-spacing statistics of the bound states in the continuum (cusp forms) at the same time as the formation of a set of resonances all with width \\frac{1}{4} and real parts determined by the zeros of Riemann's zeta function, is closely examined. Regimes are found which obey the universal predictions of random matrix theory (RMT) as well as exhibiting non-universal long-range correlations. The Brody parameter is used to describe the transitions between different regimes.

Hemi-wedge osteotomy in the management of large angular deformities around the knee joint.

PubMed

El-Alfy, Barakat Sayed

2016-08-01

Angular deformity around the knee joint is a common orthopedic problem. Many options are available for the management of such problem with varying degrees of success and failure. The aim of the present study was to assess the results of hemi-wedge osteotomy in the management of big angular deformities about the knee joint. Twenty-eight limbs in 21 patients with large angular deformities around the knee joint were treated by the hemi-wedge osteotomy technique. The ages ranged from 12 to 43 years with an average of 19.8 years. The deformity ranged from 20° to 40° with a mean of 30.39° ± 5.99°. The deformities were genu varum in 12 cases and genu valgum in 9 cases. Seven cases had bilateral deformities. Small wedge was removed from the convex side of the bone and put in the gap created in the other side after correction of the deformity. At the final follow-up, the deformity was corrected in all cases except two. Full range of knee movement was regained in all cases. The complications included superficial wound infection in two cases, overcorrection in one case, pain along the lateral aspect of the knee in one case and recurrence of the deformity in one case. No cases were complicated by nerve injury or vascular injury. Hemi-wedge osteotomy is a good method for treatment of deformities around the knee joint. It can correct large angular deformities without major complications.

A Non-Intuitionist's Approach To The Interpretation Problem Of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Grelland, Hans Herlof

2005-02-01

A philosophy of physics called "linguistic empiricism" is presented and applied to the interpretation problem of quantum mechanics. This philosophical position is based on the works of Jacques Derrida. The main propositions are (i) that meaning, included the meaning attached to observations, are language-dependent and (ii) that mathematics in physics should be considered as a proper language, not necessary translatable to a more basic language of intuition and immediate experience. This has fundamental implications for quantum mechanics, which is a mathematically coherent and consistent theory; its interpretation problem is associated with its lack of physical images expressible in ordinary language.

Global bending quantum number and the absence of monodromy in the HCN{r_reversible}CNH molecule

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

Efstathiou, K.; Sadovskii, D.A.; Joyeux, M.

We introduce and analyze a model system based on a deformation of a spherical pendulum that can be used to reproduce large amplitude bending vibrations of flexible triatomic molecules with two stable linear equilibria. On the basis of our model and the recent vibrational potential [ J. Chem. Phys. 115, 3706 (2001) ], we analyze the HCN/CNH isomerizing molecule. We find that HCN/CNH has no monodromy and introduce the second global bending quantum number for this system at all energies where the potential is expected to work. We also show that LiNC/LiCN is a qualitatively different system with monodromy.

The IINS/quantum chemical studies of 17α- and 21-hydroxy-derivatives of progesterone

NASA Astrophysics Data System (ADS)

Szyczewski, A.; Hołderna-Natkaniec, K.; Natkaniec, I.

2003-05-01

The inelastic incoherent neutron scattering and quantum chemical studies have been performed on 17 and 21 hydroxy progesterone and the assignment of internal modes have been proposed in the range up to 700 cm -1. The lattice branch of PDS reveals modes which could be attributed to torsions of rings A and D (cyclohexane and cyclopentane) of the pregnane skeleton. An assignment of the torsional vibrations of methyl groups in the range 150-300 cm -1 and the deformation and out-of plane vibrations of CCOH groups has been proposed. An analysis of the effect of hydrogen bonds on PDS spectra has been performed.

Hidden symmetry in the confined hydrogen atom problem

NASA Astrophysics Data System (ADS)

Pupyshev, Vladimir I.; Scherbinin, Andrei V.

2002-07-01

The classical counterpart of the well-known quantum mechanical model of a spherically confined hydrogen atom is examined in terms of the Lenz vector, a dynamic variable featuring the conventional Kepler problem. It is shown that a conditional conservation law associated with the Lenz vector is true, in fair agreement with the corresponding quantum problem previously found to exhibit a hidden symmetry as well.

The Problem of Representation and Experience in Quantum Mechanics

NASA Astrophysics Data System (ADS)

Ronde, Christian De

2014-03-01

In this paper we discuss the problem of representation and experience in quantum mechanics. We analyze the importance of metaphysics in physical thought and its relation to empiricism and analytic philosophy. We argue against both instrumentalism and scientific realism and claim that both perspectives tend to bypass the problem of representation and justify a "common sense" type experience. Finally, we present our expressionist conception of physics.

Practical solution of plastic deformation problems in elastic-plastic range

NASA Technical Reports Server (NTRS)

Mendelson, A; Manson, S

1957-01-01

A practical method for solving plastic deformation problems in the elastic-plastic range is presented. The method is one of successive approximations and is illustrated by four examples which include a flat plate with temperature distribution across the width, a thin shell with axial temperature distribution, a solid cylinder with radial temperature distribution, and a rotating disk with radial temperature distribution.

Workshop on Advancing Experimental Rock Deformation Research: Scientific and Technical Needs

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

Tullis, Terry E.

A workshop for the experimental rock deformation community was held in Boston on August 16-19, 2012, following some similar but smaller preliminary meetings. It was sponsored primarily by the NSF, with additional support from the DOE, the SCEC, and in-kind support by the USGS. A white paper summarizing the active discussions at the workshop and the outcomes is available (https://brownbox.brown.edu/download.php?hash=0b854d11). Those attending included practitioners of experimental rock deformation, i.e., those who conduct laboratory experiments, as well as users of the data provided by practitioners, namely field geologists, seismologists, geodynamicists, earthquake modelers, and scientists from the oil and gas industry. Amore » considerable fraction of those attending were early-career scientists. The discussion initially focused on identifying the most important unsolved scientific problems in all of the research areas represented by the users that experiments would help solve. This initial session was followed by wide-ranging discussions of the most critical problems faced by practitioners, particularly by early-career scientists. The discussion also focused on the need for designing and building the next generation of experimental rock deformation equipment required to meet the identified scientific challenges. The workshop participants concluded that creation of an experimental rock deformation community organization is needed to address many of the scientific, technical, and demographic problems faced by this community. A decision was made to hold an organizational meeting of this new organization in San Francisco on December 1-2, 2012, just prior to the Fall Meeting of the AGU. The community has decided to name this new organization “Deformation Experimentation at the Frontier Of Rock and Mineral research” or DEFORM. As of May 1, 2013, 64 institutions have asked to be members of DEFORM.« less

Entropy-driven phase transitions of entanglement

NASA Astrophysics Data System (ADS)

Facchi, Paolo; Florio, Giuseppe; Parisi, Giorgio; Pascazio, Saverio; Yuasa, Kazuya

2013-05-01

We study the behavior of bipartite entanglement at fixed von Neumann entropy. We look at the distribution of the entanglement spectrum, that is, the eigenvalues of the reduced density matrix of a quantum system in a pure state. We report the presence of two continuous phase transitions, characterized by different entanglement spectra, which are deformations of classical eigenvalue distributions.

Finding Maximum Cliques on the D-Wave Quantum Annealer

DOE PAGES

Chapuis, Guillaume; Djidjev, Hristo; Hahn, Georg; ...

2018-05-03

This work assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. Because the size of the largest graphs DW can directly solve is quite small (usually around 45 vertices), we also consider decomposition algorithms intended for larger graphs and analyze their performance. For smaller graphs that fit DW, we provide formulations of the maximum clique problem as a quadratic unconstrained binary optimization (QUBO) problem, which is one of the two input types (together with the Ising model) acceptable by the machine, andmore » compare several quantum implementations to current classical algorithms such as simulated annealing, Gurobi, and third-party clique finding heuristics. We further estimate the contributions of the quantum phase of the quantum annealer and the classical post-processing phase typically used to enhance each solution returned by DW. We demonstrate that on random graphs that fit DW, no quantum speedup can be observed compared with the classical algorithms. On the other hand, for instances specifically designed to fit well the DW qubit interconnection network, we observe substantial speed-ups in computing time over classical approaches.« less

Finding Maximum Cliques on the D-Wave Quantum Annealer

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

Chapuis, Guillaume; Djidjev, Hristo; Hahn, Georg

This work assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. Because the size of the largest graphs DW can directly solve is quite small (usually around 45 vertices), we also consider decomposition algorithms intended for larger graphs and analyze their performance. For smaller graphs that fit DW, we provide formulations of the maximum clique problem as a quadratic unconstrained binary optimization (QUBO) problem, which is one of the two input types (together with the Ising model) acceptable by the machine, andmore » compare several quantum implementations to current classical algorithms such as simulated annealing, Gurobi, and third-party clique finding heuristics. We further estimate the contributions of the quantum phase of the quantum annealer and the classical post-processing phase typically used to enhance each solution returned by DW. We demonstrate that on random graphs that fit DW, no quantum speedup can be observed compared with the classical algorithms. On the other hand, for instances specifically designed to fit well the DW qubit interconnection network, we observe substantial speed-ups in computing time over classical approaches.« less

Quantum annealing versus classical machine learning applied to a simplified computational biology problem

PubMed Central

Li, Richard Y.; Di Felice, Rosa; Rohs, Remo; Lidar, Daniel A.

2018-01-01

Transcription factors regulate gene expression, but how these proteins recognize and specifically bind to their DNA targets is still debated. Machine learning models are effective means to reveal interaction mechanisms. Here we studied the ability of a quantum machine learning approach to predict binding specificity. Using simplified datasets of a small number of DNA sequences derived from actual binding affinity experiments, we trained a commercially available quantum annealer to classify and rank transcription factor binding. The results were compared to state-of-the-art classical approaches for the same simplified datasets, including simulated annealing, simulated quantum annealing, multiple linear regression, LASSO, and extreme gradient boosting. Despite technological limitations, we find a slight advantage in classification performance and nearly equal ranking performance using the quantum annealer for these fairly small training data sets. Thus, we propose that quantum annealing might be an effective method to implement machine learning for certain computational biology problems. PMID:29652405

Quantum annealing with all-to-all connected nonlinear oscillators

PubMed Central

Puri, Shruti; Andersen, Christian Kraglund; Grimsmo, Arne L.; Blais, Alexandre

2017-01-01

Quantum annealing aims at solving combinatorial optimization problems mapped to Ising interactions between quantum spins. Here, with the objective of developing a noise-resilient annealer, we propose a paradigm for quantum annealing with a scalable network of two-photon-driven Kerr-nonlinear resonators. Each resonator encodes an Ising spin in a robust degenerate subspace formed by two coherent states of opposite phases. A fully connected optimization problem is mapped to local fields driving the resonators, which are connected with only local four-body interactions. We describe an adiabatic annealing protocol in this system and analyse its performance in the presence of photon loss. Numerical simulations indicate substantial resilience to this noise channel, leading to a high success probability for quantum annealing. Finally, we propose a realistic circuit QED implementation of this promising platform for implementing a large-scale quantum Ising machine. PMID:28593952

Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations

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

Stottmeister, Alexander, E-mail: alexander.stottmeister@gravity.fau.de; Thiemann, Thomas, E-mail: thomas.thiemann@gravity.fau.de

2016-06-15

This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g., spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems,more » which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article and its companion affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).« less

Quantum key distribution session with 16-dimensional photonic states.

PubMed

Etcheverry, S; Cañas, G; Gómez, E S; Nogueira, W A T; Saavedra, C; Xavier, G B; Lima, G

2013-01-01

The secure transfer of information is an important problem in modern telecommunications. Quantum key distribution (QKD) provides a solution to this problem by using individual quantum systems to generate correlated bits between remote parties, that can be used to extract a secret key. QKD with D-dimensional quantum channels provides security advantages that grow with increasing D. However, the vast majority of QKD implementations has been restricted to two dimensions. Here we demonstrate the feasibility of using higher dimensions for real-world quantum cryptography by performing, for the first time, a fully automated QKD session based on the BB84 protocol with 16-dimensional quantum states. Information is encoded in the single-photon transverse momentum and the required states are dynamically generated with programmable spatial light modulators. Our setup paves the way for future developments in the field of experimental high-dimensional QKD.

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.

An adaptive quantum mechanics/molecular mechanics method for the infrared spectrum of water: incorporation of the quantum effect between solute and solvent.

PubMed

Watanabe, Hiroshi C; Banno, Misa; Sakurai, Minoru

2016-03-14

Quantum effects in solute-solvent interactions, such as the many-body effect and the dipole-induced dipole, are known to be critical factors influencing the infrared spectra of species in the liquid phase. For accurate spectrum evaluation, the surrounding solvent molecules, in addition to the solute of interest, should be treated using a quantum mechanical method. However, conventional quantum mechanics/molecular mechanics (QM/MM) methods cannot handle free QM solvent molecules during molecular dynamics (MD) simulation because of the diffusion problem. To deal with this problem, we have previously proposed an adaptive QM/MM "size-consistent multipartitioning (SCMP) method". In the present study, as the first application of the SCMP method, we demonstrate the reproduction of the infrared spectrum of liquid-phase water, and evaluate the quantum effect in comparison with conventional QM/MM simulations.

Quantum key distribution session with 16-dimensional photonic states

NASA Astrophysics Data System (ADS)

Etcheverry, S.; Cañas, G.; Gómez, E. S.; Nogueira, W. A. T.; Saavedra, C.; Xavier, G. B.; Lima, G.

2013-07-01

The secure transfer of information is an important problem in modern telecommunications. Quantum key distribution (QKD) provides a solution to this problem by using individual quantum systems to generate correlated bits between remote parties, that can be used to extract a secret key. QKD with D-dimensional quantum channels provides security advantages that grow with increasing D. However, the vast majority of QKD implementations has been restricted to two dimensions. Here we demonstrate the feasibility of using higher dimensions for real-world quantum cryptography by performing, for the first time, a fully automated QKD session based on the BB84 protocol with 16-dimensional quantum states. Information is encoded in the single-photon transverse momentum and the required states are dynamically generated with programmable spatial light modulators. Our setup paves the way for future developments in the field of experimental high-dimensional QKD.

Experimental loss-tolerant quantum coin flipping

PubMed Central

Berlín, Guido; Brassard, Gilles; Bussières, Félix; Godbout, Nicolas; Slater, Joshua A.; Tittel, Wolfgang

2011-01-01

Coin flipping is a cryptographic primitive in which two distrustful parties wish to generate a random bit to choose between two alternatives. This task is impossible to realize when it relies solely on the asynchronous exchange of classical bits: one dishonest player has complete control over the final outcome. It is only when coin flipping is supplemented with quantum communication that this problem can be alleviated, although partial bias remains. Unfortunately, practical systems are subject to loss of quantum data, which allows a cheater to force a bias that is complete or arbitrarily close to complete in all previous protocols and implementations. Here we report on the first experimental demonstration of a quantum coin-flipping protocol for which loss cannot be exploited to cheat better. By eliminating the problem of loss, which is unavoidable in any realistic setting, quantum coin flipping takes a significant step towards real-world applications of quantum communication. PMID:22127057

Quantum key distribution session with 16-dimensional photonic states

PubMed Central

Etcheverry, S.; Cañas, G.; Gómez, E. S.; Nogueira, W. A. T.; Saavedra, C.; Xavier, G. B.; Lima, G.

2013-01-01

The secure transfer of information is an important problem in modern telecommunications. Quantum key distribution (QKD) provides a solution to this problem by using individual quantum systems to generate correlated bits between remote parties, that can be used to extract a secret key. QKD with D-dimensional quantum channels provides security advantages that grow with increasing D. However, the vast majority of QKD implementations has been restricted to two dimensions. Here we demonstrate the feasibility of using higher dimensions for real-world quantum cryptography by performing, for the first time, a fully automated QKD session based on the BB84 protocol with 16-dimensional quantum states. Information is encoded in the single-photon transverse momentum and the required states are dynamically generated with programmable spatial light modulators. Our setup paves the way for future developments in the field of experimental high-dimensional QKD. PMID:23897033

Hybrid annealing: Coupling a quantum simulator to a classical computer

NASA Astrophysics Data System (ADS)

Graß, Tobias; Lewenstein, Maciej

2017-05-01

Finding the global minimum in a rugged potential landscape is a computationally hard task, often equivalent to relevant optimization problems. Annealing strategies, either classical or quantum, explore the configuration space by evolving the system under the influence of thermal or quantum fluctuations. The thermal annealing dynamics can rapidly freeze the system into a low-energy configuration, and it can be simulated well on a classical computer, but it easily gets stuck in local minima. Quantum annealing, on the other hand, can be guaranteed to find the true ground state and can be implemented in modern quantum simulators; however, quantum adiabatic schemes become prohibitively slow in the presence of quasidegeneracies. Here, we propose a strategy which combines ideas from simulated annealing and quantum annealing. In such a hybrid algorithm, the outcome of a quantum simulator is processed on a classical device. While the quantum simulator explores the configuration space by repeatedly applying quantum fluctuations and performing projective measurements, the classical computer evaluates each configuration and enforces a lowering of the energy. We have simulated this algorithm for small instances of the random energy model, showing that it potentially outperforms both simulated thermal annealing and adiabatic quantum annealing. It becomes most efficient for problems involving many quasidegenerate ground states.

PLATFORM DEFORMATION PHASE CORRECTION FOR THE AMiBA-13 COPLANAR INTERFEROMETER

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

Liao, Yu-Wei; Lin, Kai-Yang; Huang, Yau-De

2013-05-20

We present a new way to solve the platform deformation problem of coplanar interferometers. The platform of a coplanar interferometer can be deformed due to driving forces and gravity. A deformed platform will induce extra components into the geometric delay of each baseline and change the phases of observed visibilities. The reconstructed images will also be diluted due to the errors of the phases. The platform deformations of The Yuan-Tseh Lee Array for Microwave Background Anisotropy (AMiBA) were modeled based on photogrammetry data with about 20 mount pointing positions. We then used the differential optical pointing error between two opticalmore » telescopes to fit the model parameters in the entire horizontal coordinate space. With the platform deformation model, we can predict the errors of the geometric phase delays due to platform deformation with a given azimuth and elevation of the targets and calibrators. After correcting the phases of the radio point sources in the AMiBA interferometric data, we recover 50%-70% flux loss due to phase errors. This allows us to restore more than 90% of a source flux. The method outlined in this work is not only applicable to the correction of deformation for other coplanar telescopes but also to single-dish telescopes with deformation problems. This work also forms the basis of the upcoming science results of AMiBA-13.« less

Quantum machine learning: a classical perspective

NASA Astrophysics Data System (ADS)

Ciliberto, Carlo; Herbster, Mark; Ialongo, Alessandro Davide; Pontil, Massimiliano; Rocchetto, Andrea; Severini, Simone; Wossnig, Leonard

2018-01-01

Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning (ML) techniques to impressive results in regression, classification, data generation and reinforcement learning tasks. Despite these successes, the proximity to the physical limits of chip fabrication alongside the increasing size of datasets is motivating a growing number of researchers to explore the possibility of harnessing the power of quantum computation to speed up classical ML algorithms. Here we review the literature in quantum ML and discuss perspectives for a mixed readership of classical ML and quantum computation experts. Particular emphasis will be placed on clarifying the limitations of quantum algorithms, how they compare with their best classical counterparts and why quantum resources are expected to provide advantages for learning problems. Learning in the presence of noise and certain computationally hard problems in ML are identified as promising directions for the field. Practical questions, such as how to upload classical data into quantum form, will also be addressed.

Quantum machine learning: a classical perspective

PubMed Central

Ciliberto, Carlo; Herbster, Mark; Ialongo, Alessandro Davide; Pontil, Massimiliano; Severini, Simone; Wossnig, Leonard

2018-01-01

Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning (ML) techniques to impressive results in regression, classification, data generation and reinforcement learning tasks. Despite these successes, the proximity to the physical limits of chip fabrication alongside the increasing size of datasets is motivating a growing number of researchers to explore the possibility of harnessing the power of quantum computation to speed up classical ML algorithms. Here we review the literature in quantum ML and discuss perspectives for a mixed readership of classical ML and quantum computation experts. Particular emphasis will be placed on clarifying the limitations of quantum algorithms, how they compare with their best classical counterparts and why quantum resources are expected to provide advantages for learning problems. Learning in the presence of noise and certain computationally hard problems in ML are identified as promising directions for the field. Practical questions, such as how to upload classical data into quantum form, will also be addressed. PMID:29434508

Quantum machine learning: a classical perspective.

PubMed

Ciliberto, Carlo; Herbster, Mark; Ialongo, Alessandro Davide; Pontil, Massimiliano; Rocchetto, Andrea; Severini, Simone; Wossnig, Leonard

2018-01-01

Recently, increased computational power and data availability, as well as algorithmic advances, have led machine learning (ML) techniques to impressive results in regression, classification, data generation and reinforcement learning tasks. Despite these successes, the proximity to the physical limits of chip fabrication alongside the increasing size of datasets is motivating a growing number of researchers to explore the possibility of harnessing the power of quantum computation to speed up classical ML algorithms. Here we review the literature in quantum ML and discuss perspectives for a mixed readership of classical ML and quantum computation experts. Particular emphasis will be placed on clarifying the limitations of quantum algorithms, how they compare with their best classical counterparts and why quantum resources are expected to provide advantages for learning problems. Learning in the presence of noise and certain computationally hard problems in ML are identified as promising directions for the field. Practical questions, such as how to upload classical data into quantum form, will also be addressed.

Physical theories, eternal inflation, and the quantum universe

NASA Astrophysics Data System (ADS)

Nomura, Yasunori

2011-11-01

Infinities in eternal inflation have long been plaguing cosmology, making any predictions highly sensitive to how they are regulated. The problem exists already at the level of semi-classical general relativity, and has a priori nothing to do with quantum gravity. On the other hand, we know that certain problems in semi-classical gravity, for example physics of black holes and their evaporation, have led to understanding of surprising, quantum natures of spacetime and gravity, such as the holographic principle and horizon complementarity. In this paper, we present a framework in which well-defined predictions are obtained in an eternally inflating multiverse, based on the principles of quantum mechanics. We propose that the entire multiverse is described purely from the viewpoint of a single "observer," who describes the world as a quantum state defined on his/her past light cones bounded by the (stretched) apparent horizons. We find that quantum mechanics plays an essential role in regulating infinities. The framework is "gauge invariant," i.e. predictions do not depend on how spacetime is parametrized, as it should be in a theory of quantum gravity. Our framework provides a fully unified treatment of quantum measurement processes and the multiverse. We conclude that the eternally inflating multiverse and many worlds in quantum mechanics are the same. Other important implications include: global spacetime can be viewed as a derived concept; the multiverse is a transient phenomenon during the world relaxing into a supersymmetric Minkowski state. We also present a model of "initial conditions" for the multiverse. By extrapolating our framework to the extreme, we arrive at a picture that the entire multiverse is a fluctuation in the stationary, fractal "mega-multiverse," in which an infinite sequence of multiverse productions occurs. The framework discussed here does not suffer from problems/paradoxes plaguing other measures proposed earlier, such as the youngness paradox and the Boltzmann brain problem.

Geometry of quantum state manifolds generated by the Lie algebra operators

NASA Astrophysics Data System (ADS)

Kuzmak, A. R.

2018-03-01

The Fubini-Study metric of quantum state manifold generated by the operators which satisfy the Heisenberg Lie algebra is calculated. The similar problem is studied for the manifold generated by the so(3) Lie algebra operators. Using these results, we calculate the Fubini-Study metrics of state manifolds generated by the position and momentum operators. Also the metrics of quantum state manifolds generated by some spin systems are obtained. Finally, we generalize this problem for operators of an arbitrary Lie algebra.

Quantum annealing of the traveling-salesman problem.

PubMed

Martonák, Roman; Santoro, Giuseppe E; Tosatti, Erio

2004-11-01

We propose a path-integral Monte Carlo quantum annealing scheme for the symmetric traveling-salesman problem, based on a highly constrained Ising-like representation, and we compare its performance against standard thermal simulated annealing. The Monte Carlo moves implemented are standard, and consist in restructuring a tour by exchanging two links (two-opt moves). The quantum annealing scheme, even with a drastically simple form of kinetic energy, appears definitely superior to the classical one, when tested on a 1002-city instance of the standard TSPLIB.

Adapting the traveling salesman problem to an adiabatic quantum computer

NASA Astrophysics Data System (ADS)

Warren, Richard H.

2013-04-01

We show how to guide a quantum computer to select an optimal tour for the traveling salesman. This is significant because it opens a rapid solution method for the wide range of applications of the traveling salesman problem, which include vehicle routing, job sequencing and data clustering.

The Soccer-Ball Problem

NASA Astrophysics Data System (ADS)

Hossenfelder, Sabine

2014-07-01

The idea that Lorentz-symmetry in momentum space could be modified but still remain observer-independent has received quite some attention in the recent years. This modified Lorentz-symmetry, which has been argued to arise in Loop Quantum Gravity, is being used as a phenomenological model to test possibly observable effects of quantum gravity. The most pressing problem in these models is the treatment of multi-particle states, known as the 'soccer-ball problem'. This article briefly reviews the problem and the status of existing solution attempts.

Integrated Approach to the Dynamics and Control of Maneuvering Flexible Aircraft

NASA Technical Reports Server (NTRS)

Waszak, Martin R. (Technical Monitor); Meirovitch, Leonard; Tuzcu, Ilhan

2003-01-01

This work uses a fundamental approach to the problem of simulating the flight of flexible aircraft. To this end, it integrates into a single formulation the pertinent disciplines, namely, analytical dynamics, structural dynamics, aerodynamics, and controls. It considers both the rigid body motions of the aircraft, three translations (forward motion, sideslip and plunge) and three rotations (roll, pitch and yaw), and the elastic deformations of every point of the aircraft, as well as the aerodynamic, propulsion, gravity and control forces. The equations of motion are expressed in a form ideally suited for computer processing. A perturbation approach yields a flight dynamics problem for the motions of a quasi-rigid aircraft and an 'extended aeroelasticity' problem for the elastic deformations and perturbations in the rigid body motions, with the solution of the first problem entering as an input into the second problem. The control forces for the flight dynamics problem are obtained by an 'inverse' process and the feedback controls for the extended aeroservoelasticity problem are determined by the LQG theory. A numerical example presents time simulations of rigid body perturbations and elastic deformations about 1) a steady level flight and 2) a level steady turn maneuver.

Tulip deformity with Cera atrial septal defect devices: a report of 3 cases.

PubMed

Kohli, Vikas

2015-02-01

Device closure of secundum atrial septal defect (ASD) is the treatment of choice when anatomy is favourable. Amplatzer device has remained the gold standard for closure of ASD. Cobra deformity is a well-reported problem with devices. Recently, Tulip deformity has been reported in a single case. We report a series of cases where we noted Tulip deformity along with inability to retract the device in the sheath in Cera Lifetech devices. This resulted in prolongation of procedure, excessive fluoroscopic exposure and additional interventional procedures not usually anticipated in ASD device closure. We believe that the problem is due to the stiffness of the device resulting in its inability to be retracted into the sheath. We also report a unique way of retrieving the device.

Quantum information, cognition, and music.

PubMed

Dalla Chiara, Maria L; Giuntini, Roberto; Leporini, Roberto; Negri, Eleonora; Sergioli, Giuseppe

2015-01-01

Parallelism represents an essential aspect of human mind/brain activities. One can recognize some common features between psychological parallelism and the characteristic parallel structures that arise in quantum theory and in quantum computation. The article is devoted to a discussion of the following questions: a comparison between classical probabilistic Turing machines and quantum Turing machines.possible applications of the quantum computational semantics to cognitive problems.parallelism in music.

Quantum information, cognition, and music

PubMed Central

Dalla Chiara, Maria L.; Giuntini, Roberto; Leporini, Roberto; Negri, Eleonora; Sergioli, Giuseppe

2015-01-01

Parallelism represents an essential aspect of human mind/brain activities. One can recognize some common features between psychological parallelism and the characteristic parallel structures that arise in quantum theory and in quantum computation. The article is devoted to a discussion of the following questions: a comparison between classical probabilistic Turing machines and quantum Turing machines.possible applications of the quantum computational semantics to cognitive problems.parallelism in music. PMID:26539139

Quantum-enhanced Sensing and Efficient Quantum Computation

DTIC Science & Technology

2015-07-27

accuracy. The system was used to improve quantum boson sampling tests. 15. SUBJECT TERMS EOARD, Quantum Information Processing, Transition Edge Sensors...quantum  boson  sampling (QBS) problem are reported in Ref. [7]. To substantially  increase the scale of feasible tests, we developed a new variation

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

McCaskey, Alexander J.

There is a lack of state-of-the-art HPC simulation tools for simulating general quantum computing. Furthermore, there are no real software tools that integrate current quantum computers into existing classical HPC workflows. This product, the Quantum Virtual Machine (QVM), solves this problem by providing an extensible framework for pluggable virtual, or physical, quantum processing units (QPUs). It enables the execution of low level quantum assembly codes and returns the results of such executions.

Student Understanding of Time Dependence in Quantum Mechanics

ERIC Educational Resources Information Center

Emigh, Paul J.; Passante, Gina; Shaffer, Peter S.

2015-01-01

The time evolution of quantum states is arguably one of the more difficult ideas in quantum mechanics. In this article, we report on results from an investigation of student understanding of this topic after lecture instruction. We demonstrate specific problems that students have in applying time dependence to quantum systems and in recognizing…

Adiabatic quantum simulation of quantum chemistry.

PubMed

Babbush, Ryan; Love, Peter J; Aspuru-Guzik, Alán

2014-10-13

We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-body qubit Hamiltonians with a small set of physically realizable couplings. By combining the Bravyi-Kitaev construction to map fermions to qubits with perturbative gadgets to reduce the Hamiltonian to 2-body, we obtain precision requirements on the coupling strengths and a number of ancilla qubits that scale polynomially in the problem size. Hence our mapping is efficient. The required set of controllable interactions includes only two types of interaction beyond the Ising interactions required to apply the quantum adiabatic algorithm to combinatorial optimization problems. Our mapping may also be of interest to chemists directly as it defines a dictionary from electronic structure to spin Hamiltonians with physical interactions.

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.

Undecidability of the spectral gap.

PubMed

Cubitt, Toby S; Perez-Garcia, David; Wolf, Michael M

2015-12-10

The spectral gap--the energy difference between the ground state and first excited state of a system--is central to quantum many-body physics. Many challenging open problems, such as the Haldane conjecture, the question of the existence of gapped topological spin liquid phases, and the Yang-Mills gap conjecture, concern spectral gaps. These and other problems are particular cases of the general spectral gap problem: given the Hamiltonian of a quantum many-body system, is it gapped or gapless? Here we prove that this is an undecidable problem. Specifically, we construct families of quantum spin systems on a two-dimensional lattice with translationally invariant, nearest-neighbour interactions, for which the spectral gap problem is undecidable. This result extends to undecidability of other low-energy properties, such as the existence of algebraically decaying ground-state correlations. The proof combines Hamiltonian complexity techniques with aperiodic tilings, to construct a Hamiltonian whose ground state encodes the evolution of a quantum phase-estimation algorithm followed by a universal Turing machine. The spectral gap depends on the outcome of the corresponding 'halting problem'. Our result implies that there exists no algorithm to determine whether an arbitrary model is gapped or gapless, and that there exist models for which the presence or absence of a spectral gap is independent of the axioms of mathematics.

Qubits in phase space: Wigner-function approach to quantum-error correction and the mean-king problem

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

Paz, Juan Pablo; Roncaglia, Augusto Jose; Theoretical Division, LANL, MSB213, Los Alamos, New Mexico 87545

2005-07-15

We analyze and further develop a method to represent the quantum state of a system of n qubits in a phase-space grid of NxN points (where N=2{sup n}). The method, which was recently proposed by Wootters and co-workers (Gibbons et al., Phys. Rev. A 70, 062101 (2004).), is based on the use of the elements of the finite field GF(2{sup n}) to label the phase-space axes. We present a self-contained overview of the method, we give insights into some of its features, and we apply it to investigate problems which are of interest for quantum-information theory: We analyze the phase-spacemore » representation of stabilizer states and quantum error-correction codes and present a phase-space solution to the so-called mean king problem.« less

Quantum and semiclassical spin networks: from atomic and molecular physics to quantum computing and gravity

NASA Astrophysics Data System (ADS)

Aquilanti, Vincenzo; Bitencourt, Ana Carla P.; Ferreira, Cristiane da S.; Marzuoli, Annalisa; Ragni, Mirco

2008-11-01

The mathematical apparatus of quantum-mechanical angular momentum (re)coupling, developed originally to describe spectroscopic phenomena in atomic, molecular, optical and nuclear physics, is embedded in modern algebraic settings which emphasize the underlying combinatorial aspects. SU(2) recoupling theory, involving Wigner's 3nj symbols, as well as the related problems of their calculations, general properties, asymptotic limits for large entries, nowadays plays a prominent role also in quantum gravity and quantum computing applications. We refer to the ingredients of this theory—and of its extension to other Lie and quantum groups—by using the collective term of 'spin networks'. Recent progress is recorded about the already established connections with the mathematical theory of discrete orthogonal polynomials (the so-called Askey scheme), providing powerful tools based on asymptotic expansions, which correspond on the physical side to various levels of semi-classical limits. These results are useful not only in theoretical molecular physics but also in motivating algorithms for the computationally demanding problems of molecular dynamics and chemical reaction theory, where large angular momenta are typically involved. As for quantum chemistry, applications of these techniques include selection and classification of complete orthogonal basis sets in atomic and molecular problems, either in configuration space (Sturmian orbitals) or in momentum space. In this paper, we list and discuss some aspects of these developments—such as for instance the hyperquantization algorithm—as well as a few applications to quantum gravity and topology, thus providing evidence of a unifying background structure.

Quantum Measurement, Correlation, and Contextuality

NASA Astrophysics Data System (ADS)

Ozawa, Masanao

2011-03-01

The problem has long been discussed as to whether non-commuting observables are simultaneously measurable, since Heisenberg introduced the uncertainty principle in 1927. The problem was settled state-independently: Two observables are simultaneously measurable in every state if and only if the corresponding operators commute. However, the problem has been open for state-dependent formulation. Saying that two observables are nowhere commuting if there exist no common eigenstates, the problem at stake is whether nowhere commuting observable can be simultaneously measurable in a certain state. There have been two historical arguments claiming the case: (i) In an eigenstate of an observable A one can determine both the values of A and any other observable B . (ii) In an EPR state one can determine both the values of Q ⊗ 1 and P ⊗ 1 . In this talk, we give a necessary and sufficient condition for two observables to be simultaneously measurable in a given state, show that the above two cases actually satisfy the required mathematical conditions, and give a classification of all the possible simultaneous measurements of nowhere commuting observables for the Hilbert space with dimension 2. Related problems on quantum contextuality will also be discussed using a linguistic method based on quantum logic and quantum set theory.

Team decision problems with classical and quantum signals

PubMed Central

Brandenburger, Adam; La Mura, Pierfrancesco

2016-01-01

We study team decision problems where communication is not possible, but coordination among team members can be realized via signals in a shared environment. We consider a variety of decision problems that differ in what team members know about one another's actions and knowledge. For each type of decision problem, we investigate how different assumptions on the available signals affect team performance. Specifically, we consider the cases of perfectly correlated, i.i.d., and exchangeable classical signals, as well as the case of quantum signals. We find that, whereas in perfect-recall trees (Kuhn 1950 Proc. Natl Acad. Sci. USA 36, 570–576; Kuhn 1953 In Contributions to the theory of games, vol. II (eds H Kuhn, A Tucker), pp. 193–216) no type of signal improves performance, in imperfect-recall trees quantum signals may bring an improvement. Isbell (Isbell 1957 In Contributions to the theory of games, vol. III (eds M Drescher, A Tucker, P Wolfe), pp. 79–96) proved that, in non-Kuhn trees, classical i.i.d. signals may improve performance. We show that further improvement may be possible by use of classical exchangeable or quantum signals. We include an example of the effect of quantum signals in the context of high-frequency trading. PMID:26621985

Team decision problems with classical and quantum signals.

PubMed

Brandenburger, Adam; La Mura, Pierfrancesco

2016-01-13

We study team decision problems where communication is not possible, but coordination among team members can be realized via signals in a shared environment. We consider a variety of decision problems that differ in what team members know about one another's actions and knowledge. For each type of decision problem, we investigate how different assumptions on the available signals affect team performance. Specifically, we consider the cases of perfectly correlated, i.i.d., and exchangeable classical signals, as well as the case of quantum signals. We find that, whereas in perfect-recall trees (Kuhn 1950 Proc. Natl Acad. Sci. USA 36, 570-576; Kuhn 1953 In Contributions to the theory of games, vol. II (eds H Kuhn, A Tucker), pp. 193-216) no type of signal improves performance, in imperfect-recall trees quantum signals may bring an improvement. Isbell (Isbell 1957 In Contributions to the theory of games, vol. III (eds M Drescher, A Tucker, P Wolfe), pp. 79-96) proved that, in non-Kuhn trees, classical i.i.d. signals may improve performance. We show that further improvement may be possible by use of classical exchangeable or quantum signals. We include an example of the effect of quantum signals in the context of high-frequency trading. © 2015 The Authors.

Decodoku: Quantum error rorrection as a simple puzzle game

NASA Astrophysics Data System (ADS)

Wootton, James

To build quantum computers, we need to detect and manage any noise that occurs. This will be done using quantum error correction. At the hardware level, QEC is a multipartite system that stores information non-locally. Certain measurements are made which do not disturb the stored information, but which do allow signatures of errors to be detected. Then there is a software problem. How to take these measurement outcomes and determine: a) The errors that caused them, and (b) how to remove their effects. For qubit error correction, the algorithms required to do this are well known. For qudits, however, current methods are far from optimal. We consider the error correction problem of qubit surface codes. At the most basic level, this is a problem that can be expressed in terms of a grid of numbers. Using this fact, we take the inherent problem at the heart of quantum error correction, remove it from its quantum context, and presented in terms of simple grid based puzzle games. We have developed three versions of these puzzle games, focussing on different aspects of the required algorithms. These have been presented and iOS and Android apps, allowing the public to try their hand at developing good algorithms to solve the puzzles. For more information, see www.decodoku.com. Funding from the NCCR QSIT.

BOOK REVIEW: The Quantum Mechanics Solver: How to Apply Quantum Theory to Modern Physics, 2nd edition

NASA Astrophysics Data System (ADS)

Robbin, J. M.

2007-07-01

he hallmark of a good book of problems is that it allows you to become acquainted with an unfamiliar topic quickly and efficiently. The Quantum Mechanics Solver fits this description admirably. The book contains 27 problems based mainly on recent experimental developments, including neutrino oscillations, tests of Bell's inequality, Bose Einstein condensates, and laser cooling and trapping of atoms, to name a few. Unlike many collections, in which problems are designed around a particular mathematical method, here each problem is devoted to a small group of phenomena or experiments. Most problems contain experimental data from the literature, and readers are asked to estimate parameters from the data, or compare theory to experiment, or both. Standard techniques (e.g., degenerate perturbation theory, addition of angular momentum, asymptotics of special functions) are introduced only as they are needed. The style is closer to a non-specialist seminar rather than an undergraduate lecture. The physical models are kept simple; the emphasis is on cultivating conceptual and qualitative understanding (although in many of the problems, the simple models fit the data quite well). Some less familiar theoretical techniques are introduced, e.g. a variational method for lower (not upper) bounds on ground-state energies for many-body systems with two-body interactions, which is then used to derive a surprisingly accurate relation between baryon and meson masses. The exposition is succinct but clear; the solutions can be read as worked examples if you don't want to do the problems yourself. Many problems have additional discussion on limitations and extensions of the theory, or further applications outside physics (e.g., the accuracy of GPS positioning in connection with atomic clocks; proton and ion tumor therapies in connection with the Bethe Bloch formula for charged particles in solids). The problems use mainly non-relativistic quantum mechanics and are organised into three sections: Elementary Particles, Nuclei and Atoms; Quantum Entanglement and Measurement; and Complex Systems. The coverage is not comprehensive; there is little on scattering theory, for example, and some areas of recent interest, such as topological aspects of quantum mechanics and semiclassics, are not included. The problems are based on examination questions given at the École Polytechnique in the last 15 years. The book is accessible to undergraduates, but working physicists should find it a delight.

Subspace projection method for unstructured searches with noisy quantum oracles using a signal-based quantum emulation device

NASA Astrophysics Data System (ADS)

La Cour, Brian R.; Ostrove, Corey I.

2017-01-01

This paper describes a novel approach to solving unstructured search problems using a classical, signal-based emulation of a quantum computer. The classical nature of the representation allows one to perform subspace projections in addition to the usual unitary gate operations. Although bandwidth requirements will limit the scale of problems that can be solved by this method, it can nevertheless provide a significant computational advantage for problems of limited size. In particular, we find that, for the same number of noisy oracle calls, the proposed subspace projection method provides a higher probability of success for finding a solution than does an single application of Grover's algorithm on the same device.

Fine Structure of Dark Energy and New Physics

DOE PAGES

Jejjala, Vishnu; Kavic, Michael; Minic, Djordje

2007-01-01

Following our recent work on the cosmological constant problem, in this letter we make a specific proposal regarding the fine structure (i.e., the spectrum) of dark energy. The proposal is motivated by a deep analogy between the blackbody radiation problem, which led to the development of quantum theory, and the cosmological constant problem, for which we have recently argued calls for a conceptual extension of the quantum theory. We argue that the fine structure of dark energy is governed by a Wien distribution, indicating its dual quantum and classical nature. We discuss observational consequences of such a picture of darkmore » energy and constrain the distribution function.« less

Computational studies of thermal and quantum phase transitions approached through non-equilibrium quenching

NASA Astrophysics Data System (ADS)

Liu, Cheng-Wei

Phase transitions and their associated critical phenomena are of fundamental importance and play a crucial role in the development of statistical physics for both classical and quantum systems. Phase transitions embody diverse aspects of physics and also have numerous applications outside physics, e.g., in chemistry, biology, and combinatorial optimization problems in computer science. Many problems can be reduced to a system consisting of a large number of interacting agents, which under some circumstances (e.g., changes of external parameters) exhibit collective behavior; this type of scenario also underlies phase transitions. The theoretical understanding of equilibrium phase transitions was put on a solid footing with the establishment of the renormalization group. In contrast, non-equilibrium phase transition are relatively less understood and currently a very active research topic. One important milestone here is the Kibble-Zurek (KZ) mechanism, which provides a useful framework for describing a system with a transition point approached through a non-equilibrium quench process. I developed two efficient Monte Carlo techniques for studying phase transitions, one is for classical phase transition and the other is for quantum phase transitions, both are under the framework of KZ scaling. For classical phase transition, I develop a non-equilibrium quench (NEQ) simulation that can completely avoid the critical slowing down problem. For quantum phase transitions, I develop a new algorithm, named quasi-adiabatic quantum Monte Carlo (QAQMC) algorithm for studying quantum quenches. I demonstrate the utility of QAQMC quantum Ising model and obtain high-precision results at the transition point, in particular showing generalized dynamic scaling in the quantum system. To further extend the methods, I study more complex systems such as spin-glasses and random graphs. The techniques allow us to investigate the problems efficiently. From the classical perspective, using the NEQ approach I verify the universality class of the 3D Ising spin-glasses. I also investigate the random 3-regular graphs in terms of both classical and quantum phase transitions. I demonstrate that under this simulation scheme, one can extract information associated with the classical and quantum spin-glass transitions without any knowledge prior to the simulation.

An Efficient Quantum Somewhat Homomorphic Symmetric Searchable Encryption

NASA Astrophysics Data System (ADS)

Sun, Xiaoqiang; Wang, Ting; Sun, Zhiwei; Wang, Ping; Yu, Jianping; Xie, Weixin

2017-04-01

In 2009, Gentry first introduced an ideal lattices fully homomorphic encryption (FHE) scheme. Later, based on the approximate greatest common divisor problem, learning with errors problem or learning with errors over rings problem, FHE has developed rapidly, along with the low efficiency and computational security. Combined with quantum mechanics, Liang proposed a symmetric quantum somewhat homomorphic encryption (QSHE) scheme based on quantum one-time pad, which is unconditional security. And it was converted to a quantum fully homomorphic encryption scheme, whose evaluation algorithm is based on the secret key. Compared with Liang's QSHE scheme, we propose a more efficient QSHE scheme for classical input states with perfect security, which is used to encrypt the classical message, and the secret key is not required in the evaluation algorithm. Furthermore, an efficient symmetric searchable encryption (SSE) scheme is constructed based on our QSHE scheme. SSE is important in the cloud storage, which allows users to offload search queries to the untrusted cloud. Then the cloud is responsible for returning encrypted files that match search queries (also encrypted), which protects users' privacy.

Necessary and sufficient optimality conditions for classical simulations of quantum communication processes

NASA Astrophysics Data System (ADS)

Montina, Alberto; Wolf, Stefan

2014-07-01

We consider the process consisting of preparation, transmission through a quantum channel, and subsequent measurement of quantum states. The communication complexity of the channel is the minimal amount of classical communication required for classically simulating it. Recently, we reduced the computation of this quantity to a convex minimization problem with linear constraints. Every solution of the constraints provides an upper bound on the communication complexity. In this paper, we derive the dual maximization problem of the original one. The feasible points of the dual constraints, which are inequalities, give lower bounds on the communication complexity, as illustrated with an example. The optimal values of the two problems turn out to be equal (zero duality gap). By this property, we provide necessary and sufficient conditions for optimality in terms of a set of equalities and inequalities. We use these conditions and two reasonable but unproven hypotheses to derive the lower bound n ×2n -1 for a noiseless quantum channel with capacity equal to n qubits. This lower bound can have interesting consequences in the context of the recent debate on the reality of the quantum state.

On the Possibility to Combine the Order Effect with Sequential Reproducibility for Quantum Measurements

NASA Astrophysics Data System (ADS)

Basieva, Irina; Khrennikov, Andrei

2015-10-01

In this paper we study the problem of a possibility to use quantum observables to describe a possible combination of the order effect with sequential reproducibility for quantum measurements. By the order effect we mean a dependence of probability distributions (of measurement results) on the order of measurements. We consider two types of the sequential reproducibility: adjacent reproducibility (A-A) (the standard perfect repeatability) and separated reproducibility(A-B-A). The first one is reproducibility with probability 1 of a result of measurement of some observable A measured twice, one A measurement after the other. The second one, A-B-A, is reproducibility with probability 1 of a result of A measurement when another quantum observable B is measured between two A's. Heuristically, it is clear that the second type of reproducibility is complementary to the order effect. We show that, surprisingly, this may not be the case. The order effect can coexist with a separated reproducibility as well as adjacent reproducibility for both observables A and B. However, the additional constraint in the form of separated reproducibility of the B-A-B type makes this coexistence impossible. The problem under consideration was motivated by attempts to apply the quantum formalism outside of physics, especially, in cognitive psychology and psychophysics. However, it is also important for foundations of quantum physics as a part of the problem about the structure of sequential quantum measurements.

Contrasting grading approaches in introductory physics and quantum mechanics: The case of graduate teaching assistants

NASA Astrophysics Data System (ADS)

Marshman, Emily; Sayer, Ryan; Henderson, Charles; Singh, Chandralekha

2017-06-01

At large research universities, physics graduate teaching assistants (TAs) are often responsible for grading in courses at all levels. However, few studies have focused on TAs' grading practices in introductory and advanced physics courses. This study was designed to investigate whether physics graduate TAs grade students in introductory physics and quantum mechanics using different criteria and if so, why they may be inclined to do so. To investigate possible discrepancies in TAs' grading approaches in courses at different levels, we implemented a sequence of instructional activities in a TA professional development course that asked TAs to grade student solutions of introductory physics and upper-level quantum mechanics problems and explain why, if at all, their grading approaches were different or similar in the two contexts. We analyzed the differences in TAs' grading approaches in the two contexts and discuss the reasons they provided for the differences in their grading approaches in introductory physics and quantum mechanics in individual interviews, class discussions, and written responses. We find that a majority of the TAs graded solutions to quantum mechanics problems differently than solutions to introductory physics problems. In quantum mechanics, the TAs focused more on physics concepts and reasoning and penalized students for not showing evidence of understanding. The findings of the study have implications for TA professional development programs, e.g., the importance of helping TAs think about the difficulty of a problem from an introductory students' perspective and reflecting on the benefits of formative assessment.

From bosonic topological transition to symmetric fermion mass generation

NASA Astrophysics Data System (ADS)

You, Yi-Zhuang; He, Yin-Chen; Vishwanath, Ashvin; Xu, Cenke

2018-03-01

A bosonic topological transition (BTT) is a quantum critical point between the bosonic symmetry-protected topological phase and the trivial phase. In this work, we investigate such a transition in a (2+1)-dimensional lattice model with the maximal microscopic symmetry: an internal SO (4 ) symmetry. We derive a description for this transition in terms of compact quantum electrodynamics (QED) with four fermion flavors (Nf=4 ). Within a systematic renormalization group analysis, we identify the critical point with the desired O (4 ) emergent symmetry and all expected deformations. By lowering the microscopic symmetry, we recover the previous Nf=2 noncompact QED description of the BTT. Finally, by merging two BTTs we recover a previously discussed theory of symmetric mass generation, as an SU (2 ) quantum chromodynamics-Higgs theory with Nf=4 flavors of SU (2 ) fundamental fermions and one SU (2 ) fundamental Higgs boson. This provides a consistency check on both theories.

Strain-enhanced tunneling magnetoresistance in MgO magnetic tunnel junctions

PubMed Central

Loong, Li Ming; Qiu, Xuepeng; Neo, Zhi Peng; Deorani, Praveen; Wu, Yang; Bhatia, Charanjit S.; Saeys, Mark; Yang, Hyunsoo

2014-01-01

While the effects of lattice mismatch-induced strain, mechanical strain, as well as the intrinsic strain of thin films are sometimes detrimental, resulting in mechanical deformation and failure, strain can also be usefully harnessed for applications such as data storage, transistors, solar cells, and strain gauges, among other things. Here, we demonstrate that quantum transport across magnetic tunnel junctions (MTJs) can be significantly affected by the introduction of controllable mechanical strain, achieving an enhancement factor of ~2 in the experimental tunneling magnetoresistance (TMR) ratio. We further correlate this strain-enhanced TMR with coherent spin tunneling through the MgO barrier. Moreover, the strain-enhanced TMR is analyzed using non-equilibrium Green's function (NEGF) quantum transport calculations. Our results help elucidate the TMR mechanism at the atomic level and can provide a new way to enhance, as well as tune, the quantum properties in nanoscale materials and devices. PMID:25266219

Applications and error correction for adiabatic quantum optimization

NASA Astrophysics Data System (ADS)

Pudenz, Kristen

Adiabatic quantum optimization (AQO) is a fast-developing subfield of quantum information processing which holds great promise in the relatively near future. Here we develop an application, quantum anomaly detection, and an error correction code, Quantum Annealing Correction (QAC), for use with AQO. The motivation for the anomaly detection algorithm is the problematic nature of classical software verification and validation (V&V). The number of lines of code written for safety-critical applications such as cars and aircraft increases each year, and with it the cost of finding errors grows exponentially (the cost of overlooking errors, which can be measured in human safety, is arguably even higher). We approach the V&V problem by using a quantum machine learning algorithm to identify charateristics of software operations that are implemented outside of specifications, then define an AQO to return these anomalous operations as its result. Our error correction work is the first large-scale experimental demonstration of quantum error correcting codes. We develop QAC and apply it to USC's equipment, the first and second generation of commercially available D-Wave AQO processors. We first show comprehensive experimental results for the code's performance on antiferromagnetic chains, scaling the problem size up to 86 logical qubits (344 physical qubits) and recovering significant encoded success rates even when the unencoded success rates drop to almost nothing. A broader set of randomized benchmarking problems is then introduced, for which we observe similar behavior to the antiferromagnetic chain, specifically that the use of QAC is almost always advantageous for problems of sufficient size and difficulty. Along the way, we develop problem-specific optimizations for the code and gain insight into the various on-chip error mechanisms (most prominently thermal noise, since the hardware operates at finite temperature) and the ways QAC counteracts them. We finish by showing that the scheme is robust to qubit loss on-chip, a significant benefit when considering an implemented system.

Proposed Test of Relative Phase as Hidden Variable in Quantum Mechanics

DTIC Science & Technology

2012-01-01

implicitly due to its ubiquity in quantum theory , but searches for dependence of measurement outcome on other parameters have been lacking. For a two -state...implemen- tation for the specific case of an atomic two -state system with laser-induced fluores- cence for measurement. Keywords Quantum measurement...Measurement postulate · Born rule 1 Introduction 1.1 Problems with Quantum Measurement Quantum theory prescribes probabilities for outcomes of measurements

Quantum correlations in non-inertial cavity systems

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

2016-10-15

Non-inertial cavities are utilized to store and send Quantum Information between mode pairs. A two-cavity system is considered where one is inertial and the other accelerated in a finite time. Maclaurian series are applied to expand the related Bogoliubov coefficients and the problem is treated perturbatively. It is shown that Quantum Discord, which is a measure of quantumness of correlations, is degraded periodically. This is almost in agreement with previous results reached in accelerated systems where increment of acceleration decreases the degree of quantum correlations. As another finding of the study, it is explicitly shown that degradation of Quantum Discordmore » disappears when the state is in a single cavity which is accelerated for a finite time. This feature makes accelerating cavities useful instruments in Quantum Information Theory. - Highlights: • Non-inertial cavities are utilized to store and send information in Quantum Information Theory. • Cavities include boundary conditions which will protect the entanglement once it has been created. • The problem is treated perturbatively and the maclaurian series are applied to expand the related Bogoliubov coefficients. • When two cavities are considered degradation in the degree of quantum correlation happens and it appears periodically. • The interesting issue is when a single cavity is studied and the degradation in quantum correlations disappears.« less

The Holographic F Theorem

NASA Astrophysics Data System (ADS)

Taylor, Marika; Woodhead, William

2017-12-01

The F theorem states that, for a unitary three dimensional quantum field theory, the F quantity defined in terms of the partition function on a three sphere is positive, stationary at fixed point and decreases monotonically along a renormalization group flow. We construct holographic renormalization group flows corresponding to relevant deformations of three-dimensional conformal field theories on spheres, working to quadratic order in the source. For these renormalization group flows, the F quantity at the IR fixed point is always less than F at the UV fixed point, but F increases along the RG flow for deformations by operators of dimension between 3/2 and 5/2. Therefore the strongest version of the F theorem is in general violated.

Emergence of spaces and the dynamic equations of FRW universes in the f(R) theory and deformed Hořava-Lifshitz theory

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

Tu, Fei-Quan; Chen, Yi-Xin, E-mail: fqtuzju@foxmail.com, E-mail: yxchen@zimp.zju.edu.cn

It has been shown that Friedmann equation of FRW universe can be derived from the idea which says cosmic space is emergent as cosmic time progresses and our universe is expanding towards the state with the holographic equipartition by Padmanabhan. In this note, we give a general relationship between the horizon entropy and the number of the degrees of freedom on the surface, which can be applied to quantum gravity. we also obtain the corresponding dynamic equations by using the idea of emergence of spaces in the f(R) theory and deformed Hořava-Lifshitz(HL) theory.

Nonlocal teleparallel cosmology.

PubMed

Bahamonde, Sebastian; Capozziello, Salvatore; Faizal, Mir; Nunes, Rafael C

2017-01-01

Even though it is not possible to differentiate general relativity from teleparallel gravity using classical experiments, it could be possible to discriminate between them by quantum gravitational effects. These effects have motivated the introduction of nonlocal deformations of general relativity, and similar effects are also expected to occur in teleparallel gravity. Here, we study nonlocal deformations of teleparallel gravity along with its cosmological solutions. We observe that nonlocal teleparallel gravity (like nonlocal general relativity) is consistent with the present cosmological data obtained by SNe Ia + BAO + CC + [Formula: see text] observations. Along this track, future experiments probing nonlocal effects could be used to test whether general relativity or teleparallel gravity gives the most consistent picture of gravitational interaction.

Microscopic mechanism analyses on influence of metabolism of erythrocyte membrane-lipid etc. by LLLIB

NASA Astrophysics Data System (ADS)

Xu, Lin; Zhang, Canbang; Wen, Yuanbin; Liu, Shuxiao; Zhou, Lingyun

2009-08-01

Some cases with cerebral infarction were treated by He-Ne laser irradiation on blood. In the treatment before and after, membrane-cholesterol(C)/membrane-phosphatide(P), membrane fluidity(F) and deformability of erythrocyte were determined. The results showed that low level laser irradiation on blood (LLLIB) can sure reduce the ratio of (C)/(P), can heighten fluidity and improve deformability of erythrocyte .Thus the metabolism ability of erythrocyte membrane-lipid ,the blood circulation and the properties of hemorheology can be improved. In this paper, the microscopic mechanism of those aforesaid action effects by low level laser irradiation on blood were analyzed by means of Quantum theory and some corresponding models.

Effects of structural deformations on optical properties of tetrabenzoporphyrins: free-bases and Pd complexes.

PubMed

Lebedev, Artem Y; Filatov, Mikhail A; Cheprakov, Andrei V; Vinogradov, Sergei A

2008-08-21

A recently developed method of synthesis of pi-extended porphyrins made it possible to prepare a series of tetrabenzoporphyrins (TBP) with different numbers of meso-aryl substituents. The photophysical parameters of free-bases and Pd complexes of meso-unsubstituted TBP's, 5,15-diaryl-TBP's (Ar2TBP's) and 5,10,15,20-tetraaryl-TBP's (Ar4TBP's) were measured. For comparison, similarly meso-arylsubstituted porphyrins fused with nonaromatic cyclohexeno-rings, i.e. Ar(n)-tetracyclohexenoporphyrins (Ar(n)TCHP's, n = 0, 2, 4), were also synthesized and studied. Structural information was obtained by ab initio (DFT) calculations and X-ray crystallography. It was found that: 1) Free-base Ar4TBP's are strongly distorted out-of-plane (saddled), possess broadened, red-shifted spectra, short excited-state lifetimes and low fluorescence quantum yields (tau(fl) = 2-3 ns, phi(fl) = 0.02-0.03). These features are characteristic of other nonplanar free-base porphyrins, including Ar4TCHP's. 2) Ar2TBP free-bases possess completely planar geometries, although with significant in-plane deformations. These deformations have practically no effect on the singlet excited-state properties of Ar2TBP's as compared to planar meso-unsubstituted TBP's. Both types of porphyrins retain strong fluorescence (tau(fl) = 10-12 ns, phi(fl) = 0.3-0.4), and their radiative rate constants (k(r)) are 3-4 times higher than those of planar H2TCHP's. 3) Nonplanar deformations dramatically enhance nonradiative decay of triplet states of regular Pd porphyrins. For example, planar PdTCHP phosphoresces with high quantum yield (phi(phos) = 0.45, tau(phos) = 1118 micros), while saddled PdPh4TCHP is practically nonemissive. In contrast, both ruffled and saddled PdAr(n)TBP's retain strong phosphorescence at ambient temperatures (PdPh2TBP: tau(phos) = 496 micros, phi(phos) = 0.15; PdPh4TBP: tau(phos) = 258 micros, phi(phos) = 0.08). It appears that pi-extension is capable of counterbalancing deleterious effects of nonplanar deformations on triplet emissivity of Pd porphyrins.

Effects of Structural Deformations on Optical Properties of Tetrabenzoporphyrins: Free-Bases and Pd Complexes

PubMed Central

Lebedev, Artem Y.; Filatov, Mikhail A.; Cheprakov, Andrei V.; Vinogradov, Sergei A.

2009-01-01

A recently developed method of synthesis of π-extended porphyrins made it possible to prepare a series of tetrabenzoporphyrins (TBP) with different numbers of meso-aryl substituents. The photophysical parameters of free-bases and Pd complexes of meso-unsubstituted TBP’s, 5,15-diaryl-TBP’s (Ar2TBP’s) and 5,10,15,20-tetraaryl-TBP’s (Ar4TBP’s) were measured. For comparison, similarly meso-arylsubstituted porphyrins fused with nonaromatic cyclohexeno-rings, i.e. Arn-tetracyclohexenoporphyrins (ArnTCHP’s, n = 0, 2, 4), were also synthesized and studied. Structural information was obtained by ab initio (DFT) calculations and X-ray crystallography. It was found that: 1) Free-base Ar4TBP’s are strongly distorted out-of-plane (saddled), possess broadened, red-shifted spectra, short excited-state lifetimes and low fluorescence quantum yields (τfl = 2–3 ns, ϕfl = 0.02–0.03). These features are characteristic of other nonplanar free-base porphyrins, including Ar4TCHP’s. 2) Ar2TBP free-bases possess completely planar geometries, although with significant in-plane deformations. These deformations have practically no effect on the singlet excited-state properties of Ar2TBP’s as compared to planar meso-unsubstituted TBP’s. Both types of porphyrins retain strong fluorescence (τfl = 10–12 ns, ϕfl = 0.3–0.4), and their radiative rate constants (kr) are 3–4 times higher than those of planar H2TCHP’s. 3) Nonplanar deformations dramatically enhance nonradiative decay of triplet states of regular Pd porphyrins. For example, planar PdTCHP phosphoresces with high quantum yield (ϕphos = 0.45, τphos = 1118 µs), while saddled PdPh4TCHP is practically nonemissive. In contrast, both ruffled and saddled PdArnTBP’s retain strong phosphorescence at ambient temperatures (PdPh2TBP: τphos = 496 µs, ϕphos = 0.15; PdPh4TBP: τphos = 258 µs, ϕphos = 0.08). It appears that π-extension is capable of counterbalancing deleterious effects of nonplanar deformations on triplet emissivity of Pd porphyrins. PMID:18665576

Teaching Quantum Physics in Upper Secondary School in France:

ERIC Educational Resources Information Center

Lautesse, Philippe; Vila Valls, Adrien; Ferlin, Fabrice; Héraud, Jean-Loup; Chabot, Hugues

2015-01-01

One of the main problems in trying to understand quantum physics is the nature of the referent of quantum theory. This point is addressed in the official French curriculum in upper secondary school. Starting in 2012, after about 20 years of absence, quantum physics has returned to the national program. On the basis of the historical construction…

Hidden algebra method (quasi-exact-solvability in quantum mechanics)

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

Turbiner, Alexander; Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado, Postal 70-543, 04510 Mexico, D. F.

1996-02-20

A general introduction to quasi-exactly-solvable problems of quantum mechanics is presented. Main attention is given to multidimensional quasi-exactly-solvable and exactly-solvable Schroedinger operators. Exact-solvability of the Calogero and Sutherland N-body problems ass ociated with an existence of the hidden algebra slN is discussed extensively.

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.

Redesigning the Quantum Mechanics Curriculum to Incorporate Problem Solving Using a Computer Algebra System

NASA Astrophysics Data System (ADS)

Roussel, Marc R.

1999-10-01

One of the traditional obstacles to learning quantum mechanics is the relatively high level of mathematical proficiency required to solve even routine problems. Modern computer algebra systems are now sufficiently reliable that they can be used as mathematical assistants to alleviate this difficulty. In the quantum mechanics course at the University of Lethbridge, the traditional three lecture hours per week have been replaced by two lecture hours and a one-hour computer-aided problem solving session using a computer algebra system (Maple). While this somewhat reduces the number of topics that can be tackled during the term, students have a better opportunity to familiarize themselves with the underlying theory with this course design. Maple is also available to students during examinations. The use of a computer algebra system expands the class of feasible problems during a time-limited exercise such as a midterm or final examination. A modern computer algebra system is a complex piece of software, so some time needs to be devoted to teaching the students its proper use. However, the advantages to the teaching of quantum mechanics appear to outweigh the disadvantages.

Influence of irradiation conditions on the deformation of pure titanium frames in laser welding.

PubMed

Shimakura, Michio; Yamada, Satoshi; Takeuchi, Misao; Miura, Koki; Ikeyama, Joji

2009-03-01

Due to its ease of use in connecting metal frames, laser welding is now applied in dentistry. However, to achieve precise laser welding, several problems remain to be resolved. One such problem is the influence of irradiation conditions on the deformation of titanium frameworks during laser welding, which this study sought to investigate. Board-shaped pure titanium specimens were prepared with two different joint types. Two specimens were abutted against each other to form a welding block with gypsum. For welding, three different laser waveforms were used. Deformation of the specimen caused by laser welding was measured as a rise from the gypsum surface at the opposite, free end of the specimen. It was observed that specimens with a beveled edge registered a smaller deformation than specimens with a square edge. In addition, a double laser pulse waveform--whereby a supplementary laser pulse was delivered immediately after the main pulse--resulted in a smaller deformation than with a single laser pulse waveform.

On the emergence of the structure of physics

NASA Astrophysics Data System (ADS)

Majid, S.

2018-04-01

We consider Hilbert's problem of the axioms of physics at a qualitative or conceptual level. This is more pressing than ever as we seek to understand how both general relativity and quantum theory could emerge from some deeper theory of quantum gravity, and in this regard I have previously proposed a principle of self-duality or quantum Born reciprocity as a key structure. Here, I outline some of my recent work around the idea of quantum space-time as motivated by this non-standard philosophy, including a new toy model of gravity on a space-time consisting of four points forming a square. This article is part of the theme issue `Hilbert's sixth problem'.

Asymptotic quantum inelastic generalized Lorenz Mie theory

NASA Astrophysics Data System (ADS)

Gouesbet, G.

2007-10-01

The (electromagnetic) generalized Lorenz-Mie theory describes the interaction between an electromagnetic arbitrary shaped beam and a homogeneous sphere. It is a generalization of the Lorenz-Mie theory which deals with the simpler case of a plane wave illumination. In a recent paper, we consider (i) elastic cross-sections in electromagnetic generalized Lorenz-Mie theory and (ii) elastic cross-sections in an associated quantum generalized Lorenz-Mie theory. We demonstrated that the electromagnetic problem is equivalent to a superposition of two effective quantum problems. We now intend to generalize this result from elastic cross-sections to inelastic cross-sections. A prerequisite is to build an asymptotic quantum inelastic generalized Lorenz-Mie theory, which is presented in this paper.

Solving the Nonlocality Riddle by Conformal Quantum Geometrodynamics

NASA Astrophysics Data System (ADS)

Santamato, Enrico; de Martini, Francesco

2012-01-01

Since the 1935 proposal by Einstein, Podolsky and Rosen the riddle of nonlocality, today demonstrated by the violation of Bell's inequalities within innumerable experiments, has been a cause of concern and confusion within the debate over the foundations of quantum mechanics. The present paper tackles the problem by a nonrelativistic approach based on conformal differential geometry applied to the solution of the dynamical problem of two entangled spin 1/2 particles. It is found that the quantum nonlocality may be understood on the basis of a conformal quantum geometrodynamics acting necessarily on the full "configuration space" of the entangled particles. At the end, the violation of the Bell inequalities is demonstrated without making recourse to the common nonlocality paradigm.

On the emergence of the structure of physics.

PubMed

Majid, S

2018-04-28

We consider Hilbert's problem of the axioms of physics at a qualitative or conceptual level. This is more pressing than ever as we seek to understand how both general relativity and quantum theory could emerge from some deeper theory of quantum gravity, and in this regard I have previously proposed a principle of self-duality or quantum Born reciprocity as a key structure. Here, I outline some of my recent work around the idea of quantum space-time as motivated by this non-standard philosophy, including a new toy model of gravity on a space-time consisting of four points forming a square.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Less Decoherence and More Coherence in Quantum Gravity, Inflationary Cosmology and Elsewhere

NASA Astrophysics Data System (ADS)

Okon, Elias; Sudarsky, Daniel

2016-07-01

In Crull (Found Phys 45:1019-1045, 2015) it is argued that, in order to confront outstanding problems in cosmology and quantum gravity, interpretational aspects of quantum theory can by bypassed because decoherence is able to resolve them. As a result, Crull (Found Phys 45:1019-1045, 2015) concludes that our focus on conceptual and interpretational issues, while dealing with such matters in Okon and Sudarsky (Found Phys 44:114-143, 2014), is avoidable and even pernicious. Here we will defend our position by showing in detail why decoherence does not help in the resolution of foundational questions in quantum mechanics, such as the measurement problem or the emergence of classicality.

Experimental demonstration of a BDCZ quantum repeater node.

PubMed

Yuan, Zhen-Sheng; Chen, Yu-Ao; Zhao, Bo; Chen, Shuai; Schmiedmayer, Jörg; Pan, Jian-Wei

2008-08-28

Quantum communication is a method that offers efficient and secure ways for the exchange of information in a network. Large-scale quantum communication (of the order of 100 km) has been achieved; however, serious problems occur beyond this distance scale, mainly due to inevitable photon loss in the transmission channel. Quantum communication eventually fails when the probability of a dark count in the photon detectors becomes comparable to the probability that a photon is correctly detected. To overcome this problem, Briegel, Dür, Cirac and Zoller (BDCZ) introduced the concept of quantum repeaters, combining entanglement swapping and quantum memory to efficiently extend the achievable distances. Although entanglement swapping has been experimentally demonstrated, the implementation of BDCZ quantum repeaters has proved challenging owing to the difficulty of integrating a quantum memory. Here we realize entanglement swapping with storage and retrieval of light, a building block of the BDCZ quantum repeater. We follow a scheme that incorporates the strategy of BDCZ with atomic quantum memories. Two atomic ensembles, each originally entangled with a single emitted photon, are projected into an entangled state by performing a joint Bell state measurement on the two single photons after they have passed through a 300-m fibre-based communication channel. The entanglement is stored in the atomic ensembles and later verified by converting the atomic excitations into photons. Our method is intrinsically phase insensitive and establishes the essential element needed to realize quantum repeaters with stationary atomic qubits as quantum memories and flying photonic qubits as quantum messengers.

Generalized Finsler geometric continuum physics with applications in fracture and phase transformations

NASA Astrophysics Data System (ADS)

Clayton, J. D.

2017-02-01

A theory of deformation of continuous media based on concepts from Finsler differential geometry is presented. The general theory accounts for finite deformations, nonlinear elasticity, and changes in internal state of the material, the latter represented by elements of a state vector of generalized Finsler space whose entries consist of one or more order parameter(s). Two descriptive representations of the deformation gradient are considered. The first invokes an additive decomposition and is applied to problems involving localized inelastic deformation mechanisms such as fracture. The second invokes a multiplicative decomposition and is applied to problems involving distributed deformation mechanisms such as phase transformations or twinning. Appropriate free energy functions are posited for each case, and Euler-Lagrange equations of equilibrium are derived. Solutions are obtained for specific problems of tensile fracture of an elastic cylinder and for amorphization of a crystal under spherical and uniaxial compression. The Finsler-based approach is demonstrated to be more general and potentially more physically descriptive than existing hyperelasticity models couched in Riemannian geometry or Euclidean space, without incorporation of supplementary ad hoc equations or spurious fitting parameters. Predictions for single crystals of boron carbide ceramic agree qualitatively, and in many instances quantitatively, with results from physical experiments and atomic simulations involving structural collapse and failure of the crystal along its c-axis.

Local subsystems in gauge theory and gravity

DOE PAGES

Donnelly, William; Freidel, Laurent

2016-09-16

We consider the problem of defining localized subsystems in gauge theory and gravity. Such systems are associated to spacelike hypersurfaces with boundaries and provide the natural setting for studying entanglement entropy of regions of space. We present a general formalism to associate a gauge-invariant classical phase space to a spatial slice with boundary by introducing new degrees of freedom on the boundary. In Yang-Mills theory the new degrees of freedom are a choice of gauge on the boundary, transformations of which are generated by the normal component of the nonabelian electric field. In general relativity the new degrees of freedommore » are the location of a codimension-2 surface and a choice of conformal normal frame. These degrees of freedom transform under a group of surface symmetries, consisting of diffeomorphisms of the codimension-2 boundary, and position-dependent linear deformations of its normal plane. We find the observables which generate these symmetries, consisting of the conformal normal metric and curvature of the normal connection. We discuss the implications for the problem of defining entanglement entropy in quantum gravity. Finally, our work suggests that the Bekenstein-Hawking entropy may arise from the different ways of gluing together two partial Cauchy surfaces at a cross-section of the horizon.« less

Quantum factorization of 143 on a dipolar-coupling nuclear magnetic resonance system.

PubMed

Xu, Nanyang; Zhu, Jing; Lu, Dawei; Zhou, Xianyi; Peng, Xinhua; Du, Jiangfeng

2012-03-30

Quantum algorithms could be much faster than classical ones in solving the factoring problem. Adiabatic quantum computation for this is an alternative approach other than Shor's algorithm. Here we report an improved adiabatic factoring algorithm and its experimental realization to factor the number 143 on a liquid-crystal NMR quantum processor with dipole-dipole couplings. We believe this to be the largest number factored in quantum-computation realizations, which shows the practical importance of adiabatic quantum algorithms.

Snyder-like modified gravity in Newton's spacetime

NASA Astrophysics Data System (ADS)

Leiva, Carlos

This work is focused on searching a geodesic interpretation of the dynamics of a particle under the effects of a Snyder-like deformation in the background of the Kepler problem. In order to accomplish that task, a Newtonian spacetime is used. Newtonian spacetime is not a metric manifold, but allows to introduce a torsion-free connection in order to interpret the dynamic equations of the deformed Kepler problem as geodesics in a curved spacetime. These geodesics and the curvature terms of the Riemann and Ricci tensors show a mass and a fundamental length dependence as expected, but are velocity-independent that is a feature present in other classical approaches to the problem. In this sense, the effect of introducing a deformed algebra is examined and the corresponding curvature terms calculated, as well as the modifications of the integrals of motion.

Schwarzschild, Karl (1873-1916)

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

Mathematical physicist, born in Frankfurt am Main, Germany, at first worked on celestial mechanics, including POINCARÉ's theory of rotating bodies, the tidal deformation of moons and LAPLACE's origin of the solar system. He became professor at Göttingen and Potsdam. He wrote on relativity and quantum theory. He early on proposed that space was non-Euclidean, giving a lower limit for the radius of...

Deformations of W A,D,E SCFTs

DOE PAGES

Intriligator, Ken; Nardoni, Emily

2016-09-08

We discuss aspects of theories with superpotentials given by Arnold’s A, D, E singularities, particularly the novelties that arise when the fields are matrices. We focus on 4d N=1 variants of susy QCD, with U(N c ) or SU(N c ) gauge group, N f fundamental flavors, and adjoint matter fields X and Y appearing in W A,D,E (X, Y) superpotentials. Many of our considerations also apply in other possible contexts for matrix-variable W A,D,E . The 4d W A,D,E SQCD-type theories RG flow to superconformal field theories, and there are proposed duals in the literature for the W Ak,more » W Dk, and W E7 cases. As we review, the W Deven and W E7 duals rely on a conjectural, quantum truncation of the chiral ring. We explore these issues by considering various deformations of the W A,D,E superpotentials, and the resulting RG flows and IR theories. Rather than finding supporting evidence for the quantum truncation and W Deven and W E7 duals, we note some challenging evidence to the contrary.« less

Number-phase entropic squeezing and nonclassical properties of a three-level atom interacting with a two-mode field: intensity-dependent coupling, deformed Kerr medium, and detuning effects

NASA Astrophysics Data System (ADS)

Faghihi, Mohammad Javad; Tavassoly, Mohammad Kazem

2013-11-01

In this paper, we follow our presented model in J. Opt. Soc. Am. B {\\bf 30}, 1109--1117 (2013), in which the interaction between a $\\Lambda$-type three-level atom and a quantized two-mode radiation field in a cavity in the presence of nonlinearities is studied. After giving a brief review on the procedure of obtaining the state vector of the atom-field system, some further interesting and important physical features (which are of particular interest in the quantum optics field of research) of the whole system state, i.e., the number-phase entropic uncertainty relation (based on the two-mode Pegg-Barnett formalism) and some of the nonclassicality signs consist of sub-Poissonian statistics, Cauchy-Schwartz inequality and two kinds of squeezing phenomenon are investigated. During our presentation, the effects of intensity-dependent coupling, deformed Kerr medium and the detuning parameters on the depth and domain of each of the mentioned nonclassical criteria of the considered quantum system are studied, in detail. It is shown that each of the mentioned nonclassicality aspects can be obtained by appropriately choosing the related parameters.