QDENSITY—A Mathematica quantum computer simulation

NASA Astrophysics Data System (ADS)

Juliá-Díaz, Bruno; Burdis, Joseph M.; Tabakin, Frank

2009-03-01

This Mathematica 6.0 package is a simulation of a Quantum Computer. The program provides a modular, instructive approach for generating the basic elements that make up a quantum circuit. The main emphasis is on using the density matrix, although an approach using state vectors is also implemented in the package. The package commands are defined in Qdensity.m which contains the tools needed in quantum circuits, e.g., multiqubit kets, projectors, gates, etc. New version program summaryProgram title: QDENSITY 2.0 Catalogue identifier: ADXH_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXH_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 26 055 No. of bytes in distributed program, including test data, etc.: 227 540 Distribution format: tar.gz Programming language: Mathematica 6.0 Operating system: Any which supports Mathematica; tested under Microsoft Windows XP, Macintosh OS X, and Linux FC4 Catalogue identifier of previous version: ADXH_v1_0 Journal reference of previous version: Comput. Phys. Comm. 174 (2006) 914 Classification: 4.15 Does the new version supersede the previous version?: Offers an alternative, more up to date, implementation Nature of problem: Analysis and design of quantum circuits, quantum algorithms and quantum clusters. Solution method: A Mathematica package is provided which contains commands to create and analyze quantum circuits. Several Mathematica notebooks containing relevant examples: Teleportation, Shor's Algorithm and Grover's search are explained in detail. A tutorial, Tutorial.nb is also enclosed. Reasons for new version: The package has been updated to make it fully compatible with Mathematica 6.0 Summary of revisions: The package has been updated to make it fully compatible with Mathematica 6.0 Running time: Most examples

Numerical simulation of NQR/NMR: Applications in quantum computing.

PubMed

Possa, Denimar; Gaudio, Anderson C; Freitas, Jair C C

2011-04-01

A numerical simulation program able to simulate nuclear quadrupole resonance (NQR) as well as nuclear magnetic resonance (NMR) experiments is presented, written using the Mathematica package, aiming especially applications in quantum computing. The program makes use of the interaction picture to compute the effect of the relevant nuclear spin interactions, without any assumption about the relative size of each interaction. This makes the program flexible and versatile, being useful in a wide range of experimental situations, going from NQR (at zero or under small applied magnetic field) to high-field NMR experiments. Some conditions specifically required for quantum computing applications are implemented in the program, such as the possibility of use of elliptically polarized radiofrequency and the inclusion of first- and second-order terms in the average Hamiltonian expansion. A number of examples dealing with simple NQR and quadrupole-perturbed NMR experiments are presented, along with the proposal of experiments to create quantum pseudopure states and logic gates using NQR. The program and the various application examples are freely available through the link http://www.profanderson.net/files/nmr_nqr.php. Copyright © 2011 Elsevier Inc. All rights reserved.

Duality quantum algorithm efficiently simulates open quantum systems

PubMed Central

Wei, Shi-Jie; Ruan, Dong; Long, Gui-Lu

2016-01-01

Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d3) in contrast to O(d4) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm. PMID:27464855

Adaptive quantum computation in changing environments using projective simulation

NASA Astrophysics Data System (ADS)

Tiersch, M.; Ganahl, E. J.; Briegel, H. J.

2015-08-01

Quantum information processing devices need to be robust and stable against external noise and internal imperfections to ensure correct operation. In a setting of measurement-based quantum computation, we explore how an intelligent agent endowed with a projective simulator can act as controller to adapt measurement directions to an external stray field of unknown magnitude in a fixed direction. We assess the agent’s learning behavior in static and time-varying fields and explore composition strategies in the projective simulator to improve the agent’s performance. We demonstrate the applicability by correcting for stray fields in a measurement-based algorithm for Grover’s search. Thereby, we lay out a path for adaptive controllers based on intelligent agents for quantum information tasks.

Adaptive quantum computation in changing environments using projective simulation

PubMed Central

Tiersch, M.; Ganahl, E. J.; Briegel, H. J.

2015-01-01

Quantum information processing devices need to be robust and stable against external noise and internal imperfections to ensure correct operation. In a setting of measurement-based quantum computation, we explore how an intelligent agent endowed with a projective simulator can act as controller to adapt measurement directions to an external stray field of unknown magnitude in a fixed direction. We assess the agent’s learning behavior in static and time-varying fields and explore composition strategies in the projective simulator to improve the agent’s performance. We demonstrate the applicability by correcting for stray fields in a measurement-based algorithm for Grover’s search. Thereby, we lay out a path for adaptive controllers based on intelligent agents for quantum information tasks. PMID:26260263

A space-efficient quantum computer simulator suitable for high-speed FPGA implementation

NASA Astrophysics Data System (ADS)

Frank, Michael P.; Oniciuc, Liviu; Meyer-Baese, Uwe H.; Chiorescu, Irinel

2009-05-01

Conventional vector-based simulators for quantum computers are quite limited in the size of the quantum circuits they can handle, due to the worst-case exponential growth of even sparse representations of the full quantum state vector as a function of the number of quantum operations applied. However, this exponential-space requirement can be avoided by using general space-time tradeoffs long known to complexity theorists, which can be appropriately optimized for this particular problem in a way that also illustrates some interesting reformulations of quantum mechanics. In this paper, we describe the design and empirical space/time complexity measurements of a working software prototype of a quantum computer simulator that avoids excessive space requirements. Due to its space-efficiency, this design is well-suited to embedding in single-chip environments, permitting especially fast execution that avoids access latencies to main memory. We plan to prototype our design on a standard FPGA development board.

Higher-order methods for simulations on quantum computers

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

Sornborger, A.T.; Stewart, E.D.

1999-09-01

To implement many-qubit gates for use in quantum simulations on quantum computers efficiently, we develop and present methods reexpressing exp[[minus]i(H[sub 1]+H[sub 2]+[center dot][center dot][center dot])[Delta]t] as a product of factors exp[[minus]iH[sub 1][Delta]t], exp[[minus]iH[sub 2][Delta]t],[hor ellipsis], which is accurate to third or fourth order in [Delta]t. The methods we derive are an extended form of the symplectic method, and can also be used for an integration of classical Hamiltonians on classical computers. We derive both integral and irrational methods, and find the most efficient methods in both cases. [copyright] [ital 1999] [ital The American Physical Society

Undergraduate computational physics projects on quantum computing

NASA Astrophysics Data System (ADS)

Candela, D.

2015-08-01

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

Bravyi-Kitaev Superfast simulation of electronic structure on a quantum computer.

PubMed

Setia, Kanav; Whitfield, James D

2018-04-28

Present quantum computers often work with distinguishable qubits as their computational units. In order to simulate indistinguishable fermionic particles, it is first required to map the fermionic state to the state of the qubits. The Bravyi-Kitaev Superfast (BKSF) algorithm can be used to accomplish this mapping. The BKSF mapping has connections to quantum error correction and opens the door to new ways of understanding fermionic simulation in a topological context. Here, we present the first detailed exposition of the BKSF algorithm for molecular simulation. We provide the BKSF transformed qubit operators and report on our implementation of the BKSF fermion-to-qubits transform in OpenFermion. In this initial study of a hydrogen molecule we have compared BKSF, Jordan-Wigner, and Bravyi-Kitaev transforms under the Trotter approximation. The gate count to implement BKSF is lower than Jordan-Wigner but higher than Bravyi-Kitaev. We considered different orderings of the exponentiated terms and found lower Trotter errors than the previously reported for Jordan-Wigner and Bravyi-Kitaev algorithms. These results open the door to the further study of the BKSF algorithm for quantum simulation.

Elucidating reaction mechanisms on quantum computers.

PubMed

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

2017-07-18

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

Elucidating reaction mechanisms on quantum computers

PubMed Central

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

2017-01-01

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

Elucidating reaction mechanisms on quantum computers

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

QDENSITY—A Mathematica Quantum Computer simulation

NASA Astrophysics Data System (ADS)

Juliá-Díaz, Bruno; Burdis, Joseph M.; Tabakin, Frank

2006-06-01

This Mathematica 5.2 package is a simulation of a Quantum Computer. The program provides a modular, instructive approach for generating the basic elements that make up a quantum circuit. The main emphasis is on using the density matrix, although an approach using state vectors is also implemented in the package. The package commands are defined in Qdensity.m which contains the tools needed in quantum circuits, e.g., multiqubit kets, projectors, gates, etc. Selected examples of the basic commands are presented here and a tutorial notebook, Tutorial.nb is provided with the package (available on our website) that serves as a full guide to the package. Finally, application is made to a variety of relevant cases, including Teleportation, Quantum Fourier transform, Grover's search and Shor's algorithm, in separate notebooks: QFT.nb, Teleportation.nb, Grover.nb and Shor.nb where each algorithm is explained in detail. Finally, two examples of the construction and manipulation of cluster states, which are part of "one way computing" ideas, are included as an additional tool in the notebook Cluster.nb. A Mathematica palette containing most commands in QDENSITY is also included: QDENSpalette.nb. Program summaryTitle of program: QDENSITY Catalogue identifier: ADXH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADXH_v1_0 Program available from: CPC Program Library, Queen's University of Belfast, N. Ireland Operating systems: Any which supports Mathematica; tested under Microsoft Windows XP, Macintosh OS X, and Linux FC4 Programming language used: Mathematica 5.2 No. of bytes in distributed program, including test data, etc.: 180 581 No. of lines in distributed program, including test data, etc.: 19 382 Distribution format: tar.gz Method of solution: A Mathematica package is provided which contains commands to create and analyze quantum circuits. Several Mathematica notebooks containing relevant examples: Teleportation, Shor's Algorithm and Grover's search are

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.

Architectures for Quantum Simulation Showing a Quantum Speedup

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Quantum Spin Glasses, Annealing and Computation

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

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

Efficient free energy calculations of quantum systems through computer simulations

NASA Astrophysics Data System (ADS)

Antonelli, Alex; Ramirez, Rafael; Herrero, Carlos; Hernandez, Eduardo

2009-03-01

In general, the classical limit is assumed in computer simulation calculations of free energy. This approximation, however, is not justifiable for a class of systems in which quantum contributions for the free energy cannot be neglected. The inclusion of quantum effects is important for the determination of reliable phase diagrams of these systems. In this work, we present a new methodology to compute the free energy of many-body quantum systems [1]. This methodology results from the combination of the path integral formulation of statistical mechanics and efficient non-equilibrium methods to estimate free energy, namely, the adiabatic switching and reversible scaling methods. A quantum Einstein crystal is used as a model to show the accuracy and reliability the methodology. This new method is applied to the calculation of solid-liquid coexistence properties of neon. Our findings indicate that quantum contributions to properties such as, melting point, latent heat of fusion, entropy of fusion, and slope of melting line can be up to 10% of the calculated values using the classical approximation. [1] R. M. Ramirez, C. P. Herrero, A. Antonelli, and E. R. Hernández, Journal of Chemical Physics 129, 064110 (2008)

The Promise of Quantum Simulation.

PubMed

Muller, Richard P; Blume-Kohout, Robin

2015-08-25

Quantum simulations promise to be one of the primary applications of quantum computers, should one be constructed. This article briefly summarizes the history of quantum simulation in light of the recent result of Wang and co-workers, demonstrating calculation of the ground and excited states for a HeH(+) molecule, and concludes with a discussion of why this and other recent progress in the field suggest that quantum simulations of quantum chemistry have a bright future.

The promise of quantum simulation

DOE PAGES

Muller, Richard P.; Blume-Kohout, Robin

2015-07-21

In this study, quantum simulations promise to be one of the primary applications of quantum computers, should one be constructed. This article briefly summarizes the history of quantum simulation in light of the recent result of Wang and co-workers, demonstrating calculation of the ground and excited states for a HeH + molecule, and concludes with a discussion of why this and other recent progress in the field suggest that quantum simulations of quantum chemistry have a bright future.

Can one trust quantum simulators?

PubMed

Hauke, Philipp; Cucchietti, Fernando M; Tagliacozzo, Luca; Deutsch, Ivan; Lewenstein, Maciej

2012-08-01

Various fundamental phenomena of strongly correlated quantum systems such as high-T(c) superconductivity, the fractional quantum-Hall effect and quark confinement are still awaiting a universally accepted explanation. The main obstacle is the computational complexity of solving even the most simplified theoretical models which are designed to capture the relevant quantum correlations of the many-body system of interest. In his seminal 1982 paper (Feynman 1982 Int. J. Theor. Phys. 21 467), Richard Feynman suggested that such models might be solved by 'simulation' with a new type of computer whose constituent parts are effectively governed by a desired quantum many-body dynamics. Measurements on this engineered machine, now known as a 'quantum simulator,' would reveal some unknown or difficult to compute properties of a model of interest. We argue that a useful quantum simulator must satisfy four conditions: relevance, controllability, reliability and efficiency. We review the current state of the art of digital and analog quantum simulators. Whereas so far the majority of the focus, both theoretically and experimentally, has been on controllability of relevant models, we emphasize here the need for a careful analysis of reliability and efficiency in the presence of imperfections. We discuss how disorder and noise can impact these conditions, and illustrate our concerns with novel numerical simulations of a paradigmatic example: a disordered quantum spin chain governed by the Ising model in a transverse magnetic field. We find that disorder can decrease the reliability of an analog quantum simulator of this model, although large errors in local observables are introduced only for strong levels of disorder. We conclude that the answer to the question 'Can we trust quantum simulators?' is … to some extent.

Can one trust quantum simulators?

NASA Astrophysics Data System (ADS)

Hauke, Philipp; Cucchietti, Fernando M.; Tagliacozzo, Luca; Deutsch, Ivan; Lewenstein, Maciej

2012-08-01

Various fundamental phenomena of strongly correlated quantum systems such as high-Tc superconductivity, the fractional quantum-Hall effect and quark confinement are still awaiting a universally accepted explanation. The main obstacle is the computational complexity of solving even the most simplified theoretical models which are designed to capture the relevant quantum correlations of the many-body system of interest. In his seminal 1982 paper (Feynman 1982 Int. J. Theor. Phys. 21 467), Richard Feynman suggested that such models might be solved by ‘simulation’ with a new type of computer whose constituent parts are effectively governed by a desired quantum many-body dynamics. Measurements on this engineered machine, now known as a ‘quantum simulator,’ would reveal some unknown or difficult to compute properties of a model of interest. We argue that a useful quantum simulator must satisfy four conditions: relevance, controllability, reliability and efficiency. We review the current state of the art of digital and analog quantum simulators. Whereas so far the majority of the focus, both theoretically and experimentally, has been on controllability of relevant models, we emphasize here the need for a careful analysis of reliability and efficiency in the presence of imperfections. We discuss how disorder and noise can impact these conditions, and illustrate our concerns with novel numerical simulations of a paradigmatic example: a disordered quantum spin chain governed by the Ising model in a transverse magnetic field. We find that disorder can decrease the reliability of an analog quantum simulator of this model, although large errors in local observables are introduced only for strong levels of disorder. We conclude that the answer to the question ‘Can we trust quantum simulators?’ is … to some extent.

Possible 6-qubit NMR quantum computer device material; simulator of the NMR line width

NASA Astrophysics Data System (ADS)

Hashi, K.; Kitazawa, H.; Shimizu, T.; Goto, A.; Eguchi, S.; Ohki, S.

2002-12-01

For an NMR quantum computer, splitting of an NMR spectrum must be larger than a line width. In order to find a best device material for a solid-state NMR quantum computer, we have made a simulation program to calculate the NMR line width due to the nuclear dipole field by the 2nd moment method. The program utilizes the lattice information prepared by commercial software to draw a crystal structure. By applying this program, we can estimate the NMR line width due to the nuclear dipole field without measurements and find a candidate material for a 6-qubit solid-state NMR quantum computer device.

Intermediate quantum maps for quantum computation

NASA Astrophysics Data System (ADS)

Giraud, O.; Georgeot, B.

2005-10-01

We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity decay or spectral statistics. We study their matrix elements and entanglement production and show that they converge with time to distributions which differ from random matrix predictions. A randomized version of these maps can be implemented even more economically and yields pseudorandom operators with original properties, enabling, for example, one to produce fractal random vectors. These algorithms are within reach of present-day quantum computers.

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

PubMed

Tempel, David G; Aspuru-Guzik, Alán

2012-01-01

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

Electromechanical quantum simulators

NASA Astrophysics Data System (ADS)

Tacchino, F.; Chiesa, A.; LaHaye, M. D.; Carretta, S.; Gerace, D.

2018-06-01

Digital quantum simulators are among the most appealing applications of a quantum computer. Here we propose a universal, scalable, and integrated quantum computing platform based on tunable nonlinear electromechanical nano-oscillators. It is shown that very high operational fidelities for single- and two-qubits gates can be achieved in a minimal architecture, where qubits are encoded in the anharmonic vibrational modes of mechanical nanoresonators, whose effective coupling is mediated by virtual fluctuations of an intermediate superconducting artificial atom. An effective scheme to induce large single-phonon nonlinearities in nanoelectromechanical devices is explicitly discussed, thus opening the route to experimental investigation in this direction. Finally, we explicitly show the very high fidelities that can be reached for the digital quantum simulation of model Hamiltonians, by using realistic experimental parameters in state-of-the-art devices, and considering the transverse field Ising model as a paradigmatic example.

Majorana-Based Fermionic Quantum Computation.

PubMed

O'Brien, T E; Rożek, P; Akhmerov, A R

2018-06-01

Because Majorana zero modes store quantum information nonlocally, they are protected from noise, and have been proposed as a building block for a quantum computer. We show how to use the same protection from noise to implement universal fermionic quantum computation. Our architecture requires only two Majorana modes to encode a fermionic quantum degree of freedom, compared to alternative implementations which require a minimum of four Majorana modes for a spin quantum degree of freedom. The fermionic degrees of freedom support both unitary coupled cluster variational quantum eigensolver and quantum phase estimation algorithms, proposed for quantum chemistry simulations. Because we avoid the Jordan-Wigner transformation, our scheme has a lower overhead for implementing both of these algorithms, allowing for simulation of the Trotterized Hubbard Hamiltonian in O(1) time per unitary step. We finally demonstrate magic state distillation in our fermionic architecture, giving a universal set of topologically protected fermionic quantum gates.

Majorana-Based Fermionic Quantum Computation

NASA Astrophysics Data System (ADS)

O'Brien, T. E.; RoŻek, P.; Akhmerov, A. R.

2018-06-01

Because Majorana zero modes store quantum information nonlocally, they are protected from noise, and have been proposed as a building block for a quantum computer. We show how to use the same protection from noise to implement universal fermionic quantum computation. Our architecture requires only two Majorana modes to encode a fermionic quantum degree of freedom, compared to alternative implementations which require a minimum of four Majorana modes for a spin quantum degree of freedom. The fermionic degrees of freedom support both unitary coupled cluster variational quantum eigensolver and quantum phase estimation algorithms, proposed for quantum chemistry simulations. Because we avoid the Jordan-Wigner transformation, our scheme has a lower overhead for implementing both of these algorithms, allowing for simulation of the Trotterized Hubbard Hamiltonian in O (1 ) time per unitary step. We finally demonstrate magic state distillation in our fermionic architecture, giving a universal set of topologically protected fermionic quantum gates.

pyCTQW: A continuous-time quantum walk simulator on distributed memory computers

NASA Astrophysics Data System (ADS)

Izaac, Josh A.; Wang, Jingbo B.

2015-01-01

In the general field of quantum information and computation, quantum walks are playing an increasingly important role in constructing physical models and quantum algorithms. We have recently developed a distributed memory software package pyCTQW, with an object-oriented Python interface, that allows efficient simulation of large multi-particle CTQW (continuous-time quantum walk)-based systems. In this paper, we present an introduction to the Python and Fortran interfaces of pyCTQW, discuss various numerical methods of calculating the matrix exponential, and demonstrate the performance behavior of pyCTQW on a distributed memory cluster. In particular, the Chebyshev and Krylov-subspace methods for calculating the quantum walk propagation are provided, as well as methods for visualization and data analysis.

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.

Decoherence in adiabatic quantum computation

NASA Astrophysics Data System (ADS)

Albash, Tameem; Lidar, Daniel A.

2015-06-01

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

Hidden Statistics Approach to Quantum Simulations

NASA Technical Reports Server (NTRS)

Zak, Michail

2010-01-01

Recent advances in quantum information theory have inspired an explosion of interest in new quantum algorithms for solving hard computational (quantum and non-quantum) problems. The basic principle of quantum computation is that the quantum properties can be used to represent structure data, and that quantum mechanisms can be devised and built to perform operations with this data. Three basic non-classical properties of quantum mechanics superposition, entanglement, and direct-product decomposability were main reasons for optimism about capabilities of quantum computers that promised simultaneous processing of large massifs of highly correlated data. Unfortunately, these advantages of quantum mechanics came with a high price. One major problem is keeping the components of the computer in a coherent state, as the slightest interaction with the external world would cause the system to decohere. That is why the hardware implementation of a quantum computer is still unsolved. The basic idea of this work is to create a new kind of dynamical system that would preserve the main three properties of quantum physics superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. In other words, such a system would reinforce the advantages and minimize limitations of both quantum and classical aspects. Based upon a concept of hidden statistics, a new kind of dynamical system for simulation of Schroedinger equation is proposed. The system represents a modified Madelung version of Schroedinger equation. It preserves superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods. Such an optimal combination of characteristics is a perfect match for simulating quantum systems. The model includes a transitional component of quantum potential (that has been overlooked in previous treatment of the Madelung equation). The role of the

Quantum Accelerators for High-performance Computing Systems

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

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

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

Quantum phases with differing computational power.

PubMed

Cui, Jian; Gu, Mile; Kwek, Leong Chuan; Santos, Marcelo França; Fan, Heng; Vedral, Vlatko

2012-05-01

The observation that concepts from quantum information has generated many alternative indicators of quantum phase transitions hints that quantum phase transitions possess operational significance with respect to the processing of quantum information. Yet, studies on whether such transitions lead to quantum phases that differ in their capacity to process information remain limited. Here we show that there exist quantum phase transitions that cause a distinct qualitative change in our ability to simulate certain quantum systems under perturbation of an external field by local operations and classical communication. In particular, we show that in certain quantum phases of the XY model, adiabatic perturbations of the external magnetic field can be simulated by local spin operations, whereas the resulting effect within other phases results in coherent non-local interactions. We discuss the potential implications to adiabatic quantum computation, where a computational advantage exists only when adiabatic perturbation results in coherent multi-body interactions.

A Generic Simulation Framework for Non-Entangled based Experimental Quantum Cryptography and Communication: Quantum Cryptography and Communication Simulator (QuCCs)

NASA Astrophysics Data System (ADS)

Buhari, Abudhahir; Zukarnain, Zuriati Ahmad; Khalid, Roszelinda; Zakir Dato', Wira Jaafar Ahmad

2016-11-01

The applications of quantum information science move towards bigger and better heights for the next generation technology. Especially, in the field of quantum cryptography and quantum computation, the world already witnessed various ground-breaking tangible product and promising results. Quantum cryptography is one of the mature field from quantum mechanics and already available in the markets. The current state of quantum cryptography is still under various researches in order to reach the heights of digital cryptography. The complexity of quantum cryptography is higher due to combination of hardware and software. The lack of effective simulation tool to design and analyze the quantum cryptography experiments delays the reaching distance of the success. In this paper, we propose a framework to achieve an effective non-entanglement based quantum cryptography simulation tool. We applied hybrid simulation technique i.e. discrete event, continuous event and system dynamics. We also highlight the limitations of a commercial photonic simulation tool based experiments. Finally, we discuss ideas for achieving one-stop simulation package for quantum based secure key distribution experiments. All the modules of simulation framework are viewed from the computer science perspective.

Quantum Simulation of Tunneling in Small Systems

PubMed Central

Sornborger, Andrew T.

2012-01-01

A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because of the number of gates and qubits necessary, however, digital quantum particle simulations remain untested. A contributing factor to the system size required is the number of ancillary qubits needed to implement matrix exponentials of the potential operator. Here, we show that a set of tunneling problems may be investigated with no ancillary qubits and a cost of one single-qubit operator per time step for the potential evolution, eliminating at least half of the quantum gates required for the algorithm and more than that in the general case. Such simulations are within reach of current quantum computer architectures. PMID:22916333

Quantum simulation from the bottom up: the case of rebits

NASA Astrophysics Data System (ADS)

Enshan Koh, Dax; Yuezhen Niu, Murphy; Yoder, Theodore J.

2018-05-01

Typically, quantum mechanics is thought of as a linear theory with unitary evolution governed by the Schrödinger equation. While this is technically true and useful for a physicist, with regards to computation it is an unfortunately narrow point of view. Just as a classical computer can simulate highly nonlinear functions of classical states, so too can the more general quantum computer simulate nonlinear evolutions of quantum states. We detail one particular simulation of nonlinearity on a quantum computer, showing how the entire class of -unitary evolutions (on n qubits) can be simulated using a unitary, real-amplitude quantum computer (consisting of n  +  1 qubits in total). These operators can be represented as the sum of a linear and antilinear operator, and add an intriguing new set of nonlinear quantum gates to the toolbox of the quantum algorithm designer. Furthermore, a subgroup of these nonlinear evolutions, called the -Cliffords, can be efficiently classically simulated, by making use of the fact that Clifford operators can simulate non-Clifford (in fact, non-linear) operators. This perspective of using the physical operators that we have to simulate non-physical ones that we do not is what we call bottom-up simulation, and we give some examples of its broader implications.

ASCR Workshop on Quantum Computing for Science

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

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

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

Computer simulation of liquid-vapor coexistence of confined quantum fluids

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

Trejos, Víctor M.; Gil-Villegas, Alejandro, E-mail: gil@fisica.ugto.mx; Martinez, Alejandro

2013-11-14

The liquid-vapor coexistence (LV) of bulk and confined quantum fluids has been studied by Monte Carlo computer simulation for particles interacting via a semiclassical effective pair potential V{sub eff}(r) = V{sub LJ} + V{sub Q}, where V{sub LJ} is the Lennard-Jones 12-6 potential (LJ) and V{sub Q} is the first-order Wigner-Kirkwood (WK-1) quantum potential, that depends on β = 1/kT and de Boer's quantumness parameter Λ=h/σ√(mε), where k and h are the Boltzmann's and Planck's constants, respectively, m is the particle's mass, T is the temperature of the system, and σ and ε are the LJ potential parameters. The non-conformalmore » properties of the system of particles interacting via the effective pair potential V{sub eff}(r) are due to Λ, since the LV phase diagram is modified by varying Λ. We found that the WK-1 system gives an accurate description of the LV coexistence for bulk phases of several quantum fluids, obtained by the Gibbs Ensemble Monte Carlo method (GEMC). Confinement effects were introduced using the Canonical Ensemble (NVT) to simulate quantum fluids contained within parallel hard walls separated by a distance L{sub p}, within the range 2σ ⩽ L{sub p} ⩽ 6σ. The critical temperature of the system is reduced by decreasing L{sub p} and increasing Λ, and the liquid-vapor transition is not longer observed for L{sub p}/σ < 2, in contrast to what has been observed for the classical system.« less

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.

Experimental quantum computing without entanglement.

PubMed

Lanyon, B P; Barbieri, M; Almeida, M P; White, A G

2008-11-14

Deterministic quantum computation with one pure qubit (DQC1) is an efficient model of computation that uses highly mixed states. Unlike pure-state models, its power is not derived from the generation of a large amount of entanglement. Instead it has been proposed that other nonclassical correlations are responsible for the computational speedup, and that these can be captured by the quantum discord. In this Letter we implement DQC1 in an all-optical architecture, and experimentally observe the generated correlations. We find no entanglement, but large amounts of quantum discord-except in three cases where an efficient classical simulation is always possible. Our results show that even fully separable, highly mixed, states can contain intrinsically quantum mechanical correlations and that these could offer a valuable resource for quantum information technologies.

Quantum simulation of a quantum stochastic walk

NASA Astrophysics Data System (ADS)

Govia, Luke C. G.; Taketani, Bruno G.; Schuhmacher, Peter K.; Wilhelm, Frank K.

2017-03-01

The study of quantum walks has been shown to have a wide range of applications in areas such as artificial intelligence, the study of biological processes, and quantum transport. The quantum stochastic walk (QSW), which allows for incoherent movement of the walker, and therefore, directionality, is a generalization on the fully coherent quantum walk. While a QSW can always be described in Lindblad formalism, this does not mean that it can be microscopically derived in the standard weak-coupling limit under the Born-Markov approximation. This restricts the class of QSWs that can be experimentally realized in a simple manner. To circumvent this restriction, we introduce a technique to simulate open system evolution on a fully coherent quantum computer, using a quantum trajectories style approach. We apply this technique to a broad class of QSWs, and show that they can be simulated with minimal experimental resources. Our work opens the path towards the experimental realization of QSWs on large graphs with existing quantum technologies.

Cloud Quantum Computing of an Atomic Nucleus

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Cloud Quantum Computing of an Atomic Nucleus

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

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

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

Cloud Quantum Computing of an Atomic Nucleus.

PubMed

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

2018-05-25

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

Cloud Quantum Computing of an Atomic Nucleus

DOE PAGES

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

2018-05-23

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

Embracing the quantum limit in silicon computing.

PubMed

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

2011-11-16

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

Contextuality supplies the 'magic' for quantum computation.

PubMed

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

2014-06-19

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

Quantum Computation

NASA Astrophysics Data System (ADS)

Aharonov, Dorit

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

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

PubMed

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

2017-02-24

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

Ramsey numbers and adiabatic quantum computing.

PubMed

Gaitan, Frank; Clark, Lane

2012-01-06

The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.

Computational quantum-classical boundary of noisy commuting quantum circuits

PubMed Central

Fujii, Keisuke; Tamate, Shuhei

2016-01-01

It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projected-entangled-pair-state picture and the Gottesman-Knill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computational quantum-classical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantum-classical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region. PMID:27189039

Computational quantum-classical boundary of noisy commuting quantum circuits.

PubMed

Fujii, Keisuke; Tamate, Shuhei

2016-05-18

It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projected-entangled-pair-state picture and the Gottesman-Knill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computational quantum-classical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantum-classical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region.

Computational quantum-classical boundary of noisy commuting quantum circuits

NASA Astrophysics Data System (ADS)

Fujii, Keisuke; Tamate, Shuhei

2016-05-01

It is often said that the transition from quantum to classical worlds is caused by decoherence originated from an interaction between a system of interest and its surrounding environment. Here we establish a computational quantum-classical boundary from the viewpoint of classical simulatability of a quantum system under decoherence. Specifically, we consider commuting quantum circuits being subject to decoherence. Or equivalently, we can regard them as measurement-based quantum computation on decohered weighted graph states. To show intractability of classical simulation in the quantum side, we utilize the postselection argument and crucially strengthen it by taking noise effect into account. Classical simulatability in the classical side is also shown constructively by using both separable criteria in a projected-entangled-pair-state picture and the Gottesman-Knill theorem for mixed state Clifford circuits. We found that when each qubit is subject to a single-qubit complete-positive-trace-preserving noise, the computational quantum-classical boundary is sharply given by the noise rate required for the distillability of a magic state. The obtained quantum-classical boundary of noisy quantum dynamics reveals a complexity landscape of controlled quantum systems. This paves a way to an experimentally feasible verification of quantum mechanics in a high complexity limit beyond classically simulatable region.

Continuous variable quantum optical simulation for time evolution of quantum harmonic oscillators

PubMed Central

Deng, Xiaowei; Hao, Shuhong; Guo, Hong; Xie, Changde; Su, Xiaolong

2016-01-01

Quantum simulation enables one to mimic the evolution of other quantum systems using a controllable quantum system. Quantum harmonic oscillator (QHO) is one of the most important model systems in quantum physics. To observe the transient dynamics of a QHO with high oscillation frequency directly is difficult. We experimentally simulate the transient behaviors of QHO in an open system during time evolution with an optical mode and a logical operation system of continuous variable quantum computation. The time evolution of an atomic ensemble in the collective spontaneous emission is analytically simulated by mapping the atomic ensemble onto a QHO. The measured fidelity, which is used for quantifying the quality of the simulation, is higher than its classical limit. The presented simulation scheme provides a new tool for studying the dynamic behaviors of QHO. PMID:26961962

Architecture Framework for Trapped-Ion Quantum Computer based on Performance Simulation Tool

NASA Astrophysics Data System (ADS)

Ahsan, Muhammad

The challenge of building scalable quantum computer lies in striking appropriate balance between designing a reliable system architecture from large number of faulty computational resources and improving the physical quality of system components. The detailed investigation of performance variation with physics of the components and the system architecture requires adequate performance simulation tool. In this thesis we demonstrate a software tool capable of (1) mapping and scheduling the quantum circuit on a realistic quantum hardware architecture with physical resource constraints, (2) evaluating the performance metrics such as the execution time and the success probability of the algorithm execution, and (3) analyzing the constituents of these metrics and visualizing resource utilization to identify system components which crucially define the overall performance. Using this versatile tool, we explore vast design space for modular quantum computer architecture based on trapped ions. We find that while success probability is uniformly determined by the fidelity of physical quantum operation, the execution time is a function of system resources invested at various layers of design hierarchy. At physical level, the number of lasers performing quantum gates, impact the latency of the fault-tolerant circuit blocks execution. When these blocks are used to construct meaningful arithmetic circuit such as quantum adders, the number of ancilla qubits for complicated non-clifford gates and entanglement resources to establish long-distance communication channels, become major performance limiting factors. Next, in order to factorize large integers, these adders are assembled into modular exponentiation circuit comprising bulk of Shor's algorithm. At this stage, the overall scaling of resource-constraint performance with the size of problem, describes the effectiveness of chosen design. By matching the resource investment with the pace of advancement in hardware technology

Computer Simulations of Quantum Theory of Hydrogen Atom for Natural Science Education Students in a Virtual Lab

ERIC Educational Resources Information Center

Singh, Gurmukh

2012-01-01

The present article is primarily targeted for the advanced college/university undergraduate students of chemistry/physics education, computational physics/chemistry, and computer science. The most recent software system such as MS Visual Studio .NET version 2010 is employed to perform computer simulations for modeling Bohr's quantum theory of…

Simulation of n-qubit quantum systems. V. Quantum measurements

NASA Astrophysics Data System (ADS)

Radtke, T.; Fritzsche, S.

2010-02-01

The FEYNMAN program has been developed during the last years to support case studies on the dynamics and entanglement of n-qubit quantum registers. Apart from basic transformations and (gate) operations, it currently supports a good number of separability criteria and entanglement measures, quantum channels as well as the parametrizations of various frequently applied objects in quantum information theory, such as (pure and mixed) quantum states, hermitian and unitary matrices or classical probability distributions. With the present update of the FEYNMAN program, we provide a simple access to (the simulation of) quantum measurements. This includes not only the widely-applied projective measurements upon the eigenspaces of some given operator but also single-qubit measurements in various pre- and user-defined bases as well as the support for two-qubit Bell measurements. In addition, we help perform generalized and POVM measurements. Knowing the importance of measurements for many quantum information protocols, e.g., one-way computing, we hope that this update makes the FEYNMAN code an attractive and versatile tool for both, research and education. New version program summaryProgram title: FEYNMAN Catalogue identifier: ADWE_v5_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE_v5_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 27 210 No. of bytes in distributed program, including test data, etc.: 1 960 471 Distribution format: tar.gz Programming language: Maple 12 Computer: Any computer with Maple software installed Operating system: Any system that supports Maple; the program has been tested under Microsoft Windows XP and Linux Classification: 4.15 Catalogue identifier of previous version: ADWE_v4_0 Journal reference of previous version: Comput. Phys. Commun

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

Quantum Computing Architectural Design

NASA Astrophysics Data System (ADS)

West, Jacob; Simms, Geoffrey; Gyure, Mark

2006-03-01

Large scale quantum computers will invariably require scalable architectures in addition to high fidelity gate operations. Quantum computing architectural design (QCAD) addresses the problems of actually implementing fault-tolerant algorithms given physical and architectural constraints beyond those of basic gate-level fidelity. Here we introduce a unified framework for QCAD that enables the scientist to study the impact of varying error correction schemes, architectural parameters including layout and scheduling, and physical operations native to a given architecture. Our software package, aptly named QCAD, provides compilation, manipulation/transformation, multi-paradigm simulation, and visualization tools. We demonstrate various features of the QCAD software package through several examples.

Blind Quantum Signature with Blind Quantum Computation

NASA Astrophysics Data System (ADS)

Li, Wei; Shi, Ronghua; Guo, Ying

2017-04-01

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

Divide and conquer approach to quantum Hamiltonian simulation

NASA Astrophysics Data System (ADS)

Hadfield, Stuart; Papageorgiou, Anargyros

2018-04-01

We show a divide and conquer approach for simulating quantum mechanical systems on quantum computers. We can obtain fast simulation algorithms using Hamiltonian structure. Considering a sum of Hamiltonians we split them into groups, simulate each group separately, and combine the partial results. Simulation is customized to take advantage of the properties of each group, and hence yield refined bounds to the overall simulation cost. We illustrate our results using the electronic structure problem of quantum chemistry, where we obtain significantly improved cost estimates under very mild assumptions.

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

NASA Astrophysics Data System (ADS)

Svore, Krysta

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

Quantum walk computation

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

Kendon, Viv

2014-12-04

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

Efficient Variational Quantum Simulator Incorporating Active Error Minimization

NASA Astrophysics Data System (ADS)

Li, Ying; Benjamin, Simon C.

2017-04-01

One of the key applications for quantum computers will be the simulation of other quantum systems that arise in chemistry, materials science, etc., in order to accelerate the process of discovery. It is important to ask the following question: Can this simulation be achieved using near-future quantum processors, of modest size and under imperfect control, or must it await the more distant era of large-scale fault-tolerant quantum computing? Here, we propose a variational method involving closely integrated classical and quantum coprocessors. We presume that all operations in the quantum coprocessor are prone to error. The impact of such errors is minimized by boosting them artificially and then extrapolating to the zero-error case. In comparison to a more conventional optimized Trotterization technique, we find that our protocol is efficient and appears to be fundamentally more robust against error accumulation.

Quantum decision-maker theory and simulation

NASA Astrophysics Data System (ADS)

Zak, Michail; Meyers, Ronald E.; Deacon, Keith S.

2000-07-01

A quantum device simulating the human decision making process is introduced. It consists of quantum recurrent nets generating stochastic processes which represent the motor dynamics, and of classical neural nets describing the evolution of probabilities of these processes which represent the mental dynamics. The autonomy of the decision making process is achieved by a feedback from the mental to motor dynamics which changes the stochastic matrix based upon the probability distribution. This feedback replaces unavailable external information by an internal knowledge- base stored in the mental model in the form of probability distributions. As a result, the coupled motor-mental dynamics is described by a nonlinear version of Markov chains which can decrease entropy without an external source of information. Applications to common sense based decisions as well as to evolutionary games are discussed. An example exhibiting self-organization is computed using quantum computer simulation. Force on force and mutual aircraft engagements using the quantum decision maker dynamics are considered.

Here and now: the intersection of computational science, quantum-mechanical simulations, and materials science

NASA Astrophysics Data System (ADS)

Marzari, Nicola

The last 30 years have seen the steady and exhilarating development of powerful quantum-simulation engines for extended systems, dedicated to the solution of the Kohn-Sham equations of density-functional theory, often augmented by density-functional perturbation theory, many-body perturbation theory, time-dependent density-functional theory, dynamical mean-field theory, and quantum Monte Carlo. Their implementation on massively parallel architectures, now leveraging also GPUs and accelerators, has started a massive effort in the prediction from first principles of many or of complex materials properties, leading the way to the exascale through the combination of HPC (high-performance computing) and HTC (high-throughput computing). Challenges and opportunities abound: complementing hardware and software investments and design; developing the materials' informatics infrastructure needed to encode knowledge into complex protocols and workflows of calculations; managing and curating data; resisting the complacency that we have already reached the predictive accuracy needed for materials design, or a robust level of verification of the different quantum engines. In this talk I will provide an overview of these challenges, with the ultimate prize being the computational understanding, prediction, and design of properties and performance for novel or complex materials and devices.

Application of Blind Quantum Computation to Two-Party Quantum Computation

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Application of Blind Quantum Computation to Two-Party Quantum Computation

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Digital quantum simulators in a scalable architecture of hybrid spin-photon qubits

PubMed Central

Chiesa, Alessandro; Santini, Paolo; Gerace, Dario; Raftery, James; Houck, Andrew A.; Carretta, Stefano

2015-01-01

Resolving quantum many-body problems represents one of the greatest challenges in physics and physical chemistry, due to the prohibitively large computational resources that would be required by using classical computers. A solution has been foreseen by directly simulating the time evolution through sequences of quantum gates applied to arrays of qubits, i.e. by implementing a digital quantum simulator. Superconducting circuits and resonators are emerging as an extremely promising platform for quantum computation architectures, but a digital quantum simulator proposal that is straightforwardly scalable, universal, and realizable with state-of-the-art technology is presently lacking. Here we propose a viable scheme to implement a universal quantum simulator with hybrid spin-photon qubits in an array of superconducting resonators, which is intrinsically scalable and allows for local control. As representative examples we consider the transverse-field Ising model, a spin-1 Hamiltonian, and the two-dimensional Hubbard model and we numerically simulate the scheme by including the main sources of decoherence. PMID:26563516

Improving Quantum Gate Simulation using a GPU

NASA Astrophysics Data System (ADS)

Gutierrez, Eladio; Romero, Sergio; Trenas, Maria A.; Zapata, Emilio L.

2008-11-01

Due to the increasing computing power of the graphics processing units (GPU), they are becoming more and more popular when solving general purpose algorithms. As the simulation of quantum computers results on a problem with exponential complexity, it is advisable to perform a parallel computation, such as the one provided by the SIMD multiprocessors present in recent GPUs. In this paper, we focus on an important quantum algorithm, the quantum Fourier transform (QTF), in order to evaluate different parallelization strategies on a novel GPU architecture. Our implementation makes use of the new CUDA software/hardware architecture developed recently by NVIDIA.

Polynomial-time quantum algorithm for the simulation of chemical dynamics

PubMed Central

Kassal, Ivan; Jordan, Stephen P.; Love, Peter J.; Mohseni, Masoud; Aspuru-Guzik, Alán

2008-01-01

The computational cost of exact methods for quantum simulation using classical computers grows exponentially with system size. As a consequence, these techniques can be applied only to small systems. By contrast, we demonstrate that quantum computers could exactly simulate chemical reactions in polynomial time. Our algorithm uses the split-operator approach and explicitly simulates all electron-nuclear and interelectronic interactions in quadratic time. Surprisingly, this treatment is not only more accurate than the Born–Oppenheimer approximation but faster and more efficient as well, for all reactions with more than about four atoms. This is the case even though the entire electronic wave function is propagated on a grid with appropriately short time steps. Although the preparation and measurement of arbitrary states on a quantum computer is inefficient, here we demonstrate how to prepare states of chemical interest efficiently. We also show how to efficiently obtain chemically relevant observables, such as state-to-state transition probabilities and thermal reaction rates. Quantum computers using these techniques could outperform current classical computers with 100 qubits. PMID:19033207

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

PubMed

Goto, Hayato

2016-02-22

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

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

PubMed Central

Goto, Hayato

2016-01-01

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

Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

NASA Astrophysics Data System (ADS)

Goto, Hayato

2016-02-01

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

QCAD simulation and optimization of semiconductor double quantum dots

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

Nielsen, Erik; Gao, Xujiao; Kalashnikova, Irina

2013-12-01

We present the Quantum Computer Aided Design (QCAD) simulator that targets modeling quantum devices, particularly silicon double quantum dots (DQDs) developed for quantum qubits. The simulator has three di erentiating features: (i) its core contains nonlinear Poisson, e ective mass Schrodinger, and Con guration Interaction solvers that have massively parallel capability for high simulation throughput, and can be run individually or combined self-consistently for 1D/2D/3D quantum devices; (ii) the core solvers show superior convergence even at near-zero-Kelvin temperatures, which is critical for modeling quantum computing devices; (iii) it couples with an optimization engine Dakota that enables optimization of gate voltagesmore » in DQDs for multiple desired targets. The Poisson solver includes Maxwell- Boltzmann and Fermi-Dirac statistics, supports Dirichlet, Neumann, interface charge, and Robin boundary conditions, and includes the e ect of dopant incomplete ionization. The solver has shown robust nonlinear convergence even in the milli-Kelvin temperature range, and has been extensively used to quickly obtain the semiclassical electrostatic potential in DQD devices. The self-consistent Schrodinger-Poisson solver has achieved robust and monotonic convergence behavior for 1D/2D/3D quantum devices at very low temperatures by using a predictor-correct iteration scheme. The QCAD simulator enables the calculation of dot-to-gate capacitances, and comparison with experiment and between solvers. It is observed that computed capacitances are in the right ballpark when compared to experiment, and quantum con nement increases capacitance when the number of electrons is xed in a quantum dot. In addition, the coupling of QCAD with Dakota allows to rapidly identify which device layouts are more likely leading to few-electron quantum dots. Very efficient QCAD simulations on a large number of fabricated and proposed Si DQDs have made it possible to provide fast feedback for

The Bravyi-Kitaev transformation for quantum computation of electronic structure

NASA Astrophysics Data System (ADS)

Seeley, Jacob T.; Richard, Martin J.; Love, Peter J.

2012-12-01

Quantum simulation is an important application of future quantum computers with applications in quantum chemistry, condensed matter, and beyond. Quantum simulation of fermionic systems presents a specific challenge. The Jordan-Wigner transformation allows for representation of a fermionic operator by O(n) qubit operations. Here, we develop an alternative method of simulating fermions with qubits, first proposed by Bravyi and Kitaev [Ann. Phys. 298, 210 (2002), 10.1006/aphy.2002.6254; e-print arXiv:quant-ph/0003137v2], that reduces the simulation cost to O(log n) qubit operations for one fermionic operation. We apply this new Bravyi-Kitaev transformation to the task of simulating quantum chemical Hamiltonians, and give a detailed example for the simplest possible case of molecular hydrogen in a minimal basis. We show that the quantum circuit for simulating a single Trotter time step of the Bravyi-Kitaev derived Hamiltonian for H2 requires fewer gate applications than the equivalent circuit derived from the Jordan-Wigner transformation. Since the scaling of the Bravyi-Kitaev method is asymptotically better than the Jordan-Wigner method, this result for molecular hydrogen in a minimal basis demonstrates the superior efficiency of the Bravyi-Kitaev method for all quantum computations of electronic structure.

Provably unbounded memory advantage in stochastic simulation using quantum mechanics

NASA Astrophysics Data System (ADS)

Garner, Andrew J. P.; Liu, Qing; Thompson, Jayne; Vedral, Vlatko; Gu, mile

2017-10-01

Simulating the stochastic evolution of real quantities on a digital computer requires a trade-off between the precision to which these quantities are approximated, and the memory required to store them. The statistical accuracy of the simulation is thus generally limited by the internal memory available to the simulator. Here, using tools from computational mechanics, we show that quantum processors with a fixed finite memory can simulate stochastic processes of real variables to arbitrarily high precision. This demonstrates a provable, unbounded memory advantage that a quantum simulator can exhibit over its best possible classical counterpart.

Time reversal and charge conjugation in an embedding quantum simulator.

PubMed

Zhang, Xiang; Shen, Yangchao; Zhang, Junhua; Casanova, Jorge; Lamata, Lucas; Solano, Enrique; Yung, Man-Hong; Zhang, Jing-Ning; Kim, Kihwan

2015-08-04

A quantum simulator is an important device that may soon outperform current classical computations. A basic arithmetic operation, the complex conjugate, however, is considered to be impossible to be implemented in such a quantum system due to the linear character of quantum mechanics. Here, we present the experimental quantum simulation of such an unphysical operation beyond the regime of unitary and dissipative evolutions through the embedding of a quantum dynamics in the electronic multilevels of a (171)Yb(+) ion. We perform time reversal and charge conjugation, which are paradigmatic examples of antiunitary symmetry operators, in the evolution of a Majorana equation without the tomographic knowledge of the evolving state. Thus, these operations can be applied regardless of the system size. Our approach offers the possibility to add unphysical operations to the toolbox of quantum simulation, and provides a route to efficiently compute otherwise intractable quantities, such as entanglement monotones.

Time reversal and charge conjugation in an embedding quantum simulator

PubMed Central

Zhang, Xiang; Shen, Yangchao; Zhang, Junhua; Casanova, Jorge; Lamata, Lucas; Solano, Enrique; Yung, Man-Hong; Zhang, Jing-Ning; Kim, Kihwan

2015-01-01

A quantum simulator is an important device that may soon outperform current classical computations. A basic arithmetic operation, the complex conjugate, however, is considered to be impossible to be implemented in such a quantum system due to the linear character of quantum mechanics. Here, we present the experimental quantum simulation of such an unphysical operation beyond the regime of unitary and dissipative evolutions through the embedding of a quantum dynamics in the electronic multilevels of a 171Yb+ ion. We perform time reversal and charge conjugation, which are paradigmatic examples of antiunitary symmetry operators, in the evolution of a Majorana equation without the tomographic knowledge of the evolving state. Thus, these operations can be applied regardless of the system size. Our approach offers the possibility to add unphysical operations to the toolbox of quantum simulation, and provides a route to efficiently compute otherwise intractable quantities, such as entanglement monotones. PMID:26239028

Simulation of n-qubit quantum systems. I. Quantum registers and quantum gates

NASA Astrophysics Data System (ADS)

Radtke, T.; Fritzsche, S.

2005-12-01

During recent years, quantum computations and the study of n-qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing quantum computations, however, these investigations also revealed a great deal of difficulties which still need to be solved in practice. In quantum computing, unitary and non-unitary quantum operations act on a given set of qubits to form (entangled) states, in which the information is encoded by the overall system often referred to as quantum registers. To facilitate the simulation of such n-qubit quantum systems, we present the FEYNMAN program to provide all necessary tools in order to define and to deal with quantum registers and quantum operations. Although the present version of the program is restricted to unitary transformations, it equally supports—whenever possible—the representation of the quantum registers both, in terms of their state vectors and density matrices. In addition to the composition of two or more quantum registers, moreover, the program also supports their decomposition into various parts by applying the partial trace operation and the concept of the reduced density matrix. Using an interactive design within the framework of MAPLE, therefore, we expect the FEYNMAN program to be helpful not only for teaching the basic elements of quantum computing but also for studying their physical realization in the future. Program summaryTitle of program:FEYNMAN Catalogue number:ADWE Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE Program obtainable from:CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:None Computers for which the program is designed:All computers with a license of the computer algebra system MAPLE [Maple is a registered trademark of Waterlo Maple Inc.] Operating systems or monitors under which the program has been tested:Linux, MS Windows XP Programming language used:MAPLE 9.5 (but should be compatible

Ultracold-atom quantum simulator for attosecond science

NASA Astrophysics Data System (ADS)

Sala, Simon; Förster, Johann; Saenz, Alejandro

2017-01-01

A quantum simulator based on ultracold optically trapped atoms for simulating the physics of atoms and molecules in ultrashort intense laser fields is introduced. The slowing down by about 13 orders of magnitude allows one to watch in slow motion the tunneling and recollision processes that form the heart of attosecond science. The extreme flexibility of the simulator promises a deeper understanding of strong-field physics, especially for many-body systems beyond the reach of classical computers. The quantum simulator can experimentally straightforwardly be realized and is shown to recover the ionization characteristics of atoms in the different regimes of laser-matter interaction.

Interfacing External Quantum Devices to a Universal Quantum Computer

PubMed Central

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

2011-01-01

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

Interfacing external quantum devices to a universal quantum computer.

PubMed

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

2011-01-01

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

Compressed quantum simulation of the Ising model.

PubMed

Kraus, B

2011-12-16

Jozsa et al. [Proc. R. Soc. A 466, 809 2009)] have shown that a match gate circuit running on n qubits can be compressed to a universal quantum computation on log(n)+3 qubits. Here, we show how this compression can be employed to simulate the Ising interaction of a 1D chain consisting of n qubits using a universal quantum computer running on log(n) qubits. We demonstrate how the adiabatic evolution can be realized on this exponentially smaller system and how the magnetization, which displays a quantum phase transition, can be measured. This shows that the quantum phase transition of very large systems can be observed experimentally with current technology. © 2011 American Physical Society

From transistor to trapped-ion computers for quantum chemistry.

PubMed

Yung, M-H; Casanova, J; Mezzacapo, A; McClean, J; Lamata, L; Aspuru-Guzik, A; Solano, E

2014-01-07

Over the last few decades, quantum chemistry has progressed through the development of computational methods based on modern digital computers. However, these methods can hardly fulfill the exponentially-growing resource requirements when applied to large quantum systems. As pointed out by Feynman, this restriction is intrinsic to all computational models based on classical physics. Recently, the rapid advancement of trapped-ion technologies has opened new possibilities for quantum control and quantum simulations. Here, we present an efficient toolkit that exploits both the internal and motional degrees of freedom of trapped ions for solving problems in quantum chemistry, including molecular electronic structure, molecular dynamics, and vibronic coupling. We focus on applications that go beyond the capacity of classical computers, but may be realizable on state-of-the-art trapped-ion systems. These results allow us to envision a new paradigm of quantum chemistry that shifts from the current transistor to a near-future trapped-ion-based technology.

From transistor to trapped-ion computers for quantum chemistry

PubMed Central

Yung, M.-H.; Casanova, J.; Mezzacapo, A.; McClean, J.; Lamata, L.; Aspuru-Guzik, A.; Solano, E.

2014-01-01

Over the last few decades, quantum chemistry has progressed through the development of computational methods based on modern digital computers. However, these methods can hardly fulfill the exponentially-growing resource requirements when applied to large quantum systems. As pointed out by Feynman, this restriction is intrinsic to all computational models based on classical physics. Recently, the rapid advancement of trapped-ion technologies has opened new possibilities for quantum control and quantum simulations. Here, we present an efficient toolkit that exploits both the internal and motional degrees of freedom of trapped ions for solving problems in quantum chemistry, including molecular electronic structure, molecular dynamics, and vibronic coupling. We focus on applications that go beyond the capacity of classical computers, but may be realizable on state-of-the-art trapped-ion systems. These results allow us to envision a new paradigm of quantum chemistry that shifts from the current transistor to a near-future trapped-ion-based technology. PMID:24395054

Simulation of quantum dynamics based on the quantum stochastic differential equation.

PubMed

Li, Ming

2013-01-01

The quantum stochastic differential equation derived from the Lindblad form quantum master equation is investigated. The general formulation in terms of environment operators representing the quantum state diffusion is given. The numerical simulation algorithm of stochastic process of direct photodetection of a driven two-level system for the predictions of the dynamical behavior is proposed. The effectiveness and superiority of the algorithm are verified by the performance analysis of the accuracy and the computational cost in comparison with the classical Runge-Kutta algorithm.

Quantum Computer Science

NASA Astrophysics Data System (ADS)

Mermin, N. David

2007-08-01

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

Quantum computation with indefinite causal structures

NASA Astrophysics Data System (ADS)

Araújo, Mateus; Guérin, Philippe Allard; Baumeler, ńmin

2017-11-01

One way to study the physical plausibility of closed timelike curves (CTCs) is to examine their computational power. This has been done for Deutschian CTCs (D-CTCs) and postselection CTCs (P-CTCs), with the result that they allow for the efficient solution of problems in PSPACE and PP, respectively. Since these are extremely powerful complexity classes, which are not expected to be solvable in reality, this can be taken as evidence that these models for CTCs are pathological. This problem is closely related to the nonlinearity of this models, which also allows, for example, cloning quantum states, in the case of D-CTCs, or distinguishing nonorthogonal quantum states, in the case of P-CTCs. In contrast, the process matrix formalism allows one to model indefinite causal structures in a linear way, getting rid of these effects and raising the possibility that its computational power is rather tame. In this paper, we show that process matrices correspond to a linear particular case of P-CTCs, and therefore that its computational power is upperbounded by that of PP. We show, furthermore, a family of processes that can violate causal inequalities but nevertheless can be simulated by a causally ordered quantum circuit with only a constant overhead, showing that indefinite causality is not necessarily hard to simulate.

Digitized adiabatic quantum computing with a superconducting circuit.

PubMed

Barends, R; Shabani, A; Lamata, L; Kelly, J; Mezzacapo, A; Las Heras, U; Babbush, R; Fowler, A G; Campbell, B; Chen, Yu; Chen, Z; Chiaro, B; Dunsworth, A; Jeffrey, E; Lucero, E; Megrant, A; Mutus, J Y; Neeley, M; Neill, C; O'Malley, P J J; Quintana, C; Roushan, P; Sank, D; Vainsencher, A; Wenner, J; White, T C; Solano, E; Neven, H; Martinis, John M

2016-06-09

Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable.

Quantum computer games: quantum minesweeper

NASA Astrophysics Data System (ADS)

Gordon, Michal; Gordon, Goren

2010-07-01

The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical minesweeper the goal of the game is to discover all the mines laid out on a board without triggering them, in the quantum version there are several classical boards in superposition. The goal is to know the exact quantum state, i.e. the precise layout of all the mines in all the superposed classical boards. The player can perform three types of measurement: a classical measurement that probabilistically collapses the superposition; a quantum interaction-free measurement that can detect a mine without triggering it; and an entanglement measurement that provides non-local information. The application of the concepts taught by quantum minesweeper to one-way quantum computing are also presented.

Demonstration of blind quantum computing.

PubMed

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

2012-01-20

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

Quantum Entanglement Molecular Absorption Spectrum Simulator

NASA Technical Reports Server (NTRS)

Nguyen, Quang-Viet; Kojima, Jun

2006-01-01

Quantum Entanglement Molecular Absorption Spectrum Simulator (QE-MASS) is a computer program for simulating two photon molecular-absorption spectroscopy using quantum-entangled photons. More specifically, QE-MASS simulates the molecular absorption of two quantum-entangled photons generated by the spontaneous parametric down-conversion (SPDC) of a fixed-frequency photon from a laser. The two-photon absorption process is modeled via a combination of rovibrational and electronic single-photon transitions, using a wave-function formalism. A two-photon absorption cross section as a function of the entanglement delay time between the two photons is computed, then subjected to a fast Fourier transform to produce an energy spectrum. The program then detects peaks in the Fourier spectrum and displays the energy levels of very short-lived intermediate quantum states (or virtual states) of the molecule. Such virtual states were only previously accessible using ultra-fast (femtosecond) laser systems. However, with the use of a single-frequency continuous wave laser to produce SPDC photons, and QEMASS program, these short-lived molecular states can now be studied using much simpler laser systems. QE-MASS can also show the dependence of the Fourier spectrum on the tuning range of the entanglement time of any externally introduced optical-path delay time. QE-MASS can be extended to any molecule for which an appropriate spectroscopic database is available. It is a means of performing an a priori parametric analysis of entangled photon spectroscopy for development and implementation of emerging quantum-spectroscopic sensing techniques. QE-MASS is currently implemented using the Mathcad software package.

Quantum simulation of dissipative processes without reservoir engineering

DOE PAGES

Di Candia, R.; Pedernales, J. S.; del Campo, A.; ...

2015-05-29

We present a quantum algorithm to simulate general finite dimensional Lindblad master equations without the requirement of engineering the system-environment interactions. The proposed method is able to simulate both Markovian and non-Markovian quantum dynamics. It consists in the quantum computation of the dissipative corrections to the unitary evolution of the system of interest, via the reconstruction of the response functions associated with the Lindblad operators. Our approach is equally applicable to dynamics generated by effectively non-Hermitian Hamiltonians. We confirm the quality of our method providing specific error bounds that quantify its accuracy.

Scalable quantum computation scheme based on quantum-actuated nuclear-spin decoherence-free qubits

NASA Astrophysics Data System (ADS)

Dong, Lihong; Rong, Xing; Geng, Jianpei; Shi, Fazhan; Li, Zhaokai; Duan, Changkui; Du, Jiangfeng

2017-11-01

We propose a novel theoretical scheme of quantum computation. Nuclear spin pairs are utilized to encode decoherence-free (DF) qubits. A nitrogen-vacancy center serves as a quantum actuator to initialize, readout, and quantum control the DF qubits. The realization of CNOT gates between two DF qubits are also presented. Numerical simulations show high fidelities of all these processes. Additionally, we discuss the potential of scalability. Our scheme reduces the challenge of classical interfaces from controlling and observing complex quantum systems down to a simple quantum actuator. It also provides a novel way to handle complex quantum systems.

Quantum computers: Definition and implementations

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

Perez-Delgado, Carlos A.; Kok, Pieter

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

Exploiting Locality in Quantum Computation for Quantum Chemistry.

PubMed

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

2014-12-18

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

Quantum Walk Schemes for Universal Quantum Computation

NASA Astrophysics Data System (ADS)

Underwood, Michael S.

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

Quantum ring-polymer contraction method: Including nuclear quantum effects at no additional computational cost in comparison to ab initio molecular dynamics

NASA Astrophysics Data System (ADS)

John, Christopher; Spura, Thomas; Habershon, Scott; Kühne, Thomas D.

2016-04-01

We present a simple and accurate computational method which facilitates ab initio path-integral molecular dynamics simulations, where the quantum-mechanical nature of the nuclei is explicitly taken into account, at essentially no additional computational cost in comparison to the corresponding calculation using classical nuclei. The predictive power of the proposed quantum ring-polymer contraction method is demonstrated by computing various static and dynamic properties of liquid water at ambient conditions using density functional theory. This development will enable routine inclusion of nuclear quantum effects in ab initio molecular dynamics simulations of condensed-phase systems.

Computer studies of multiple-quantum spin dynamics

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

Murdoch, J.B.

The excitation and detection of multiple-quantum (MQ) transitions in Fourier transform NMR spectroscopy is an interesting problem in the quantum mechanical dynamics of spin systems as well as an important new technique for investigation of molecular structure. In particular, multiple-quantum spectroscopy can be used to simplify overly complex spectra or to separate the various interactions between a nucleus and its environment. The emphasis of this work is on computer simulation of spin-system evolution to better relate theory and experiment.

Some foundational aspects of quantum computers and quantum robots.

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

Benioff, P.; Physics

1998-01-01

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

Spin-based quantum computation in multielectron quantum dots

NASA Astrophysics Data System (ADS)

Hu, Xuedong; Das Sarma, S.

2001-10-01

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

Video Encryption and Decryption on Quantum Computers

NASA Astrophysics Data System (ADS)

Yan, Fei; Iliyasu, Abdullah M.; Venegas-Andraca, Salvador E.; Yang, Huamin

2015-08-01

A method for video encryption and decryption on quantum computers is proposed based on color information transformations on each frame encoding the content of the encoding the content of the video. The proposed method provides a flexible operation to encrypt quantum video by means of the quantum measurement in order to enhance the security of the video. To validate the proposed approach, a tetris tile-matching puzzle game video is utilized in the experimental simulations. The results obtained suggest that the proposed method enhances the security and speed of quantum video encryption and decryption, both properties required for secure transmission and sharing of video content in quantum communication.

Measurement-only verifiable blind quantum computing with quantum input verification

NASA Astrophysics Data System (ADS)

Morimae, Tomoyuki

2016-10-01

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

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

NASA Astrophysics Data System (ADS)

Fitzsimons, Joseph F.

2017-06-01

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

Quantum Computer Games: Quantum Minesweeper

ERIC Educational Resources Information Center

Gordon, Michal; Gordon, Goren

2010-01-01

The computer game of quantum minesweeper is introduced as a quantum extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of quantum mechanics in a fun way. Quantum minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…

Computer simulations of local anesthetic mechanisms: Quantum chemical investigation of procaine

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

Smith, Jeremy C; Bondar, A.N.; Suhai, Sandor

2007-02-01

A description at the atomic level of detail of the interaction between local anesthetics, lipid membranes and membrane proteins, is essential for understanding the mechanism of local anesthesia. The importance of performing computer simulations to decipher the mechanism of local anesthesia is discussed here in the context of the current status of understanding of the local anesthetics action. As a first step towards accurate simulations of the interaction between local anesthetics, proteins, lipid and water molecules, here we use quantum mechanical methods to assess the charge distribution and structural properties of procaine in the presence and in the absence ofmore » water molecules. The calculations indicate that, in the absence of hydrogen-bonding water molecules, protonated procaine strongly prefers a compact structure enabled by intramolecular hydrogen bonding. In the presence of water molecules the torsional energy pro?le of procaine is modified, and hydrogen bonding to water molecules is favored relative to intra-molecular hydrogen bonding.« less

Quantum computing and probability.

PubMed

Ferry, David K

2009-11-25

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

Image simulations of quantum dots.

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

Lang, C.; Liao, Xiaozhou; Cockayne, D. J.

2001-01-01

Quantum dot (QD) nanostructures have drawn increased interest in recent years. Their small size leads to quantum confinement of the electrons, which is responsible for their unique electronic and optical properties. They promise to find use in a wide range of devices ranging from semiconductor lasers (Bimberg et al (2001), Ribbat et al (2001)) to quantum computing. The properties of QDs are also determined by their shape and composition. All three parameters (size, shape and composition) have a significant impact on their contrast in the transmission electron microscope (TEM), and consequently the possibility arises that these parameters can be extractedmore » from the images. Zone axis plan view images are especially sensitive to the composition of QDs, and image simulation is an important way to understand how the composition determines the contrast. This paper outlines a method of image simulation of QDs developed by Liao et. al. (1999) and presents an application of the method to QDs in wurtzite InN/GaN.« less

Research progress on quantum informatics and quantum computation

NASA Astrophysics Data System (ADS)

Zhao, Yusheng

2018-03-01

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

Nexus: A modular workflow management system for quantum simulation codes

NASA Astrophysics Data System (ADS)

Krogel, Jaron T.

2016-01-01

The management of simulation workflows represents a significant task for the individual computational researcher. Automation of the required tasks involved in simulation work can decrease the overall time to solution and reduce sources of human error. A new simulation workflow management system, Nexus, is presented to address these issues. Nexus is capable of automated job management on workstations and resources at several major supercomputing centers. Its modular design allows many quantum simulation codes to be supported within the same framework. Current support includes quantum Monte Carlo calculations with QMCPACK, density functional theory calculations with Quantum Espresso or VASP, and quantum chemical calculations with GAMESS. Users can compose workflows through a transparent, text-based interface, resembling the input file of a typical simulation code. A usage example is provided to illustrate the process.

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

Hybrid quantum computing with ancillas

NASA Astrophysics Data System (ADS)

Proctor, Timothy J.; Kendon, Viv

2016-10-01

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

Quantum Nash Equilibria and Quantum Computing

NASA Astrophysics Data System (ADS)

Fellman, Philip Vos; Post, Jonathan Vos

In 2004, At the Fifth International Conference on Complex Systems, we drew attention to some remarkable findings by researchers at the Santa Fe Institute (Sato, Farmer and Akiyama, 2001) about hitherto unsuspected complexity in the Nash Equilibrium. As we progressed from these findings about heteroclinic Hamiltonians and chaotic transients hidden within the learning patterns of the simple rock-paper-scissors game to some related findings on the theory of quantum computing, one of the arguments we put forward was just as in the late 1990's a number of new Nash equilibria were discovered in simple bi-matrix games (Shubik and Quint, 1996; Von Stengel, 1997, 2000; and McLennan and Park, 1999) we would begin to see new Nash equilibria discovered as the result of quantum computation. While actual quantum computers remain rather primitive (Toibman, 2004), and the theory of quantum computation seems to be advancing perhaps a bit more slowly than originally expected, there have, nonetheless, been a number of advances in computation and some more radical advances in an allied field, quantum game theory (Huberman and Hogg, 2004) which are quite significant. In the course of this paper we will review a few of these discoveries and illustrate some of the characteristics of these new "Quantum Nash Equilibria". The full text of this research can be found at http://necsi.org/events/iccs6/viewpaper.php?id-234

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

How to Build a Quantum Computer

NASA Astrophysics Data System (ADS)

Sanders, Barry C.

2017-11-01

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

Single-server blind quantum computation with quantum circuit model

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Control aspects of quantum computing using pure and mixed states.

PubMed

Schulte-Herbrüggen, Thomas; Marx, Raimund; Fahmy, Amr; Kauffman, Louis; Lomonaco, Samuel; Khaneja, Navin; Glaser, Steffen J

2012-10-13

Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems.

Control aspects of quantum computing using pure and mixed states

PubMed Central

Schulte-Herbrüggen, Thomas; Marx, Raimund; Fahmy, Amr; Kauffman, Louis; Lomonaco, Samuel; Khaneja, Navin; Glaser, Steffen J.

2012-01-01

Steering quantum dynamics such that the target states solve classically hard problems is paramount to quantum simulation and computation. And beyond, quantum control is also essential to pave the way to quantum technologies. Here, important control techniques are reviewed and presented in a unified frame covering quantum computational gate synthesis and spectroscopic state transfer alike. We emphasize that it does not matter whether the quantum states of interest are pure or not. While pure states underly the design of quantum circuits, ensemble mixtures of quantum states can be exploited in a more recent class of algorithms: it is illustrated by characterizing the Jones polynomial in order to distinguish between different (classes of) knots. Further applications include Josephson elements, cavity grids, ion traps and nitrogen vacancy centres in scenarios of closed as well as open quantum systems. PMID:22946034

Counterfactual quantum computation through quantum interrogation

NASA Astrophysics Data System (ADS)

Hosten, Onur; Rakher, Matthew T.; Barreiro, Julio T.; Peters, Nicholas A.; Kwiat, Paul G.

2006-02-01

The logic underlying the coherent nature of quantum information processing often deviates from intuitive reasoning, leading to surprising effects. Counterfactual computation constitutes a striking example: the potential outcome of a quantum computation can be inferred, even if the computer is not run. Relying on similar arguments to interaction-free measurements (or quantum interrogation), counterfactual computation is accomplished by putting the computer in a superposition of `running' and `not running' states, and then interfering the two histories. Conditional on the as-yet-unknown outcome of the computation, it is sometimes possible to counterfactually infer information about the solution. Here we demonstrate counterfactual computation, implementing Grover's search algorithm with an all-optical approach. It was believed that the overall probability of such counterfactual inference is intrinsically limited, so that it could not perform better on average than random guesses. However, using a novel `chained' version of the quantum Zeno effect, we show how to boost the counterfactual inference probability to unity, thereby beating the random guessing limit. Our methods are general and apply to any physical system, as illustrated by a discussion of trapped-ion systems. Finally, we briefly show that, in certain circumstances, counterfactual computation can eliminate errors induced by decoherence.

Fault-tolerant linear optical quantum computing with small-amplitude coherent States.

PubMed

Lund, A P; Ralph, T C; Haselgrove, H L

2008-01-25

Quantum computing using two coherent states as a qubit basis is a proposed alternative architecture with lower overheads but has been questioned as a practical way of performing quantum computing due to the fragility of diagonal states with large coherent amplitudes. We show that using error correction only small amplitudes (alpha>1.2) are required for fault-tolerant quantum computing. We study fault tolerance under the effects of small amplitudes and loss using a Monte Carlo simulation. The first encoding level resources are orders of magnitude lower than the best single photon scheme.

Complexity Bounds for Quantum Computation

DTIC Science & Technology

2007-06-22

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

Blind topological measurement-based quantum computation.

PubMed

Morimae, Tomoyuki; Fujii, Keisuke

2012-01-01

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

Blind topological measurement-based quantum computation

PubMed Central

Morimae, Tomoyuki; Fujii, Keisuke

2012-01-01

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

Quantum computation for solving linear systems

NASA Astrophysics Data System (ADS)

Cao, Yudong

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

Blind topological measurement-based quantum computation

NASA Astrophysics Data System (ADS)

Morimae, Tomoyuki; Fujii, Keisuke

2012-09-01

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

Quantum Statistical Mechanics on a Quantum Computer

NASA Astrophysics Data System (ADS)

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

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

Quantum Computation: Entangling with the Future

NASA Technical Reports Server (NTRS)

Jiang, Zhang

2017-01-01

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

Towards Quantum Simulation with Circular Rydberg Atoms

NASA Astrophysics Data System (ADS)

Nguyen, T. L.; Raimond, J. M.; Sayrin, C.; Cortiñas, R.; Cantat-Moltrecht, T.; Assemat, F.; Dotsenko, I.; Gleyzes, S.; Haroche, S.; Roux, G.; Jolicoeur, Th.; Brune, M.

2018-01-01

The main objective of quantum simulation is an in-depth understanding of many-body physics, which is important for fundamental issues (quantum phase transitions, transport, …) and for the development of innovative materials. Analytic approaches to many-body systems are limited, and the huge size of their Hilbert space makes numerical simulations on classical computers intractable. A quantum simulator avoids these limitations by transcribing the system of interest into another, with the same dynamics but with interaction parameters under control and with experimental access to all relevant observables. Quantum simulation of spin systems is being explored with trapped ions, neutral atoms, and superconducting devices. We propose here a new paradigm for quantum simulation of spin-1 /2 arrays, providing unprecedented flexibility and allowing one to explore domains beyond the reach of other platforms. It is based on laser-trapped circular Rydberg atoms. Their long intrinsic lifetimes, combined with the inhibition of their microwave spontaneous emission and their low sensitivity to collisions and photoionization, make trapping lifetimes in the minute range realistic with state-of-the-art techniques. Ultracold defect-free circular atom chains can be prepared by a variant of the evaporative cooling method. This method also leads to the detection of arbitrary spin observables with single-site resolution. The proposed simulator realizes an X X Z spin-1 /2 Hamiltonian with nearest-neighbor couplings ranging from a few to tens of kilohertz. All the model parameters can be dynamically tuned at will, making a large range of simulations accessible. The system evolution can be followed over times in the range of seconds, long enough to be relevant for ground-state adiabatic preparation and for the study of thermalization, disorder, or Floquet time crystals. The proposed platform already presents unrivaled features for quantum simulation of regular spin chains. We discuss

Real-time dynamics of lattice gauge theories with a few-qubit quantum computer

NASA Astrophysics Data System (ADS)

Martinez, Esteban A.; Muschik, Christine A.; Schindler, Philipp; Nigg, Daniel; Erhard, Alexander; Heyl, Markus; Hauke, Philipp; Dalmonte, Marcello; Monz, Thomas; Zoller, Peter; Blatt, Rainer

2016-06-01

Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. This has recently stimulated theoretical effort, using Feynman’s idea of a quantum simulator, to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realizing (1 + 1)-dimensional quantum electrodynamics (the Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which can be directly and efficiently implemented on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulation of high-energy theories using atomic physics experiments—the long-term intention is to extend this approach to real-time quantum simulations of non-Abelian lattice gauge theories.

Universal Blind Quantum Computation

NASA Astrophysics Data System (ADS)

Fitzsimons, Joseph; Kashefi, Elham

2012-02-01

Blind Quantum Computing (BQC) allows a client to have a server carry out a quantum computation for them such that the client's inputs, outputs and computation remain private. Recently we proposed a universal unconditionally secure BQC scheme, based on the conceptual framework of the measurement-based quantum computing model, where the client only needs to be able to prepare single qubits in separable states randomly chosen from a finite set and send them to the server, who has the balance of the required quantum computational resources. Here we present a refinement of the scheme which vastly expands the class of quantum circuits which can be directly implemented as a blind computation, by introducing a new class of resource states which we term dotted-complete graph states and expanding the set of single qubit states the client is required to prepare. These two modifications significantly simplify the overall protocol and remove the previously present restriction that only nearest-neighbor circuits could be implemented as blind computations directly. As an added benefit, the refined protocol admits a substantially more intuitive and simplified verification mechanism, allowing the correctness of a blind computation to be verified with arbitrarily small probability of error.

Understanding quantum tunneling using diffusion Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Inack, E. M.; Giudici, G.; Parolini, T.; Santoro, G.; Pilati, S.

2018-03-01

In simple ferromagnetic quantum Ising models characterized by an effective double-well energy landscape the characteristic tunneling time of path-integral Monte Carlo (PIMC) simulations has been shown to scale as the incoherent quantum-tunneling time, i.e., as 1 /Δ2 , where Δ is the tunneling gap. Since incoherent quantum tunneling is employed by quantum annealers (QAs) to solve optimization problems, this result suggests that there is no quantum advantage in using QAs with respect to quantum Monte Carlo (QMC) simulations. A counterexample is the recently introduced shamrock model (Andriyash and Amin, arXiv:1703.09277), where topological obstructions cause an exponential slowdown of the PIMC tunneling dynamics with respect to incoherent quantum tunneling, leaving open the possibility for potential quantum speedup, even for stoquastic models. In this work we investigate the tunneling time of projective QMC simulations based on the diffusion Monte Carlo (DMC) algorithm without guiding functions, showing that it scales as 1 /Δ , i.e., even more favorably than the incoherent quantum-tunneling time, both in a simple ferromagnetic system and in the more challenging shamrock model. However, a careful comparison between the DMC ground-state energies and the exact solution available for the transverse-field Ising chain indicates an exponential scaling of the computational cost required to keep a fixed relative error as the system size increases.

Quantum computing on encrypted data

NASA Astrophysics Data System (ADS)

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

2014-01-01

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

Quantum computing on encrypted data.

PubMed

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

2014-01-01

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

Continuous-Variable Instantaneous Quantum Computing is Hard to Sample.

PubMed

Douce, T; Markham, D; Kashefi, E; Diamanti, E; Coudreau, T; Milman, P; van Loock, P; Ferrini, G

2017-02-17

Instantaneous quantum computing is a subuniversal quantum complexity class, whose circuits have proven to be hard to simulate classically in the discrete-variable realm. We extend this proof to the continuous-variable (CV) domain by using squeezed states and homodyne detection, and by exploring the properties of postselected circuits. In order to treat postselection in CVs, we consider finitely resolved homodyne detectors, corresponding to a realistic scheme based on discrete probability distributions of the measurement outcomes. The unavoidable errors stemming from the use of finitely squeezed states are suppressed through a qubit-into-oscillator Gottesman-Kitaev-Preskill encoding of quantum information, which was previously shown to enable fault-tolerant CV quantum computation. Finally, we show that, in order to render postselected computational classes in CVs meaningful, a logarithmic scaling of the squeezing parameter with the circuit size is necessary, translating into a polynomial scaling of the input energy.

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

PubMed

Goto, Hayato

2014-12-16

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

Quantum Analog Computing

NASA Technical Reports Server (NTRS)

Zak, M.

1998-01-01

Quantum analog computing is based upon similarity between mathematical formalism of quantum mechanics and phenomena to be computed. It exploits a dynamical convergence of several competing phenomena to an attractor which can represent an externum of a function, an image, a solution to a system of ODE, or a stochastic process.

Universal blind quantum computation for hybrid system

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

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

DTIC Science & Technology

2017-03-02

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

Towards quantum chemistry on a quantum computer.

PubMed

Lanyon, B P; Whitfield, J D; Gillett, G G; Goggin, M E; Almeida, M P; Kassal, I; Biamonte, J D; Mohseni, M; Powell, B J; Barbieri, M; Aspuru-Guzik, A; White, A G

2010-02-01

Exact first-principles calculations of molecular properties are currently intractable because their computational cost grows exponentially with both the number of atoms and basis set size. A solution is to move to a radically different model of computing by building a quantum computer, which is a device that uses quantum systems themselves to store and process data. Here we report the application of the latest photonic quantum computer technology to calculate properties of the smallest molecular system: the hydrogen molecule in a minimal basis. We calculate the complete energy spectrum to 20 bits of precision and discuss how the technique can be expanded to solve large-scale chemical problems that lie beyond the reach of modern supercomputers. These results represent an early practical step toward a powerful tool with a broad range of quantum-chemical applications.

Dissipative quantum computing with open quantum walks

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

Sinayskiy, Ilya; Petruccione, Francesco

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

Visualizing a silicon quantum computer

NASA Astrophysics Data System (ADS)

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

2008-12-01

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

Computing quantum discord is NP-complete

NASA Astrophysics Data System (ADS)

Huang, Yichen

2014-03-01

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

Quantum 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

Two-dimensional simulation of quantum reflection

NASA Astrophysics Data System (ADS)

Galiffi, Emanuele; Sünderhauf, Christoph; DeKieviet, Maarten; Wimberger, Sandro

2017-05-01

A propagation method for the scattering of a quantum wave packet from a potential surface is presented. It is used to model the quantum reflection of single atoms from a corrugated (metallic) surface. Our numerical procedure works well in two spatial dimensions requiring only reasonable amounts of memory and computing time. The effects of the surface corrugation on the reflectivity are investigated via simulations with a paradigm potential. These indicate that our approach should allow for future tests of realistic, effective potentials obtained from theory in a quantitative comparison to experimental data.

Computation and Dynamics: Classical and Quantum

NASA Astrophysics Data System (ADS)

Kisil, Vladimir V.

2010-05-01

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

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.

Defects in Quantum Computers

DOE PAGES

Gardas, Bartłomiej; Dziarmaga, Jacek; Zurek, Wojciech H.; ...

2018-03-14

The shift of interest from general purpose quantum computers to adiabatic quantum computing or quantum annealing calls for a broadly applicable and easy to implement test to assess how quantum or adiabatic is a specific hardware. Here we propose such a test based on an exactly solvable many body system–the quantum Ising chain in transverse field–and implement it on the D-Wave machine. An ideal adiabatic quench of the quantum Ising chain should lead to an ordered broken symmetry ground state with all spins aligned in the same direction. An actual quench can be imperfect due to decoherence, noise, flaws inmore » the implemented Hamiltonian, or simply too fast to be adiabatic. Imperfections result in topological defects: Spins change orientation, kinks punctuating ordered sections of the chain. Therefore, the number of such defects quantifies the extent by which the quantum computer misses the ground state, and is imperfect.« less

Defects in Quantum Computers

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

Gardas, Bartłomiej; Dziarmaga, Jacek; Zurek, Wojciech H.

The shift of interest from general purpose quantum computers to adiabatic quantum computing or quantum annealing calls for a broadly applicable and easy to implement test to assess how quantum or adiabatic is a specific hardware. Here we propose such a test based on an exactly solvable many body system–the quantum Ising chain in transverse field–and implement it on the D-Wave machine. An ideal adiabatic quench of the quantum Ising chain should lead to an ordered broken symmetry ground state with all spins aligned in the same direction. An actual quench can be imperfect due to decoherence, noise, flaws inmore » the implemented Hamiltonian, or simply too fast to be adiabatic. Imperfections result in topological defects: Spins change orientation, kinks punctuating ordered sections of the chain. Therefore, the number of such defects quantifies the extent by which the quantum computer misses the ground state, and is imperfect.« less

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.

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.

Adiabatic quantum computation

NASA Astrophysics Data System (ADS)

Albash, Tameem; Lidar, Daniel A.

2018-01-01

Adiabatic quantum computing (AQC) started as an approach to solving optimization problems and has evolved into an important universal alternative to the standard circuit model of quantum computing, with deep connections to both classical and quantum complexity theory and condensed matter physics. This review gives an account of the major theoretical developments in the field, while focusing on the closed-system setting. The review is organized around a series of topics that are essential to an understanding of the underlying principles of AQC, its algorithmic accomplishments and limitations, and its scope in the more general setting of computational complexity theory. Several variants are presented of the adiabatic theorem, the cornerstone of AQC, and examples are given of explicit AQC algorithms that exhibit a quantum speedup. An overview of several proofs of the universality of AQC and related Hamiltonian quantum complexity theory is given. Considerable space is devoted to stoquastic AQC, the setting of most AQC work to date, where obstructions to success and their possible resolutions are discussed.

Complex Instruction Set Quantum Computing

NASA Astrophysics Data System (ADS)

Sanders, G. D.; Kim, K. W.; Holton, W. C.

1998-03-01

In proposed quantum computers, electromagnetic pulses are used to implement logic gates on quantum bits (qubits). Gates are unitary transformations applied to coherent qubit wavefunctions and a universal computer can be created using a minimal set of gates. By applying many elementary gates in sequence, desired quantum computations can be performed. This reduced instruction set approach to quantum computing (RISC QC) is characterized by serial application of a few basic pulse shapes and a long coherence time. However, the unitary matrix of the overall computation is ultimately a unitary matrix of the same size as any of the elementary matrices. This suggests that we might replace a sequence of reduced instructions with a single complex instruction using an optimally taylored pulse. We refer to this approach as complex instruction set quantum computing (CISC QC). One trades the requirement for long coherence times for the ability to design and generate potentially more complex pulses. We consider a model system of coupled qubits interacting through nearest neighbor coupling and show that CISC QC can reduce the time required to perform quantum computations.

Plasmonic resonances of nanoparticles from large-scale quantum mechanical simulations

NASA Astrophysics Data System (ADS)

Zhang, Xu; Xiang, Hongping; Zhang, Mingliang; Lu, Gang

2017-09-01

Plasmonic resonance of metallic nanoparticles results from coherent motion of its conduction electrons, driven by incident light. For the nanoparticles less than 10 nm in diameter, localized surface plasmonic resonances become sensitive to the quantum nature of the conduction electrons. Unfortunately, quantum mechanical simulations based on time-dependent Kohn-Sham density functional theory are computationally too expensive to tackle metal particles larger than 2 nm. Herein, we introduce the recently developed time-dependent orbital-free density functional theory (TD-OFDFT) approach which enables large-scale quantum mechanical simulations of plasmonic responses of metallic nanostructures. Using TD-OFDFT, we have performed quantum mechanical simulations to understand size-dependent plasmonic response of Na nanoparticles and plasmonic responses in Na nanoparticle dimers and trimers. An outlook of future development of the TD-OFDFT method is also presented.

Quantum Algorithms to Simulate Many-Body Physics of Correlated Fermions

NASA Astrophysics Data System (ADS)

Jiang, Zhang; Sung, Kevin J.; Kechedzhi, Kostyantyn; Smelyanskiy, Vadim N.; Boixo, Sergio

2018-04-01

Simulating strongly correlated fermionic systems is notoriously hard on classical computers. An alternative approach, as proposed by Feynman, is to use a quantum computer. We discuss simulating strongly correlated fermionic systems using near-term quantum devices. We focus specifically on two-dimensional (2D) or linear geometry with nearest-neighbor qubit-qubit couplings, typical for superconducting transmon qubit arrays. We improve an existing algorithm to prepare an arbitrary Slater determinant by exploiting a unitary symmetry. We also present a quantum algorithm to prepare an arbitrary fermionic Gaussian state with O (N2) gates and O (N ) circuit depth. Both algorithms are optimal in the sense that the numbers of parameters in the quantum circuits are equal to those describing the quantum states. Furthermore, we propose an algorithm to implement the 2D fermionic Fourier transformation on a 2D qubit array with only O (N1.5) gates and O (√{N }) circuit depth, which is the minimum depth required for quantum information to travel across the qubit array. We also present methods to simulate each time step in the evolution of the 2D Fermi-Hubbard model—again on a 2D qubit array—with O (N ) gates and O (√{N }) circuit depth. Finally, we discuss how these algorithms can be used to determine the ground-state properties and phase diagrams of strongly correlated quantum systems using the Hubbard model as an example.

Experimental demonstration of blind quantum computing

NASA Astrophysics Data System (ADS)

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

2012-02-01

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

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.

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

PubMed Central

Goto, Hayato

2014-01-01

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

Quantum Computing since Democritus

NASA Astrophysics Data System (ADS)

Aaronson, Scott

2013-03-01

1. Atoms and the void; 2. Sets; 3. Gödel, Turing, and friends; 4. Minds and machines; 5. Paleocomplexity; 6. P, NP, and friends; 7. Randomness; 8. Crypto; 9. Quantum; 10. Quantum computing; 11. Penrose; 12. Decoherence and hidden variables; 13. Proofs; 14. How big are quantum states?; 15. Skepticism of quantum computing; 16. Learning; 17. Interactive proofs and more; 18. Fun with the Anthropic Principle; 19. Free will; 20. Time travel; 21. Cosmology and complexity; 22. Ask me anything.

Fermion-to-qubit mappings with varying resource requirements for quantum simulation

NASA Astrophysics Data System (ADS)

Steudtner, Mark; Wehner, Stephanie

2018-06-01

The mapping of fermionic states onto qubit states, as well as the mapping of fermionic Hamiltonian into quantum gates enables us to simulate electronic systems with a quantum computer. Benefiting the understanding of many-body systems in chemistry and physics, quantum simulation is one of the great promises of the coming age of quantum computers. Interestingly, the minimal requirement of qubits for simulating Fermions seems to be agnostic of the actual number of particles as well as other symmetries. This leads to qubit requirements that are well above the minimal requirements as suggested by combinatorial considerations. In this work, we develop methods that allow us to trade-off qubit requirements against the complexity of the resulting quantum circuit. We first show that any classical code used to map the state of a fermionic Fock space to qubits gives rise to a mapping of fermionic models to quantum gates. As an illustrative example, we present a mapping based on a nonlinear classical error correcting code, which leads to significant qubit savings albeit at the expense of additional quantum gates. We proceed to use this framework to present a number of simpler mappings that lead to qubit savings with a more modest increase in gate difficulty. We discuss the role of symmetries such as particle conservation, and savings that could be obtained if an experimental platform could easily realize multi-controlled gates.

Nexus: a modular workflow management system for quantum simulation codes

DOE PAGES

Krogel, Jaron T.

2015-08-24

The management of simulation workflows is a significant task for the individual computational researcher. Automation of the required tasks involved in simulation work can decrease the overall time to solution and reduce sources of human error. A new simulation workflow management system, Nexus, is presented to address these issues. Nexus is capable of automated job management on workstations and resources at several major supercomputing centers. Its modular design allows many quantum simulation codes to be supported within the same framework. Current support includes quantum Monte Carlo calculations with QMCPACK, density functional theory calculations with Quantum Espresso or VASP, and quantummore » chemical calculations with GAMESS. Users can compose workflows through a transparent, text-based interface, resembling the input file of a typical simulation code. A usage example is provided to illustrate the process.« less

Computing quantum hashing in the model of quantum branching programs

NASA Astrophysics Data System (ADS)

Ablayev, Farid; Ablayev, Marat; Vasiliev, Alexander

2018-02-01

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

Toward simulating complex systems with quantum effects

NASA Astrophysics Data System (ADS)

Kenion-Hanrath, Rachel Lynn

Quantum effects like tunneling, coherence, and zero point energy often play a significant role in phenomena on the scales of atoms and molecules. However, the exact quantum treatment of a system scales exponentially with dimensionality, making it impractical for characterizing reaction rates and mechanisms in complex systems. An ongoing effort in the field of theoretical chemistry and physics is extending scalable, classical trajectory-based simulation methods capable of capturing quantum effects to describe dynamic processes in many-body systems; in the work presented here we explore two such techniques. First, we detail an explicit electron, path integral (PI)-based simulation protocol for predicting the rate of electron transfer in condensed-phase transition metal complex systems. Using a PI representation of the transferring electron and a classical representation of the transition metal complex and solvent atoms, we compute the outer sphere free energy barrier and dynamical recrossing factor of the electron transfer rate while accounting for quantum tunneling and zero point energy effects. We are able to achieve this employing only a single set of force field parameters to describe the system rather than parameterizing along the reaction coordinate. Following our success in describing a simple model system, we discuss our next steps in extending our protocol to technologically relevant materials systems. The latter half focuses on the Mixed Quantum-Classical Initial Value Representation (MQC-IVR) of real-time correlation functions, a semiclassical method which has demonstrated its ability to "tune'' between quantum- and classical-limit correlation functions while maintaining dynamic consistency. Specifically, this is achieved through a parameter that determines the quantumness of individual degrees of freedom. Here, we derive a semiclassical correction term for the MQC-IVR to systematically characterize the error introduced by different choices of simulation

Open Quantum Walks and Dissipative Quantum Computing

NASA Astrophysics Data System (ADS)

Petruccione, Francesco

2012-02-01

Open Quantum Walks (OQWs) have been recently introduced as quantum Markov chains on graphs [S. Attal, F. Petruccione, C. Sabot, and I. Sinayskiy, E-print: http://hal.archives-ouvertes.fr/hal-00581553/fr/]. The formulation of the OQWs is exclusively based upon the non-unitary dynamics induced by the environment. It will be shown that OQWs are a very useful tool for the formulation of dissipative quantum computing and quantum state preparation. In particular, it will be shown how to implement single qubit gates and the CNOT gate as OQWs on fully connected graphs. Also, OQWS make possible the dissipative quantum state preparation of arbitrary single qubit states and of all two-qubit Bell states. Finally, it will be shown how to reformulate efficiently a discrete time version of dissipative quantum computing in the language of OQWs.

A simulator for discrete quantum walks on lattices

NASA Astrophysics Data System (ADS)

Rodrigues, J.; Paunković, N.; Mateus, P.

In this paper, we present a simulator for two-particle quantum walks on the line and one-particle on a two-dimensional squared lattice. It can be used to investigate the equivalence between the two cases (one- and two-particle walks) for various boundary conditions (open, circular, reflecting, absorbing and their combinations). For the case of a single walker on a two-dimensional lattice, the simulator can also implement the Möbius strip. Furthermore, other topologies for the walker are also simulated by the proposed tool, like certain types of planar graphs with degree up to 4, by considering missing links over the lattice. The main purpose of the simulator is to study the genuinely quantum effects on the global properties of the two-particle joint probability distribution on the entanglement between the walkers/axis. For that purpose, the simulator is designed to compute various quantities such as: the entanglement and classical correlations, (classical and quantum) mutual information, the average distance between the two walkers, different hitting times and quantum discord. These quantities are of vital importance in designing possible algorithmic applications of quantum walks, namely in search, 3-SAT problems, etc. The simulator can also implement the static partial measurements of particle(s) positions and dynamic breaking of the links between certain nodes, both of which can be used to investigate the effects of decoherence on the walker(s). Finally, the simulator can be used to investigate the dynamic Anderson-like particle localization by varying the coin operators of certain nodes on the line/lattice. We also present some illustrative and relevant examples of one- and two-particle quantum walks in various scenarios. The tool was implemented in C and is available on-line at http://qwsim.weebly.com/.

Quantum Simulation of Helium Hydride Cation in a Solid-State Spin Register.

PubMed

Wang, Ya; Dolde, Florian; Biamonte, Jacob; Babbush, Ryan; Bergholm, Ville; Yang, Sen; Jakobi, Ingmar; Neumann, Philipp; Aspuru-Guzik, Alán; Whitfield, James D; Wrachtrup, Jörg

2015-08-25

Ab initio computation of molecular properties is one of the most promising applications of quantum computing. While this problem is widely believed to be intractable for classical computers, efficient quantum algorithms exist which have the potential to vastly accelerate research throughput in fields ranging from material science to drug discovery. Using a solid-state quantum register realized in a nitrogen-vacancy (NV) defect in diamond, we compute the bond dissociation curve of the minimal basis helium hydride cation, HeH(+). Moreover, we report an energy uncertainty (given our model basis) of the order of 10(-14) hartree, which is 10 orders of magnitude below the desired chemical precision. As NV centers in diamond provide a robust and straightforward platform for quantum information processing, our work provides an important step toward a fully scalable solid-state implementation of a quantum chemistry simulator.

Numerical stabilization of entanglement computation in auxiliary-field quantum Monte Carlo simulations of interacting many-fermion systems.

PubMed

Broecker, Peter; Trebst, Simon

2016-12-01

In the absence of a fermion sign problem, auxiliary-field (or determinantal) quantum Monte Carlo (DQMC) approaches have long been the numerical method of choice for unbiased, large-scale simulations of interacting many-fermion systems. More recently, the conceptual scope of this approach has been expanded by introducing ingenious schemes to compute entanglement entropies within its framework. On a practical level, these approaches, however, suffer from a variety of numerical instabilities that have largely impeded their applicability. Here we report on a number of algorithmic advances to overcome many of these numerical instabilities and significantly improve the calculation of entanglement measures in the zero-temperature projective DQMC approach, ultimately allowing us to reach similar system sizes as for the computation of conventional observables. We demonstrate the applicability of this improved DQMC approach by providing an entanglement perspective on the quantum phase transition from a magnetically ordered Mott insulator to a band insulator in the bilayer square lattice Hubbard model at half filling.

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.

Quantum Computation Using Optically Coupled Quantum Dot Arrays

NASA Technical Reports Server (NTRS)

Pradhan, Prabhakar; Anantram, M. P.; Wang, K. L.; Roychowhury, V. P.; Saini, Subhash (Technical Monitor)

1998-01-01

A solid state model for quantum computation has potential advantages in terms of the ease of fabrication, characterization, and integration. The fundamental requirements for a quantum computer involve the realization of basic processing units (qubits), and a scheme for controlled switching and coupling among the qubits, which enables one to perform controlled operations on qubits. We propose a model for quantum computation based on optically coupled quantum dot arrays, which is computationally similar to the atomic model proposed by Cirac and Zoller. In this model, individual qubits are comprised of two coupled quantum dots, and an array of these basic units is placed in an optical cavity. Switching among the states of the individual units is done by controlled laser pulses via near field interaction using the NSOM technology. Controlled rotations involving two or more qubits are performed via common cavity mode photon. We have calculated critical times, including the spontaneous emission and switching times, and show that they are comparable to the best times projected for other proposed models of quantum computation. We have also shown the feasibility of accessing individual quantum dots using the NSOM technology by calculating the photon density at the tip, and estimating the power necessary to perform the basic controlled operations. We are currently in the process of estimating the decoherence times for this system; however, we have formulated initial arguments which seem to indicate that the decoherence times will be comparable, if not longer, than many other proposed models.

Efficient universal blind quantum computation.

PubMed

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

2013-12-06

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

Quantum simulation of transverse Ising models with Rydberg atoms

NASA Astrophysics Data System (ADS)

Schauss, Peter

2018-04-01

Quantum Ising models are canonical models for the study of quantum phase transitions (Sachdev 1999 Quantum Phase Transitions (Cambridge: Cambridge University Press)) and are the underlying concept for many analogue quantum computing and quantum annealing ideas (Tanaka et al Quantum Spin Glasses, Annealing and Computation (Cambridge: Cambridge University Press)). Here we focus on the implementation of finite-range interacting Ising spin models, which are barely tractable numerically. Recent experiments with cold atoms have reached the interaction-dominated regime in quantum Ising magnets via optical coupling of trapped neutral atoms to Rydberg states. This approach allows for the tunability of all relevant terms in an Ising spin Hamiltonian with 1/{r}6 interactions in transverse and longitudinal fields. This review summarizes the recent progress of these implementations in Rydberg lattices with site-resolved detection. Strong correlations in quantum Ising models have been observed in several experiments, starting from a single excitation in the superatom regime up to the point of crystallization. The rapid progress in this field makes spin systems based on Rydberg atoms a promising platform for quantum simulation because of the unmatched flexibility and strength of interactions combined with high control and good isolation from the environment.

Acausal measurement-based quantum computing

NASA Astrophysics Data System (ADS)

Morimae, Tomoyuki

2014-07-01

In measurement-based quantum computing, there is a natural "causal cone" among qubits of the resource state, since the measurement angle on a qubit has to depend on previous measurement results in order to correct the effect of by-product operators. If we respect the no-signaling principle, by-product operators cannot be avoided. Here we study the possibility of acausal measurement-based quantum computing by using the process matrix framework [Oreshkov, Costa, and Brukner, Nat. Commun. 3, 1092 (2012), 10.1038/ncomms2076]. We construct a resource process matrix for acausal measurement-based quantum computing restricting local operations to projective measurements. The resource process matrix is an analog of the resource state of the standard causal measurement-based quantum computing. We find that if we restrict local operations to projective measurements the resource process matrix is (up to a normalization factor and trivial ancilla qubits) equivalent to the decorated graph state created from the graph state of the corresponding causal measurement-based quantum computing. We also show that it is possible to consider a causal game whose causal inequality is violated by acausal measurement-based quantum computing.

Quantum adiabatic computation with a constant gap is not useful in one dimension.

PubMed

Hastings, M B

2009-07-31

We show that it is possible to use a classical computer to efficiently simulate the adiabatic evolution of a quantum system in one dimension with a constant spectral gap, starting the adiabatic evolution from a known initial product state. The proof relies on a recently proven area law for such systems, implying the existence of a good matrix product representation of the ground state, combined with an appropriate algorithm to update the matrix product state as the Hamiltonian is changed. This implies that adiabatic evolution with such Hamiltonians is not useful for universal quantum computation. Therefore, adiabatic algorithms which are useful for universal quantum computation either require a spectral gap tending to zero or need to be implemented in more than one dimension (we leave open the question of the computational power of adiabatic simulation with a constant gap in more than one dimension).

Natural three-qubit interactions in one-way quantum computing

NASA Astrophysics Data System (ADS)

Tame, M. S.; Paternostro, M.; Kim, M. S.; Vedral, V.

2006-02-01

We address the effects of natural three-qubit interactions on the computational power of one-way quantum computation. A benefit of using more sophisticated entanglement structures is the ability to construct compact and economic simulations of quantum algorithms with limited resources. We show that the features of our study are embodied by suitably prepared optical lattices, where effective three-spin interactions have been theoretically demonstrated. We use this to provide a compact construction for the Toffoli gate. Information flow and two-qubit interactions are also outlined, together with a brief analysis of relevant sources of imperfection.

Scalable quantum computer architecture with coupled donor-quantum dot qubits

DOEpatents

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

2014-08-26

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

Quantum simulation of quantum field theory using continuous variables

DOE PAGES

Marshall, Kevin; Pooser, Raphael C.; Siopsis, George; ...

2015-12-14

Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonicmore » quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.« less

Quantum simulation of quantum field theory using continuous variables

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

Marshall, Kevin; Pooser, Raphael C.; Siopsis, George

Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonicmore » quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.« less

Exact and efficient simulation of concordant computation

NASA Astrophysics Data System (ADS)

Cable, Hugo; Browne, Daniel E.

2015-11-01

Concordant computation is a circuit-based model of quantum computation for mixed states, that assumes that all correlations within the register are discord-free (i.e. the correlations are essentially classical) at every step of the computation. The question of whether concordant computation always admits efficient simulation by a classical computer was first considered by Eastin in arXiv:quant-ph/1006.4402v1, where an answer in the affirmative was given for circuits consisting only of one- and two-qubit gates. Building on this work, we develop the theory of classical simulation of concordant computation. We present a new framework for understanding such computations, argue that a larger class of concordant computations admit efficient simulation, and provide alternative proofs for the main results of arXiv:quant-ph/1006.4402v1 with an emphasis on the exactness of simulation which is crucial for this model. We include detailed analysis of the arithmetic complexity for solving equations in the simulation, as well as extensions to larger gates and qudits. We explore the limitations of our approach, and discuss the challenges faced in developing efficient classical simulation algorithms for all concordant computations.

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

PubMed

Lenhard, Johannes

2014-12-01

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

One-way quantum computing in superconducting circuits

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Quantum computation and analysis of Wigner and Husimi functions: toward a quantum image treatment.

PubMed

Terraneo, M; Georgeot, B; Shepelyansky, D L

2005-06-01

We study the efficiency of quantum algorithms which aim at obtaining phase-space distribution functions of quantum systems. Wigner and Husimi functions are considered. Different quantum algorithms are envisioned to build these functions, and compared with the classical computation. Different procedures to extract more efficiently information from the final wave function of these algorithms are studied, including coarse-grained measurements, amplitude amplification, and measure of wavelet-transformed wave function. The algorithms are analyzed and numerically tested on a complex quantum system showing different behavior depending on parameters: namely, the kicked rotator. The results for the Wigner function show in particular that the use of the quantum wavelet transform gives a polynomial gain over classical computation. For the Husimi distribution, the gain is much larger than for the Wigner function and is larger with the help of amplitude amplification and wavelet transforms. We discuss the generalization of these results to the simulation of other quantum systems. We also apply the same set of techniques to the analysis of real images. The results show that the use of the quantum wavelet transform allows one to lower dramatically the number of measurements needed, but at the cost of a large loss of information.

Adiabatic quantum computing with spin qubits hosted by molecules.

PubMed

Yamamoto, Satoru; Nakazawa, Shigeaki; Sugisaki, Kenji; Sato, Kazunobu; Toyota, Kazuo; Shiomi, Daisuke; Takui, Takeji

2015-01-28

A molecular spin quantum computer (MSQC) requires electron spin qubits, which pulse-based electron spin/magnetic resonance (ESR/MR) techniques can afford to manipulate for implementing quantum gate operations in open shell molecular entities. Importantly, nuclear spins, which are topologically connected, particularly in organic molecular spin systems, are client qubits, while electron spins play a role of bus qubits. Here, we introduce the implementation for an adiabatic quantum algorithm, suggesting the possible utilization of molecular spins with optimized spin structures for MSQCs. We exemplify the utilization of an adiabatic factorization problem of 21, compared with the corresponding nuclear magnetic resonance (NMR) case. Two molecular spins are selected: one is a molecular spin composed of three exchange-coupled electrons as electron-only qubits and the other an electron-bus qubit with two client nuclear spin qubits. Their electronic spin structures are well characterized in terms of the quantum mechanical behaviour in the spin Hamiltonian. The implementation of adiabatic quantum computing/computation (AQC) has, for the first time, been achieved by establishing ESR/MR pulse sequences for effective spin Hamiltonians in a fully controlled manner of spin manipulation. The conquered pulse sequences have been compared with the NMR experiments and shown much faster CPU times corresponding to the interaction strength between the spins. Significant differences are shown in rotational operations and pulse intervals for ESR/MR operations. As a result, we suggest the advantages and possible utilization of the time-evolution based AQC approach for molecular spin quantum computers and molecular spin quantum simulators underlain by sophisticated ESR/MR pulsed spin technology.

Models of optical quantum computing

NASA Astrophysics Data System (ADS)

Krovi, Hari

2017-03-01

I review some work on models of quantum computing, optical implementations of these models, as well as the associated computational power. In particular, we discuss the circuit model and cluster state implementations using quantum optics with various encodings such as dual rail encoding, Gottesman-Kitaev-Preskill encoding, and coherent state encoding. Then we discuss intermediate models of optical computing such as boson sampling and its variants. Finally, we review some recent work in optical implementations of adiabatic quantum computing and analog optical computing. We also provide a brief description of the relevant aspects from complexity theory needed to understand the results surveyed.

PREFACE: Proceedings of the 2nd International Conference on Quantum Simulators and Design (Tokyo, Japan, 31 May-3 June 2008) Proceedings of the 2nd International Conference on Quantum Simulators and Design (Tokyo, Japan, 31 May-3 June 2008)

NASA Astrophysics Data System (ADS)

Akai, Hisazumi; Tsuneyuki, Shinji

2009-02-01

This special issue of Journal of Physics: Condensed Matter comprises selected papers from the proceedings of the 2nd International Conference on Quantum Simulators and Design (QSD2008) held in Tokyo, Japan, between 31 May and 3 June 2008. This conference was organized under the auspices of the Development of New Quantum Simulators and Quantum Design Grant-in-Aid for Scientific Research on Priority Areas, Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT). The conference focused on the development of first principles electronic structure calculations and their applications. The aim was to provide an opportunity for discussion on the progress in computational materials design and, in particular, the development of quantum simulators and quantum design. Computational materials design is a computational approach to the development of new materials. The essential ingredient is the use of quantum simulators to design a material that meets a given specification of properties and functionalities. For this to be successful, the quantum simulator should be very reliable and be applicable to systems of realistic size. During the conference, new methods of quantum simulation and quantum design were discussed including methods beyond the local density approximation of density functional theory, order-N methods, methods dealing with excitations and reactions, and the application of these methods to the design of novel materials, devices and systems. The conference provided an international forum for experimental and theoretical researchers to exchange ideas. A total of 220 delegates from eight countries participated in the conference. There were 13 invited talks, ten oral presentations and 120 posters. The 3rd International Conference on Quantum Simulators and Design will be held in Germany in the autumn of 2011.

Combining neural networks and signed particles to simulate quantum systems more efficiently

NASA Astrophysics Data System (ADS)

Sellier, Jean Michel

2018-04-01

Recently a new formulation of quantum mechanics has been suggested which describes systems by means of ensembles of classical particles provided with a sign. This novel approach mainly consists of two steps: the computation of the Wigner kernel, a multi-dimensional function describing the effects of the potential over the system, and the field-less evolution of the particles which eventually create new signed particles in the process. Although this method has proved to be extremely advantageous in terms of computational resources - as a matter of fact it is able to simulate in a time-dependent fashion many-body systems on relatively small machines - the Wigner kernel can represent the bottleneck of simulations of certain systems. Moreover, storing the kernel can be another issue as the amount of memory needed is cursed by the dimensionality of the system. In this work, we introduce a new technique which drastically reduces the computation time and memory requirement to simulate time-dependent quantum systems which is based on the use of an appropriately tailored neural network combined with the signed particle formalism. In particular, the suggested neural network is able to compute efficiently and reliably the Wigner kernel without any training as its entire set of weights and biases is specified by analytical formulas. As a consequence, the amount of memory for quantum simulations radically drops since the kernel does not need to be stored anymore as it is now computed by the neural network itself, only on the cells of the (discretized) phase-space which are occupied by particles. As its is clearly shown in the final part of this paper, not only this novel approach drastically reduces the computational time, it also remains accurate. The author believes this work opens the way towards effective design of quantum devices, with incredible practical implications.

Triple-server blind quantum computation using entanglement swapping

NASA Astrophysics Data System (ADS)

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

2014-04-01

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

Experimental quantum simulations of many-body physics with trapped ions.

PubMed

Schneider, Ch; Porras, Diego; Schaetz, Tobias

2012-02-01

Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems.

Toward prethreshold gate-based quantum simulation of chemical dynamics: using potential energy surfaces to simulate few-channel molecular collisions

DOE PAGES

Sornborger, Andrew Tyler; Stancil, Phillip; Geller, Michael R.

2018-03-22

Here, one of the most promising applications of an error-corrected universal quantum computer is the efficient simulation of complex quantum systems such as large molecular systems. In this application, one is interested in both the electronic structure such as the ground state energy and dynamical properties such as the scattering cross section and chemical reaction rates. However, most theoretical work and experimental demonstrations have focused on the quantum computation of energies and energy surfaces. In this work, we attempt to make the prethreshold (not error-corrected) quantum simulation of dynamical properties practical as well. We show that the use of precomputedmore » potential energy surfaces and couplings enables the gate-based simulation of few-channel but otherwise realistic molecular collisions. Our approach is based on the widely used Born–Oppenheimer approximation for the structure problem coupled with a semiclassical method for the dynamics. In the latter the electrons are treated quantum mechanically but the nuclei are classical, which restricts the collisions to high energy or temperature (typically above ≈10 eV). By using operator splitting techniques optimized for the resulting time-dependent Hamiltonian simulation problem, we give several physically realistic collision examples, with 3–8 channels and circuit depths < 1000.« less

Toward prethreshold gate-based quantum simulation of chemical dynamics: using potential energy surfaces to simulate few-channel molecular collisions

NASA Astrophysics Data System (ADS)

Sornborger, Andrew T.; Stancil, Phillip; Geller, Michael R.

2018-05-01

One of the most promising applications of an error-corrected universal quantum computer is the efficient simulation of complex quantum systems such as large molecular systems. In this application, one is interested in both the electronic structure such as the ground state energy and dynamical properties such as the scattering cross section and chemical reaction rates. However, most theoretical work and experimental demonstrations have focused on the quantum computation of energies and energy surfaces. In this work, we attempt to make the prethreshold (not error-corrected) quantum simulation of dynamical properties practical as well. We show that the use of precomputed potential energy surfaces and couplings enables the gate-based simulation of few-channel but otherwise realistic molecular collisions. Our approach is based on the widely used Born-Oppenheimer approximation for the structure problem coupled with a semiclassical method for the dynamics. In the latter the electrons are treated quantum mechanically but the nuclei are classical, which restricts the collisions to high energy or temperature (typically above ≈ 10 eV). By using operator splitting techniques optimized for the resulting time-dependent Hamiltonian simulation problem, we give several physically realistic collision examples, with 3-8 channels and circuit depths < 1000.

Toward prethreshold gate-based quantum simulation of chemical dynamics: using potential energy surfaces to simulate few-channel molecular collisions

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

Sornborger, Andrew Tyler; Stancil, Phillip; Geller, Michael R.

Here, one of the most promising applications of an error-corrected universal quantum computer is the efficient simulation of complex quantum systems such as large molecular systems. In this application, one is interested in both the electronic structure such as the ground state energy and dynamical properties such as the scattering cross section and chemical reaction rates. However, most theoretical work and experimental demonstrations have focused on the quantum computation of energies and energy surfaces. In this work, we attempt to make the prethreshold (not error-corrected) quantum simulation of dynamical properties practical as well. We show that the use of precomputedmore » potential energy surfaces and couplings enables the gate-based simulation of few-channel but otherwise realistic molecular collisions. Our approach is based on the widely used Born–Oppenheimer approximation for the structure problem coupled with a semiclassical method for the dynamics. In the latter the electrons are treated quantum mechanically but the nuclei are classical, which restricts the collisions to high energy or temperature (typically above ≈10 eV). By using operator splitting techniques optimized for the resulting time-dependent Hamiltonian simulation problem, we give several physically realistic collision examples, with 3–8 channels and circuit depths < 1000.« less

Software Systems for High-performance Quantum Computing

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

Humble, Travis S; Britt, Keith A

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

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.

Quantum Computing and Second Quantization

DOE PAGES

Makaruk, Hanna Ewa

2017-02-10

Quantum computers are by their nature many particle quantum systems. Both the many-particle arrangement and being quantum are necessary for the existence of the entangled states, which are responsible for the parallelism of the quantum computers. Second quantization is a very important approximate method of describing such systems. This lecture will present the general idea of the second quantization, and discuss shortly some of the most important formulations of second quantization.

Quantum Computing and Second Quantization

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

Makaruk, Hanna Ewa

Quantum computers are by their nature many particle quantum systems. Both the many-particle arrangement and being quantum are necessary for the existence of the entangled states, which are responsible for the parallelism of the quantum computers. Second quantization is a very important approximate method of describing such systems. This lecture will present the general idea of the second quantization, and discuss shortly some of the most important formulations of second quantization.

Verification for measurement-only blind quantum computing

NASA Astrophysics Data System (ADS)

Morimae, Tomoyuki

2014-06-01

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

Quantum computing with incoherent resources and quantum jumps.

PubMed

Santos, M F; Cunha, M Terra; Chaves, R; Carvalho, A R R

2012-04-27

Spontaneous emission and the inelastic scattering of photons are two natural processes usually associated with decoherence and the reduction in the capacity to process quantum information. Here we show that, when suitably detected, these photons are sufficient to build all the fundamental blocks needed to perform quantum computation in the emitting qubits while protecting them from deleterious dissipative effects. We exemplify this by showing how to efficiently prepare graph states for the implementation of measurement-based quantum computation.

Classical simulation of quantum error correction in a Fibonacci anyon code

NASA Astrophysics Data System (ADS)

Burton, Simon; Brell, Courtney G.; Flammia, Steven T.

2017-02-01

Classically simulating the dynamics of anyonic excitations in two-dimensional quantum systems is likely intractable in general because such dynamics are sufficient to implement universal quantum computation. However, processes of interest for the study of quantum error correction in anyon systems are typically drawn from a restricted class that displays significant structure over a wide range of system parameters. We exploit this structure to classically simulate, and thereby demonstrate the success of, an error-correction protocol for a quantum memory based on the universal Fibonacci anyon model. We numerically simulate a phenomenological model of the system and noise processes on lattice sizes of up to 128 ×128 sites, and find a lower bound on the error-correction threshold of approximately 0.125 errors per edge, which is comparable to those previously known for Abelian and (nonuniversal) non-Abelian anyon models.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

A programmable five qubit quantum computer using trapped atomic ions

NASA Astrophysics Data System (ADS)

Debnath, Shantanu

2017-04-01

In order to harness the power of quantum information processing, several candidate systems have been investigated, and tailored to demonstrate only specific computations. In my thesis work, we construct a general-purpose multi-qubit device using a linear chain of trapped ion qubits, which in principle can be programmed to run any quantum algorithm. To achieve such flexibility, we develop a pulse shaping technique to realize a set of fully connected two-qubit rotations that entangle arbitrary pairs of qubits using multiple motional modes of the chain. Following a computation architecture, such highly expressive two-qubit gates along with arbitrary single-qubit rotations can be used to compile modular universal logic gates that are effected by targeted optical fields and hence can be reconfigured according to any algorithm circuit programmed in the software. As a demonstration, we run the Deutsch-Jozsa and Bernstein-Vazirani algorithm, and a fully coherent quantum Fourier transform, that we use to solve the `period finding' and `quantum phase estimation' problem. Combining these results with recent demonstrations of quantum fault-tolerance, Grover's search algorithm, and simulation of boson hopping establishes the versatility of such a computation module that can potentially be connected to other modules for future large-scale computations.

Simulation and understanding of atomic and molecular quantum crystals

NASA Astrophysics Data System (ADS)

Cazorla, Claudio; Boronat, Jordi

2017-07-01

Quantum crystals abound in the whole range of solid-state species. Below a certain threshold temperature the physical behavior of rare gases (He 4 and Ne), molecular solids (H2 and CH4 ), and some ionic (LiH), covalent (graphite), and metallic (Li) crystals can be explained only in terms of quantum nuclear effects (QNE). A detailed comprehension of the nature of quantum solids is critical for achieving progress in a number of fundamental and applied scientific fields such as planetary sciences, hydrogen storage, nuclear energy, quantum computing, and nanoelectronics. This review describes the current physical understanding of quantum crystals formed by atoms and small molecules, as well as the wide palette of simulation techniques that are used to investigate them. Relevant aspects in these materials such as phase transformations, structural properties, elasticity, crystalline defects, and the effects of reduced dimensionality are discussed thoroughly. An introduction to quantum Monte Carlo techniques, which in the present context are the simulation methods of choice, and other quantum simulation approaches (e.g., path-integral molecular dynamics and quantum thermal baths) is provided. The overarching objective of this article is twofold: first, to clarify in which crystals and physical situations the disregard of QNE may incur in important bias and erroneous interpretations. And second, to promote the study and appreciation of QNE, a topic that traditionally has been treated in the context of condensed matter physics, within the broad and interdisciplinary areas of materials science.

A Study on Fast Gates for Large-Scale Quantum Simulation with Trapped Ions.

PubMed

Taylor, Richard L; Bentley, Christopher D B; Pedernales, Julen S; Lamata, Lucas; Solano, Enrique; Carvalho, André R R; Hope, Joseph J

2017-04-12

Large-scale digital quantum simulations require thousands of fundamental entangling gates to construct the simulated dynamics. Despite success in a variety of small-scale simulations, quantum information processing platforms have hitherto failed to demonstrate the combination of precise control and scalability required to systematically outmatch classical simulators. We analyse how fast gates could enable trapped-ion quantum processors to achieve the requisite scalability to outperform classical computers without error correction. We analyze the performance of a large-scale digital simulator, and find that fidelity of around 70% is realizable for π-pulse infidelities below 10 -5 in traps subject to realistic rates of heating and dephasing. This scalability relies on fast gates: entangling gates faster than the trap period.

Self-guaranteed measurement-based quantum computation

NASA Astrophysics Data System (ADS)

Hayashi, Masahito; Hajdušek, Michal

2018-05-01

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

Toward a superconducting quantum computer. Harnessing macroscopic quantum coherence.

PubMed

Tsai, Jaw-Shen

2010-01-01

Intensive research on the construction of superconducting quantum computers has produced numerous important achievements. The quantum bit (qubit), based on the Josephson junction, is at the heart of this research. This macroscopic system has the ability to control quantum coherence. This article reviews the current state of quantum computing as well as its history, and discusses its future. Although progress has been rapid, the field remains beset with unsolved issues, and there are still many new research opportunities open to physicists and engineers.

Quantum Chess: Making Quantum Phenomena Accessible

NASA Astrophysics Data System (ADS)

Cantwell, Christopher

Quantum phenomena have remained largely inaccessible to the general public. There tends to be a scare factor associated with the word ``Quantum''. This is in large part due to the alien nature of phenomena such as superposition and entanglement. However, Quantum Computing is a very active area of research and one day we will have games that run on those quantum computers. Quantum phenomena such as superposition and entanglement will seem as normal as gravity. Is it possible to create such games today? Can we make games that are built on top of a realistic quantum simulation and introduce players of any background to quantum concepts in a fun and mentally stimulating way? One of the difficulties with any quantum simulation run on a classical computer is that the Hilbert space grows exponentially, making simulations of an appreciable size physically impossible due largely to memory restrictions. Here we will discuss the conception and development of Quantum Chess, and how to overcome some of the difficulties faced. We can then ask the question, ``What's next?'' What are some of the difficulties Quantum Chess still faces, and what is the future of quantum games?

Channel Simulation in Quantum Metrology

NASA Astrophysics Data System (ADS)

Laurenza, Riccardo; Lupo, Cosmo; Spedalieri, Gaetana; Braunstein, Samuel L.; Pirandola, Stefano

2018-04-01

In this review we discuss how channel simulation can be used to simplify the most general protocols of quantum parameter estimation, where unlimited entanglement and adaptive joint operations may be employed. Whenever the unknown parameter encoded in a quantum channel is completely transferred in an environmental program state simulating the channel, the optimal adaptive estimation cannot beat the standard quantum limit. In this setting, we elucidate the crucial role of quantum teleportation as a primitive operation which allows one to completely reduce adaptive protocols over suitable teleportation-covariant channels and derive matching upper and lower bounds for parameter estimation. For these channels,wemay express the quantum Cramér Rao bound directly in terms of their Choi matrices. Our review considers both discrete- and continuous-variable systems, also presenting some new results for bosonic Gaussian channels using an alternative sub-optimal simulation. It is an open problem to design simulations for quantum channels that achieve the Heisenberg limit.

Computational Multiqubit Tunnelling in Programmable Quantum Annealers

DTIC Science & Technology

2016-08-25

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

Parametric Quantum Search Algorithm as Quantum Walk: A Quantum Simulation

NASA Astrophysics Data System (ADS)

Ellinas, Demosthenes; Konstandakis, Christos

2016-02-01

Parametric quantum search algorithm (PQSA) is a form of quantum search that results by relaxing the unitarity of the original algorithm. PQSA can naturally be cast in the form of quantum walk, by means of the formalism of oracle algebra. This is due to the fact that the completely positive trace preserving search map used by PQSA, admits a unitarization (unitary dilation) a la quantum walk, at the expense of introducing auxiliary quantum coin-qubit space. The ensuing QW describes a process of spiral motion, chosen to be driven by two unitary Kraus generators, generating planar rotations of Bloch vector around an axis. The quadratic acceleration of quantum search translates into an equivalent quadratic saving of the number of coin qubits in the QW analogue. The associated to QW model Hamiltonian operator is obtained and is shown to represent a multi-particle long-range interacting quantum system that simulates parametric search. Finally, the relation of PQSA-QW simulator to the QW search algorithm is elucidated.

Programmable Quantum Photonic Processor Using Silicon Photonics

DTIC Science & Technology

2017-04-01

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

Benchmarking gate-based quantum computers

NASA Astrophysics Data System (ADS)

Michielsen, Kristel; Nocon, Madita; Willsch, Dennis; Jin, Fengping; Lippert, Thomas; De Raedt, Hans

2017-11-01

With the advent of public access to small gate-based quantum processors, it becomes necessary to develop a benchmarking methodology such that independent researchers can validate the operation of these processors. We explore the usefulness of a number of simple quantum circuits as benchmarks for gate-based quantum computing devices and show that circuits performing identity operations are very simple, scalable and sensitive to gate errors and are therefore very well suited for this task. We illustrate the procedure by presenting benchmark results for the IBM Quantum Experience, a cloud-based platform for gate-based quantum computing.

Contextuality and Wigner-function negativity in qubit quantum computation

NASA Astrophysics Data System (ADS)

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

2017-05-01

We describe schemes of quantum computation with magic states on qubits for which contextuality and negativity of the Wigner function are necessary resources possessed by the magic states. These schemes satisfy a constraint. Namely, the non-negativity of Wigner functions must be preserved under all available measurement operations. Furthermore, we identify stringent consistency conditions on such computational schemes, revealing the general structure by which negativity of Wigner functions, hardness of classical simulation of the computation, and contextuality are connected.

Quantum computing applied to calculations of molecular energies: CH2 benchmark.

PubMed

Veis, Libor; Pittner, Jiří

2010-11-21

Quantum computers are appealing for their ability to solve some tasks much faster than their classical counterparts. It was shown in [Aspuru-Guzik et al., Science 309, 1704 (2005)] that they, if available, would be able to perform the full configuration interaction (FCI) energy calculations with a polynomial scaling. This is in contrast to conventional computers where FCI scales exponentially. We have developed a code for simulation of quantum computers and implemented our version of the quantum FCI algorithm. We provide a detailed description of this algorithm and the results of the assessment of its performance on the four lowest lying electronic states of CH(2) molecule. This molecule was chosen as a benchmark, since its two lowest lying (1)A(1) states exhibit a multireference character at the equilibrium geometry. It has been shown that with a suitably chosen initial state of the quantum register, one is able to achieve the probability amplification regime of the iterative phase estimation algorithm even in this case.

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

Toward a superconducting quantum computer

PubMed Central

Tsai, Jaw-Shen

2010-01-01

Intensive research on the construction of superconducting quantum computers has produced numerous important achievements. The quantum bit (qubit), based on the Josephson junction, is at the heart of this research. This macroscopic system has the ability to control quantum coherence. This article reviews the current state of quantum computing as well as its history, and discusses its future. Although progress has been rapid, the field remains beset with unsolved issues, and there are still many new research opportunities open to physicists and engineers. PMID:20431256

A multiscale quantum mechanics/electromagnetics method for device simulations.

PubMed

Yam, ChiYung; Meng, Lingyi; Zhang, Yu; Chen, GuanHua

2015-04-07

Multiscale modeling has become a popular tool for research applying to different areas including materials science, microelectronics, biology, chemistry, etc. In this tutorial review, we describe a newly developed multiscale computational method, incorporating quantum mechanics into electronic device modeling with the electromagnetic environment included through classical electrodynamics. In the quantum mechanics/electromagnetics (QM/EM) method, the regions of the system where active electron scattering processes take place are treated quantum mechanically, while the surroundings are described by Maxwell's equations and a semiclassical drift-diffusion model. The QM model and the EM model are solved, respectively, in different regions of the system in a self-consistent manner. Potential distributions and current densities at the interface between QM and EM regions are employed as the boundary conditions for the quantum mechanical and electromagnetic simulations, respectively. The method is illustrated in the simulation of several realistic systems. In the case of junctionless field-effect transistors, transfer characteristics are obtained and a good agreement between experiments and simulations is achieved. Optical properties of a tandem photovoltaic cell are studied and the simulations demonstrate that multiple QM regions are coupled through the classical EM model. Finally, the study of a carbon nanotube-based molecular device shows the accuracy and efficiency of the QM/EM method.

A Study on Fast Gates for Large-Scale Quantum Simulation with Trapped Ions

PubMed Central

Taylor, Richard L.; Bentley, Christopher D. B.; Pedernales, Julen S.; Lamata, Lucas; Solano, Enrique; Carvalho, André R. R.; Hope, Joseph J.

2017-01-01

Large-scale digital quantum simulations require thousands of fundamental entangling gates to construct the simulated dynamics. Despite success in a variety of small-scale simulations, quantum information processing platforms have hitherto failed to demonstrate the combination of precise control and scalability required to systematically outmatch classical simulators. We analyse how fast gates could enable trapped-ion quantum processors to achieve the requisite scalability to outperform classical computers without error correction. We analyze the performance of a large-scale digital simulator, and find that fidelity of around 70% is realizable for π-pulse infidelities below 10−5 in traps subject to realistic rates of heating and dephasing. This scalability relies on fast gates: entangling gates faster than the trap period. PMID:28401945

Reliability of analog quantum simulation

DOE PAGES

Sarovar, Mohan; Zhang, Jun; Zeng, Lishan

2017-01-03

Analog quantum simulators (AQS) will likely be the first nontrivial application of quantum technology for predictive simulation. However, there remain questions regarding the degree of confidence that can be placed in the results of AQS since they do not naturally incorporate error correction. Specifically, how do we know whether an analog simulation of a quantum model will produce predictions that agree with the ideal model in the presence of inevitable imperfections? At the same time there is a widely held expectation that certain quantum simulation questions will be robust to errors and perturbations in the underlying hardware. Resolving these twomore » points of view is a critical step in making the most of this promising technology. In this paper we formalize the notion of AQS reliability by determining sensitivity of AQS outputs to underlying parameters, and formulate conditions for robust simulation. Our approach naturally reveals the importance of model symmetries in dictating the robust properties. Finally, to demonstrate the approach, we characterize the robust features of a variety of quantum many-body models.« less

Simulation of n-qubit quantum systems. IV. Parametrizations of quantum states, matrices and probability distributions

NASA Astrophysics Data System (ADS)

Radtke, T.; Fritzsche, S.

2008-11-01

Entanglement is known today as a key resource in many protocols from quantum computation and quantum information theory. However, despite the successful demonstration of several protocols, such as teleportation or quantum key distribution, there are still many open questions of how entanglement affects the efficiency of quantum algorithms or how it can be protected against noisy environments. The investigation of these and related questions often requires a search or optimization over the set of quantum states and, hence, a parametrization of them and various other objects. To facilitate this kind of studies in quantum information theory, here we present an extension of the FEYNMAN program that was developed during recent years as a toolbox for the simulation and analysis of quantum registers. In particular, we implement parameterizations of hermitian and unitary matrices (of arbitrary order), pure and mixed quantum states as well as separable states. In addition to being a prerequisite for the study of many optimization problems, these parameterizations also provide the necessary basis for heuristic studies which make use of random states, unitary matrices and other objects. Program summaryProgram title: FEYNMAN Catalogue identifier: ADWE_v4_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWE_v4_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 24 231 No. of bytes in distributed program, including test data, etc.: 1 416 085 Distribution format: tar.gz Programming language: Maple 11 Computer: Any computer with Maple software installed Operating system: Any system that supports Maple; program has been tested under Microsoft Windows XP, Linux Classification: 4.15 Does the new version supersede the previous version?: Yes Nature of problem: During the last decades

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.

QUANTUM COMPUTING: Quantum Entangled Bits Step Closer to IT.

PubMed

Zeilinger, A

2000-07-21

In contrast to today's computers, quantum computers and information technologies may in future be able to store and transmit information not only in the state "0" or "1," but also in superpositions of the two; information will then be stored and transmitted in entangled quantum states. Zeilinger discusses recent advances toward using this principle for quantum cryptography and highlights studies into the entanglement (or controlled superposition) of several photons, atoms, or ions.

Quantum Computing

DTIC Science & Technology

1998-04-01

information representation and processing technology, although faster than the wheels and gears of the Charles Babbage computation machine, is still in...the same computational complexity class as the Babbage machine, with bits of information represented by entities which obey classical (non-quantum...nuclear double resonances Charles M Bowden and Jonathan P. Dowling Weapons Sciences Directorate, AMSMI-RD-WS-ST Missile Research, Development, and

Quantum Computation Based on Photons with Three Degrees of Freedom

PubMed Central

Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong; Wang, Xiaojun

2016-01-01

Quantum systems are important resources for quantum computer. Different from previous encoding forms using quantum systems with one degree of freedom (DoF) or two DoFs, we investigate the possibility of photon systems encoding with three DoFs consisting of the polarization DoF and two spatial DoFs. By exploring the optical circular birefringence induced by an NV center in a diamond embedded in the photonic crystal cavity, we propose several hybrid controlled-NOT (hybrid CNOT) gates operating on the two-photon or one-photon system. These hybrid CNOT gates show that three DoFs may be encoded as independent qubits without auxiliary DoFs. Our result provides a useful way to reduce quantum simulation resources by exploring complex quantum systems for quantum applications requiring large qubit systems. PMID:27174302

Quantum Computation Based on Photons with Three Degrees of Freedom.

PubMed

Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong; Wang, Xiaojun

2016-05-13

Quantum systems are important resources for quantum computer. Different from previous encoding forms using quantum systems with one degree of freedom (DoF) or two DoFs, we investigate the possibility of photon systems encoding with three DoFs consisting of the polarization DoF and two spatial DoFs. By exploring the optical circular birefringence induced by an NV center in a diamond embedded in the photonic crystal cavity, we propose several hybrid controlled-NOT (hybrid CNOT) gates operating on the two-photon or one-photon system. These hybrid CNOT gates show that three DoFs may be encoded as independent qubits without auxiliary DoFs. Our result provides a useful way to reduce quantum simulation resources by exploring complex quantum systems for quantum applications requiring large qubit systems.

Multi-party Semi-quantum Key Agreement with Delegating Quantum Computation

NASA Astrophysics Data System (ADS)

Liu, Wen-Jie; Chen, Zhen-Yu; Ji, Sai; Wang, Hai-Bin; Zhang, Jun

2017-10-01

A multi-party semi-quantum key agreement (SQKA) protocol based on delegating quantum computation (DQC) model is proposed by taking Bell states as quantum resources. In the proposed protocol, the participants only need the ability of accessing quantum channel and preparing single photons {|0〉, |1〉, |+〉, |-〉}, while the complicated quantum operations, such as the unitary operations and Bell measurement, will be delegated to the remote quantum center. Compared with previous quantum key agreement protocols, this client-server model is more feasible in the early days of the emergence of quantum computers. In order to prevent the attacks from outside eavesdroppers, inner participants and quantum center, two single photon sequences are randomly inserted into Bell states: the first sequence is used to perform the quantum channel detection, while the second is applied to disorder the positions of message qubits, which guarantees the security of the protocol.

Quantum Monte Carlo tunneling from quantum chemistry to quantum annealing

NASA Astrophysics Data System (ADS)

Mazzola, Guglielmo; Smelyanskiy, Vadim N.; Troyer, Matthias

2017-10-01

Quantum tunneling is ubiquitous across different fields, from quantum chemical reactions and magnetic materials to quantum simulators and quantum computers. While simulating the real-time quantum dynamics of tunneling is infeasible for high-dimensional systems, quantum tunneling also shows up in quantum Monte Carlo (QMC) simulations, which aim to simulate quantum statistics with resources growing only polynomially with the system size. Here we extend the recent results obtained for quantum spin models [Phys. Rev. Lett. 117, 180402 (2016), 10.1103/PhysRevLett.117.180402], and we study continuous-variable models for proton transfer reactions. We demonstrate that QMC simulations efficiently recover the scaling of ground-state tunneling rates due to the existence of an instanton path, which always connects the reactant state with the product. We discuss the implications of our results in the context of quantum chemical reactions and quantum annealing, where quantum tunneling is expected to be a valuable resource for solving combinatorial optimization problems.

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.

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.

Experimental comparison of two quantum computing architectures

PubMed Central

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

2017-01-01

We run a selection of algorithms on two state-of-the-art 5-qubit quantum computers that are based on different technology platforms. One is a publicly accessible superconducting transmon device (www.research.ibm.com/ibm-q) with limited connectivity, and the other is a fully connected trapped-ion system. Even though the two systems have different native quantum interactions, both can be programed in a way that is blind to the underlying hardware, thus allowing a comparison of identical quantum algorithms between different physical systems. We show that quantum algorithms and circuits that use more connectivity clearly benefit from a better-connected system of qubits. Although the quantum systems here are not yet large enough to eclipse classical computers, this experiment exposes critical factors of scaling quantum computers, such as qubit connectivity and gate expressivity. In addition, the results suggest that codesigning particular quantum applications with the hardware itself will be paramount in successfully using quantum computers in the future. PMID:28325879

Experimental comparison of two quantum computing architectures.

PubMed

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

2017-03-28

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

Hybrid classical/quantum simulation for infrared spectroscopy of water

NASA Astrophysics Data System (ADS)

Maekawa, Yuki; Sasaoka, Kenji; Ube, Takuji; Ishiguro, Takashi; Yamamoto, Takahiro

2018-05-01

We have developed a hybrid classical/quantum simulation method to calculate the infrared (IR) spectrum of water. The proposed method achieves much higher accuracy than conventional classical molecular dynamics (MD) simulations at a much lower computational cost than ab initio MD simulations. The IR spectrum of water is obtained as an ensemble average of the eigenvalues of the dynamical matrix constructed by ab initio calculations, using the positions of oxygen atoms that constitute water molecules obtained from the classical MD simulation. The calculated IR spectrum is in excellent agreement with the experimental IR spectrum.

Simulation of quantum dynamics with integrated photonics

NASA Astrophysics Data System (ADS)

Sansoni, Linda; Sciarrino, Fabio; Mataloni, Paolo; Crespi, Andrea; Ramponi, Roberta; Osellame, Roberto

2012-12-01

In recent years, quantum walks have been proposed as promising resources for the simulation of physical quantum systems. In fact it is widely adopted to simulate quantum dynamics. Up to now single particle quantum walks have been experimentally demonstrated by different approaches, while only few experiments involving many-particle quantum walks have been realized. Here we simulate the 2-particle dynamics on a discrete time quantum walk, built on an array of integrated waveguide beam splitters. The polarization independence of the quantum walk circuit allowed us to exploit the polarization entanglement to encode the symmetry of the two-photon wavefunction, thus the bunching-antibunching behavior of non interacting bosons and fermions has been simulated. We have also characterized the possible distinguishability and decoherence effects arising in such a structure. This study is necessary in view of the realization of a quantum simulator based on an integrated optical array built on a large number of beam splitters.

Non-unitary probabilistic quantum computing circuit and method

NASA Technical Reports Server (NTRS)

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

2009-01-01

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

Witnessing eigenstates for quantum simulation of Hamiltonian spectra

PubMed Central

Santagati, Raffaele; Wang, Jianwei; Gentile, Antonio A.; Paesani, Stefano; Wiebe, Nathan; McClean, Jarrod R.; Morley-Short, Sam; Shadbolt, Peter J.; Bonneau, Damien; Silverstone, Joshua W.; Tew, David P.; Zhou, Xiaoqi; O’Brien, Jeremy L.; Thompson, Mark G.

2018-01-01

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. We introduce the concept of an “eigenstate witness” and, through it, provide a new quantum approach that combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32 bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress toward quantum chemistry on quantum computers. PMID:29387796

Interferometric Computation Beyond Quantum Theory

NASA Astrophysics Data System (ADS)

Garner, Andrew J. P.

2018-03-01

There are quantum solutions for computational problems that make use of interference at some stage in the algorithm. These stages can be mapped into the physical setting of a single particle travelling through a many-armed interferometer. There has been recent foundational interest in theories beyond quantum theory. Here, we present a generalized formulation of computation in the context of a many-armed interferometer, and explore how theories can differ from quantum theory and still perform distributed calculations in this set-up. We shall see that quaternionic quantum theory proves a suitable candidate, whereas box-world does not. We also find that a classical hidden variable model first presented by Spekkens (Phys Rev A 75(3): 32100, 2007) can also be used for this type of computation due to the epistemic restriction placed on the hidden variable.

Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics

PubMed Central

Kreula, J. M.; Clark, S. R.; Jaksch, D.

2016-01-01

We propose a non-linear, hybrid quantum-classical scheme for simulating non-equilibrium dynamics of strongly correlated fermions described by the Hubbard model in a Bethe lattice in the thermodynamic limit. Our scheme implements non-equilibrium dynamical mean field theory (DMFT) and uses a digital quantum simulator to solve a quantum impurity problem whose parameters are iterated to self-consistency via a classically computed feedback loop where quantum gate errors can be partly accounted for. We analyse the performance of the scheme in an example case. PMID:27609673

Topics in linear optical quantum computation

NASA Astrophysics Data System (ADS)

Glancy, Scott Charles

This thesis covers several topics in optical quantum computation. A quantum computer is a computational device which is able to manipulate information by performing unitary operations on some physical system whose state can be described as a vector (or mixture of vectors) in a Hilbert space. The basic unit of information, called the qubit, is considered to be a system with two orthogonal states, which are assigned logical values of 0 and 1. Photons make excellent candidates to serve as qubits. They have little interactions with the environment. Many operations can be performed using very simple linear optical devices such as beam splitters and phase shifters. Photons can easily be processed through circuit-like networks. Operations can be performed in very short times. Photons are ideally suited for the long-distance communication of quantum information. The great difficulty in constructing an optical quantum computer is that photons naturally interact weakly with one another. This thesis first gives a brief review of two early approaches to optical quantum computation. It will describe how any discrete unitary operation can be performed using a single photon and a network of beam splitters, and how the Kerr effect can be used to construct a two photon logic gate. Second, this work provides a thorough introduction to the linear optical quantum computer developed by Knill, Laflamme, and Milburn. It then presents this author's results on the reliability of this scheme when implemented using imperfect photon detectors. This author finds that quantum computers of this sort cannot be built using current technology. Third, this dissertation describes a method for constructing a linear optical quantum computer using nearly orthogonal coherent states of light as the qubits. It shows how a universal set of logic operations can be performed, including calculations of the fidelity with which these operations may be accomplished. It discusses methods for reducing and

Arrays of individually controlled ions suitable for two-dimensional quantum simulations

DOE PAGES

Mielenz, Manuel; Kalis, Henning; Wittemer, Matthias; ...

2016-06-13

A precisely controlled quantum system may reveal a fundamental understanding of another, less accessible system of interest. A universal quantum computer is currently out of reach, but an analogue quantum simulator that makes relevant observables, interactions and states of a quantum model accessible could permit insight into complex dynamics. Several platforms have been suggested and proof-of-principle experiments have been conducted. Here, we operate two-dimensional arrays of three trapped ions in individually controlled harmonic wells forming equilateral triangles with side lengths 40 and 80 μm. In our approach, which is scalable to arbitrary two-dimensional lattices, we demonstrate individual control of themore » electronic and motional degrees of freedom, preparation of a fiducial initial state with ion motion close to the ground state, as well as a tuning of couplings between ions within experimental sequences. Lastly, our work paves the way towards a quantum simulator of two-dimensional systems designed at will.« less

Arrays of individually controlled ions suitable for two-dimensional quantum simulations

PubMed Central

Mielenz, Manuel; Kalis, Henning; Wittemer, Matthias; Hakelberg, Frederick; Warring, Ulrich; Schmied, Roman; Blain, Matthew; Maunz, Peter; Moehring, David L.; Leibfried, Dietrich; Schaetz, Tobias

2016-01-01

A precisely controlled quantum system may reveal a fundamental understanding of another, less accessible system of interest. A universal quantum computer is currently out of reach, but an analogue quantum simulator that makes relevant observables, interactions and states of a quantum model accessible could permit insight into complex dynamics. Several platforms have been suggested and proof-of-principle experiments have been conducted. Here, we operate two-dimensional arrays of three trapped ions in individually controlled harmonic wells forming equilateral triangles with side lengths 40 and 80 μm. In our approach, which is scalable to arbitrary two-dimensional lattices, we demonstrate individual control of the electronic and motional degrees of freedom, preparation of a fiducial initial state with ion motion close to the ground state, as well as a tuning of couplings between ions within experimental sequences. Our work paves the way towards a quantum simulator of two-dimensional systems designed at will. PMID:27291425

The Quantum Human Computer (QHC) Hypothesis

ERIC Educational Resources Information Center

Salmani-Nodoushan, Mohammad Ali

2008-01-01

This article attempts to suggest the existence of a human computer called Quantum Human Computer (QHC) on the basis of an analogy between human beings and computers. To date, there are two types of computers: Binary and Quantum. The former operates on the basis of binary logic where an object is said to exist in either of the two states of 1 and…

Quantum computing: Quantum advantage deferred

NASA Astrophysics Data System (ADS)

Childs, Andrew M.

2017-12-01

A type of optics experiment called a boson sampler could be among the easiest routes to demonstrating the power of quantum computers. But recent work shows that super-classical boson sampling may be a long way off.

Simulation of n-qubit quantum systems. III. Quantum operations

NASA Astrophysics Data System (ADS)

Radtke, T.; Fritzsche, S.

2007-05-01

often result in very large symbolic expressions that dramatically slow down the evaluation of measures or other quantities. In these cases, MAPLE's assume facility sometimes helps to reduce the complexity of symbolic expressions, but often only numerical evaluation is possible. Since the complexity of the FEYNMAN commands is very different, no general scaling law for the CPU time and memory usage can be given. No. of bytes in distributed program including test data, etc.: 799 265 No. of lines in distributed program including test data, etc.: 18 589 Distribution format: tar.gz Reasons for new version: While the previous program versions were designed mainly to create and manipulate the state of quantum registers, the present extension aims to support quantum operations as the essential ingredient for studying the effects of noisy environments. Does this version supersede the previous version: Yes Nature of the physical problem: Today, entanglement is identified as the essential resource in virtually all aspects of quantum information theory. In most practical implementations of quantum information protocols, however, decoherence typically limits the lifetime of entanglement. It is therefore necessary and highly desirable to understand the evolution of entanglement in noisy environments. Method of solution: Using the computer algebra system MAPLE, we have developed a set of procedures that support the definition and manipulation of n-qubit quantum registers as well as (unitary) logic gates and (nonunitary) quantum operations that act on the quantum registers. The provided hierarchy of commands can be used interactively in order to simulate and analyze the evolution of n-qubit quantum systems in ideal and nonideal quantum circuits.

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.

Radio-frequency measurement in semiconductor quantum computation

NASA Astrophysics Data System (ADS)

Han, TianYi; Chen, MingBo; Cao, Gang; Li, HaiOu; Xiao, Ming; Guo, GuoPing

2017-05-01

Semiconductor quantum dots have attracted wide interest for the potential realization of quantum computation. To realize efficient quantum computation, fast manipulation and the corresponding readout are necessary. In the past few decades, considerable progress of quantum manipulation has been achieved experimentally. To meet the requirements of high-speed readout, radio-frequency (RF) measurement has been developed in recent years, such as RF-QPC (radio-frequency quantum point contact) and RF-DGS (radio-frequency dispersive gate sensor). Here we specifically demonstrate the principle of the radio-frequency reflectometry, then review the development and applications of RF measurement, which provides a feasible way to achieve high-bandwidth readout in quantum coherent control and also enriches the methods to study these artificial mesoscopic quantum systems. Finally, we prospect the future usage of radio-frequency reflectometry in scaling-up of the quantum computing models.

Quantum plug n’ play: modular computation in the quantum regime

NASA Astrophysics Data System (ADS)

Thompson, Jayne; Modi, Kavan; Vedral, Vlatko; Gu, Mile

2018-01-01

Classical computation is modular. It exploits plug n’ play architectures which allow us to use pre-fabricated circuits without knowing their construction. This bestows advantages such as allowing parts of the computational process to be outsourced, and permitting individual circuit components to be exchanged and upgraded. Here, we introduce a formal framework to describe modularity in the quantum regime. We demonstrate a ‘no-go’ theorem, stipulating that it is not always possible to make use of quantum circuits without knowing their construction. This has significant consequences for quantum algorithms, forcing the circuit implementation of certain quantum algorithms to be rebuilt almost entirely from scratch after incremental changes in the problem—such as changing the number being factored in Shor’s algorithm. We develop a workaround capable of restoring modularity, and apply it to design a modular version of Shor’s algorithm that exhibits increased versatility and reduced complexity. In doing so we pave the way to a realistic framework whereby ‘quantum chips’ and remote servers can be invoked (or assembled) to implement various parts of a more complex quantum computation.

Demonstration of measurement-only blind quantum computing

NASA Astrophysics Data System (ADS)

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

2016-01-01

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

Blueprint for a microwave trapped ion quantum computer.

PubMed

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

2017-02-01

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

Blueprint for a microwave trapped ion quantum computer

PubMed Central

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

2017-01-01

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

A surface code quantum computer in silicon

PubMed Central

Hill, Charles D.; Peretz, Eldad; Hile, Samuel J.; House, Matthew G.; Fuechsle, Martin; Rogge, Sven; Simmons, Michelle Y.; Hollenberg, Lloyd C. L.

2015-01-01

The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel—posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited. PMID:26601310

A surface code quantum computer in silicon.

PubMed

Hill, Charles D; Peretz, Eldad; Hile, Samuel J; House, Matthew G; Fuechsle, Martin; Rogge, Sven; Simmons, Michelle Y; Hollenberg, Lloyd C L

2015-10-01

The exceptionally long quantum coherence times of phosphorus donor nuclear spin qubits in silicon, coupled with the proven scalability of silicon-based nano-electronics, make them attractive candidates for large-scale quantum computing. However, the high threshold of topological quantum error correction can only be captured in a two-dimensional array of qubits operating synchronously and in parallel-posing formidable fabrication and control challenges. We present an architecture that addresses these problems through a novel shared-control paradigm that is particularly suited to the natural uniformity of the phosphorus donor nuclear spin qubit states and electronic confinement. The architecture comprises a two-dimensional lattice of donor qubits sandwiched between two vertically separated control layers forming a mutually perpendicular crisscross gate array. Shared-control lines facilitate loading/unloading of single electrons to specific donors, thereby activating multiple qubits in parallel across the array on which the required operations for surface code quantum error correction are carried out by global spin control. The complexities of independent qubit control, wave function engineering, and ad hoc quantum interconnects are explicitly avoided. With many of the basic elements of fabrication and control based on demonstrated techniques and with simulated quantum operation below the surface code error threshold, the architecture represents a new pathway for large-scale quantum information processing in silicon and potentially in other qubit systems where uniformity can be exploited.

Performing quantum computing experiments in the cloud

NASA Astrophysics Data System (ADS)

Devitt, Simon J.

2016-09-01

Quantum computing technology has reached a second renaissance in the past five years. Increased interest from both the private and public sector combined with extraordinary theoretical and experimental progress has solidified this technology as a major advancement in the 21st century. As anticipated my many, some of the first realizations of quantum computing technology has occured over the cloud, with users logging onto dedicated hardware over the classical internet. Recently, IBM has released the Quantum Experience, which allows users to access a five-qubit quantum processor. In this paper we take advantage of this online availability of actual quantum hardware and present four quantum information experiments. We utilize the IBM chip to realize protocols in quantum error correction, quantum arithmetic, quantum graph theory, and fault-tolerant quantum computation by accessing the device remotely through the cloud. While the results are subject to significant noise, the correct results are returned from the chip. This demonstrates the power of experimental groups opening up their technology to a wider audience and will hopefully allow for the next stage of development in quantum information technology.

Quantum Computation of Fluid Dynamics

DTIC Science & Technology

1998-02-16

state of the quantum computer’s "memory". With N qubits, the quantum state IT) resides in an exponentially large Hilbert space with 2 N dimensions. A new...size of the Hilbert space in which the entanglement occurs. And to make matters worse, even if a quantum computer was constructed with a large number of...number of qubits "* 2 N is the size of the full Hilbert space "* 2 B is the size of the on-site submanifold, denoted 71 "* B is the size of the

Universal quantum computation with little entanglement.

PubMed

Van den Nest, Maarten

2013-02-08

We show that universal quantum computation can be achieved in the standard pure-state circuit model while the entanglement entropy of every bipartition is small in each step of the computation. The entanglement entropy required for large-scale quantum computation even tends to zero. Moreover we show that the same conclusion applies to many entanglement measures commonly used in the literature. This includes e.g., the geometric measure, localizable entanglement, multipartite concurrence, squashed entanglement, witness-based measures, and more generally any entanglement measure which is continuous in a certain natural sense. These results demonstrate that many entanglement measures are unsuitable tools to assess the power of quantum computers.

Materials Frontiers to Empower Quantum Computing

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

Taylor, Antoinette Jane; Sarrao, John Louis; Richardson, Christopher

This is an exciting time at the nexus of quantum computing and materials research. The materials frontiers described in this report represent a significant advance in electronic materials and our understanding of the interactions between the local material and a manufactured quantum state. Simultaneously, directed efforts to solve materials issues related to quantum computing provide an opportunity to control and probe the fundamental arrangement of matter that will impact all electronic materials. An opportunity exists to extend our understanding of materials functionality from electronic-grade to quantum-grade by achieving a predictive understanding of noise and decoherence in qubits and their originsmore » in materials defects and environmental coupling. Realizing this vision systematically and predictively will be transformative for quantum computing and will represent a qualitative step forward in materials prediction and control.« less

Geometric manipulation of trapped ions for quantum computation.

PubMed

Duan, L M; Cirac, J I; Zoller, P

2001-06-01

We propose an experimentally feasible scheme to achieve quantum computation based solely on geometric manipulations of a quantum system. The desired geometric operations are obtained by driving the quantum system to undergo appropriate adiabatic cyclic evolutions. Our implementation of the all-geometric quantum computation is based on laser manipulation of a set of trapped ions. An all-geometric approach, apart from its fundamental interest, offers a possible method for robust quantum computation.

Classical simulation of infinite-size quantum lattice systems in two spatial dimensions.

PubMed

Jordan, J; Orús, R; Vidal, G; Verstraete, F; Cirac, J I

2008-12-19

We present an algorithm to simulate two-dimensional quantum lattice systems in the thermodynamic limit. Our approach builds on the projected entangled-pair state algorithm for finite lattice systems [F. Verstraete and J. I. Cirac, arxiv:cond-mat/0407066] and the infinite time-evolving block decimation algorithm for infinite one-dimensional lattice systems [G. Vidal, Phys. Rev. Lett. 98, 070201 (2007)10.1103/PhysRevLett.98.070201]. The present algorithm allows for the computation of the ground state and the simulation of time evolution in infinite two-dimensional systems that are invariant under translations. We demonstrate its performance by obtaining the ground state of the quantum Ising model and analyzing its second order quantum phase transition.

Universal quantum computing using (Zd) 3 symmetry-protected topologically ordered states

NASA Astrophysics Data System (ADS)

Chen, Yanzhu; Prakash, Abhishodh; Wei, Tzu-Chieh

2018-02-01

Measurement-based quantum computation describes a scheme where entanglement of resource states is utilized to simulate arbitrary quantum gates via local measurements. Recent works suggest that symmetry-protected topologically nontrivial, short-ranged entangled states are promising candidates for such a resource. Miller and Miyake [npj Quantum Inf. 2, 16036 (2016), 10.1038/npjqi.2016.36] recently constructed a particular Z2×Z2×Z2 symmetry-protected topological state on the Union Jack lattice and established its quantum-computational universality. However, they suggested that the same construction on the triangular lattice might not lead to a universal resource. Instead of qubits, we generalize the construction to qudits and show that the resulting (d -1 ) qudit nontrivial Zd×Zd×Zd symmetry-protected topological states are universal on the triangular lattice, for d being a prime number greater than 2. The same construction also holds for other 3-colorable lattices, including the Union Jack lattice.

Computational applications of the many-interacting-worlds interpretation of quantum mechanics.

PubMed

Sturniolo, Simone

2018-05-01

While historically many quantum-mechanical simulations of molecular dynamics have relied on the Born-Oppenheimer approximation to separate electronic and nuclear behavior, recently a great deal of interest has arisen in quantum effects in nuclear dynamics as well. Due to the computational difficulty of solving the Schrödinger equation in full, these effects are often treated with approximate methods. In this paper, we present an algorithm to tackle these problems using an extension to the many-interacting-worlds approach to quantum mechanics. This technique uses a kernel function to rebuild the probability density, and therefore, in contrast with the approximation presented in the original paper, it can be naturally extended to n-dimensional systems. This opens up the possibility of performing quantum ground-state searches with steepest-descent methods, and it could potentially lead to real-time quantum molecular-dynamics simulations. The behavior of the algorithm is studied in different potentials and numbers of dimensions and compared both to the original approach and to exact Schrödinger equation solutions whenever possible.

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.

Non-unitary probabilistic quantum computing

NASA Technical Reports Server (NTRS)

Gingrich, Robert M.; Williams, Colin P.

2004-01-01

We present a method for designing quantum circuits that perform non-unitary quantum computations on n-qubit states probabilistically, and give analytic expressions for the success probability and fidelity.

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

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

Experimental simulation of the Unruh effect on an NMR quantum simulator

NASA Astrophysics Data System (ADS)

Jin, FangZhou; Chen, HongWei; Rong, Xing; Zhou, Hui; Shi, MingJun; Zhang, Qi; Ju, ChenYong; Cai, YiFu; Luo, ShunLong; Peng, XinHua; Du, JiangFeng

2016-03-01

The Unruh effect is one of the most fundamental manifestations of the fact that the particle content of a field theory is observer dependent. However, there has been so far no experimental verification of this effect, as the associated temperatures lie far below any observable threshold. Recently, physical phenomena, which are of great experimental challenge, have been investigated by quantum simulations in various fields. Here we perform a proof-of-principle simulation of the evolution of fermionic modes under the Unruh effect with a nuclear magnetic resonance (NMR) quantum simulator. By the quantum simulator, we experimentally demonstrate the behavior of Unruh temperature with acceleration, and we further investigate the quantum correlations quantified by quantum discord between two fermionic modes as seen by two relatively accelerated observers. It is shown that the quantum correlations can be created by the Unruh effect from the classically correlated states. Our work may provide a promising way to explore the quantum physics of accelerated systems.

Efficient quantum circuits for one-way quantum computing.

PubMed

Tanamoto, Tetsufumi; Liu, Yu-Xi; Hu, Xuedong; Nori, Franco

2009-03-13

While Ising-type interactions are ideal for implementing controlled phase flip gates in one-way quantum computing, natural interactions between solid-state qubits are most often described by either the XY or the Heisenberg models. We show an efficient way of generating cluster states directly using either the imaginary SWAP (iSWAP) gate for the XY model, or the sqrt[SWAP] gate for the Heisenberg model. Our approach thus makes one-way quantum computing more feasible for solid-state devices.

Universal quantum gates for Single Cooper Pair Box based quantum computing

NASA Technical Reports Server (NTRS)

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

2000-01-01

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

Quantum Optical Implementations of Quantum Computing and Quantum Informatics Protocols

DTIC Science & Technology

2007-11-20

4, 2005. ) 14. M. 0. Scully, "The EPR Paradox Revisted", AMO Physics Seminar, TAMU Jan. 18, 2005. 15. M. S. Zubairy, "Quantum computing: Cavity QED...the EPR dispersion relation and the average photon number. We have shown that atomic coherence is the key to the development of such a laser. In...PRISM-TAMU Symposium on Quantum Material Science, Princeton University, February 21-22, 2005. ) 21. M. 0. Scully, "From EPR to quantum eraser: The Role

Three-Dimensional Wiring for Extensible Quantum Computing: The Quantum Socket

NASA Astrophysics Data System (ADS)

Béjanin, J. H.; McConkey, T. G.; Rinehart, J. R.; Earnest, C. T.; McRae, C. R. H.; Shiri, D.; Bateman, J. D.; Rohanizadegan, Y.; Penava, B.; Breul, P.; Royak, S.; Zapatka, M.; Fowler, A. G.; Mariantoni, M.

2016-10-01

Quantum computing architectures are on the verge of scalability, a key requirement for the implementation of a universal quantum computer. The next stage in this quest is the realization of quantum error-correction codes, which will mitigate the impact of faulty quantum information on a quantum computer. Architectures with ten or more quantum bits (qubits) have been realized using trapped ions and superconducting circuits. While these implementations are potentially scalable, true scalability will require systems engineering to combine quantum and classical hardware. One technology demanding imminent efforts is the realization of a suitable wiring method for the control and the measurement of a large number of qubits. In this work, we introduce an interconnect solution for solid-state qubits: the quantum socket. The quantum socket fully exploits the third dimension to connect classical electronics to qubits with higher density and better performance than two-dimensional methods based on wire bonding. The quantum socket is based on spring-mounted microwires—the three-dimensional wires—that push directly on a microfabricated chip, making electrical contact. A small wire cross section (approximately 1 mm), nearly nonmagnetic components, and functionality at low temperatures make the quantum socket ideal for operating solid-state qubits. The wires have a coaxial geometry and operate over a frequency range from dc to 8 GHz, with a contact resistance of approximately 150 m Ω , an impedance mismatch of approximately 10 Ω , and minimal cross talk. As a proof of principle, we fabricate and use a quantum socket to measure high-quality superconducting resonators at a temperature of approximately 10 mK. Quantum error-correction codes such as the surface code will largely benefit from the quantum socket, which will make it possible to address qubits located on a two-dimensional lattice. The present implementation of the socket could be readily extended to accommodate a

Nanoscale solid-state quantum computing

NASA Astrophysics Data System (ADS)

Ardavan, A.; Austwick, M.; Benjamin, S.C.; Briggs, G.A.D.; Dennis, T.J.S.; Ferguson, A.; Hasko, D.G.; Kanai, M.; Khlobystov, A.N.; Lovett, B.W.; Morley, G.W.; Oliver, R.A.; Pettifor, D.G.; Porfyrakis, K.; Reina, J.H.; Rice, J.H.; Smith, J.D.; Taylor, R.A.; Williams, D.A.; Adelmann, C.; Mariette, H.; Hamers, R.J.

2003-07-01

Most experts agree that it is too early to say how quantum computers will eventually be built, and several nanoscale solid-state schemes are being implemented in a range of materials. Nanofabricated quantum dots can be made in designer configurations, with established technology for controlling interactions and for reading out results. Epitaxial quantum dots can be grown in vertical arrays in semiconductors, and ultrafast optical techniques are available for controlling and measuring their excitations. Single-walled carbon nanotubes can be used for molecular self-assembly of endohedral fullerenes, which can embody quantum information in the electron spin. The challenges of individual addressing in such tiny structures could rapidly become intractable with increasing numbers of qubits, but these schemes are amenable to global addressing methods for computation.

Homomorphic encryption experiments on IBM's cloud quantum computing platform

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

Reversibility and measurement in quantum computing

NASA Astrophysics Data System (ADS)

Leãao, J. P.

1998-03-01

The relation between computation and measurement at a fundamental physical level is yet to be understood. Rolf Landauer was perhaps the first to stress the strong analogy between these two concepts. His early queries have regained pertinence with the recent efforts to developed realizable models of quantum computers. In this context the irreversibility of quantum measurement appears in conflict with the requirement of reversibility of the overall computation associated with the unitary dynamics of quantum evolution. The latter in turn is responsible for the features of superposition and entanglement which make some quantum algorithms superior to classical ones for the same task in speed and resource demand. In this article we advocate an approach to this question which relies on a model of computation designed to enforce the analogy between the two concepts instead of demarcating them as it has been the case so far. The model is introduced as a symmetrization of the classical Turing machine model and is then carried on to quantum mechanics, first as a an abstract local interaction scheme (symbolic measurement) and finally in a nonlocal noninteractive implementation based on Aharonov-Bohm potentials and modular variables. It is suggested that this implementation leads to the most ubiquitous of quantum algorithms: the Discrete Fourier Transform.

Irreconcilable difference between quantum walks and adiabatic quantum computing

NASA Astrophysics Data System (ADS)

Wong, Thomas G.; Meyer, David A.

2016-06-01

Continuous-time quantum walks and adiabatic quantum evolution are two general techniques for quantum computing, both of which are described by Hamiltonians that govern their evolutions by Schrödinger's equation. In the former, the Hamiltonian is fixed, while in the latter, the Hamiltonian varies with time. As a result, their formulations of Grover's algorithm evolve differently through Hilbert space. We show that this difference is fundamental; they cannot be made to evolve along each other's path without introducing structure more powerful than the standard oracle for unstructured search. For an adiabatic quantum evolution to evolve like the quantum walk search algorithm, it must interpolate between three fixed Hamiltonians, one of which is complex and introduces structure that is stronger than the oracle for unstructured search. Conversely, for a quantum walk to evolve along the path of the adiabatic search algorithm, it must be a chiral quantum walk on a weighted, directed star graph with structure that is also stronger than the oracle for unstructured search. Thus, the two techniques, although similar in being described by Hamiltonians that govern their evolution, compute by fundamentally irreconcilable means.

Quantum and classical dynamics in adiabatic computation

NASA Astrophysics Data System (ADS)

Crowley, P. J. D.; Äńurić, T.; Vinci, W.; Warburton, P. A.; Green, A. G.

2014-10-01

Adiabatic transport provides a powerful way to manipulate quantum states. By preparing a system in a readily initialized state and then slowly changing its Hamiltonian, one may achieve quantum states that would otherwise be inaccessible. Moreover, a judicious choice of final Hamiltonian whose ground state encodes the solution to a problem allows adiabatic transport to be used for universal quantum computation. However, the dephasing effects of the environment limit the quantum correlations that an open system can support and degrade the power of such adiabatic computation. We quantify this effect by allowing the system to evolve over a restricted set of quantum states, providing a link between physically inspired classical optimization algorithms and quantum adiabatic optimization. This perspective allows us to develop benchmarks to bound the quantum correlations harnessed by an adiabatic computation. We apply these to the D-Wave Vesuvius machine with revealing—though inconclusive—results.

Monte Carlo simulations of quantum dot solar concentrators: ray tracing based on fluorescence mapping

NASA Astrophysics Data System (ADS)

Schuler, A.; Kostro, A.; Huriet, B.; Galande, C.; Scartezzini, J.-L.

2008-08-01

One promising application of semiconductor nanostructures in the field of photovoltaics might be quantum dot solar concentrators. Quantum dot containing nanocomposite thin films are synthesized at EPFL-LESO by a low cost sol-gel process. In order to study the potential of the novel planar photoluminescent concentrators, reliable computer simulations are needed. A computer code for ray tracing simulations of quantum dot solar concentrators has been developed at EPFL-LESO on the basis of Monte Carlo methods that are applied to polarization-dependent reflection/transmission at interfaces, photon absorption by the semiconductor nanocrystals and photoluminescent reemission. The software allows importing measured or theoretical absorption/reemission spectra describing the photoluminescent properties of the quantum dots. Hereby the properties of photoluminescent reemission are described by a set of emission spectra depending on the energy of the incoming photon, allowing to simulate the photoluminescent emission using the inverse function method. By our simulations, the importance of two main factors is revealed, an emission spectrum matched to the spectral efficiency curve of the photovoltaic cell, and a large Stokes shift, which is advantageous for the lateral energy transport. No significant energy losses are implied when the quantum dots are contained within a nanocomposite coating instead of being dispersed in the entire volume of the pane. Together with the knowledge on the optoelectronical properties of suitable photovoltaic cells, the simulations allow to predict the total efficiency of the envisaged concentrating PV systems, and to optimize photoluminescent emission frequencies, optical densities, and pane dimensions.

Nonadiabatic holonomic quantum computation in decoherence-free subspaces.

PubMed

Xu, G F; Zhang, J; Tong, D M; Sjöqvist, Erik; Kwek, L C

2012-10-26

Quantum computation that combines the coherence stabilization virtues of decoherence-free subspaces and the fault tolerance of geometric holonomic control is of great practical importance. Some schemes of adiabatic holonomic quantum computation in decoherence-free subspaces have been proposed in the past few years. However, nonadiabatic holonomic quantum computation in decoherence-free subspaces, which avoids a long run-time requirement but with all the robust advantages, remains an open problem. Here, we demonstrate how to realize nonadiabatic holonomic quantum computation in decoherence-free subspaces. By using only three neighboring physical qubits undergoing collective dephasing to encode one logical qubit, we realize a universal set of quantum gates.

Hybrid architecture for encoded measurement-based quantum computation

PubMed Central

Zwerger, M.; Briegel, H. J.; Dür, W.

2014-01-01

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

The ambiguity of simplicity in quantum and classical simulation

NASA Astrophysics Data System (ADS)

Aghamohammadi, Cina; Mahoney, John R.; Crutchfield, James P.

2017-04-01

A system's perceived simplicity depends on whether it is represented classically or quantally. This is not so surprising, as classical and quantum physics are descriptive frameworks built on different assumptions that capture, emphasize, and express different properties and mechanisms. What is surprising is that, as we demonstrate, simplicity is ambiguous: the relative simplicity between two systems can change sign when moving between classical and quantum descriptions. Here, we associate simplicity with small model-memory. We see that the notions of absolute physical simplicity at best form a partial, not a total, order. This suggests that appeals to principles of physical simplicity, via Ockham's Razor or to the ;elegance; of competing theories, may be fundamentally subjective. Recent rapid progress in quantum computation and quantum simulation suggest that the ambiguity of simplicity will strongly impact statistical inference and, in particular, model selection.

Adiabatic Quantum Computation: Coherent Control Back Action.

PubMed

Goswami, Debabrata

2006-11-22

Though attractive from scalability aspects, optical approaches to quantum computing are highly prone to decoherence and rapid population loss due to nonradiative processes such as vibrational redistribution. We show that such effects can be reduced by adiabatic coherent control, in which quantum interference between multiple excitation pathways is used to cancel coupling to the unwanted, non-radiative channels. We focus on experimentally demonstrated adiabatic controlled population transfer experiments wherein the details on the coherence aspects are yet to be explored theoretically but are important for quantum computation. Such quantum computing schemes also form a back-action connection to coherent control developments.

Symmetrically private information retrieval based on blind quantum computing

NASA Astrophysics Data System (ADS)

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

2015-05-01

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

Flow Ambiguity: A Path Towards Classically Driven Blind Quantum Computation

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

A new software-based architecture for quantum computer

NASA Astrophysics Data System (ADS)

Wu, Nan; Song, FangMin; Li, Xiangdong

2010-04-01

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

Classical simulation of quantum many-body systems

NASA Astrophysics Data System (ADS)

Huang, Yichen

Classical simulation of quantum many-body systems is in general a challenging problem for the simple reason that the dimension of the Hilbert space grows exponentially with the system size. In particular, merely encoding a generic quantum many-body state requires an exponential number of bits. However, condensed matter physicists are mostly interested in local Hamiltonians and especially their ground states, which are highly non-generic. Thus, we might hope that at least some physical systems allow efficient classical simulation. Starting with one-dimensional (1D) quantum systems (i.e., the simplest nontrivial case), the first basic question is: Which classes of states have efficient classical representations? It turns out that this question is quantitatively related to the amount of entanglement in the state, for states with "little entanglement'' are well approximated by matrix product states (a data structure that can be manipulated efficiently on a classical computer). At a technical level, the mathematical notion for "little entanglement'' is area law, which has been proved for unique ground states in 1D gapped systems. We establish an area law for constant-fold degenerate ground states in 1D gapped systems and thus explain the effectiveness of matrix-product-state methods in (e.g.) symmetry breaking phases. This result might not be intuitively trivial as degenerate ground states in gapped systems can be long-range correlated. Suppose an efficient classical representation exists. How can one find it efficiently? The density matrix renormalization group is the leading numerical method for computing ground states in 1D quantum systems. However, it is a heuristic algorithm and the possibility that it may fail in some cases cannot be completely ruled out. Recently, a provably efficient variant of the density matrix renormalization group has been developed for frustration-free 1D gapped systems. We generalize this algorithm to all (i.e., possibly frustrated) 1D

Arbitrated Quantum Signature with Hamiltonian Algorithm Based on Blind Quantum Computation

NASA Astrophysics Data System (ADS)

Shi, Ronghua; Ding, Wanting; Shi, Jinjing

2018-03-01

A novel arbitrated quantum signature (AQS) scheme is proposed motivated by the Hamiltonian algorithm (HA) and blind quantum computation (BQC). The generation and verification of signature algorithm is designed based on HA, which enables the scheme to rely less on computational complexity. It is unnecessary to recover original messages when verifying signatures since the blind quantum computation is applied, which can improve the simplicity and operability of our scheme. It is proved that the scheme can be deployed securely, and the extended AQS has some extensive applications in E-payment system, E-government, E-business, etc.

Arbitrated Quantum Signature with Hamiltonian Algorithm Based on Blind Quantum Computation

NASA Astrophysics Data System (ADS)

Shi, Ronghua; Ding, Wanting; Shi, Jinjing

2018-07-01

A novel arbitrated quantum signature (AQS) scheme is proposed motivated by the Hamiltonian algorithm (HA) and blind quantum computation (BQC). The generation and verification of signature algorithm is designed based on HA, which enables the scheme to rely less on computational complexity. It is unnecessary to recover original messages when verifying signatures since the blind quantum computation is applied, which can improve the simplicity and operability of our scheme. It is proved that the scheme can be deployed securely, and the extended AQS has some extensive applications in E-payment system, E-government, E-business, etc.

PREFACE: International Conference on Quantum Simulators and Design, Hiroshima, Japan, 3 6 December 2006

NASA Astrophysics Data System (ADS)

Akai, Hisazumi; Oguchi, Tamio

2007-09-01

This special issue of Journal of Physics: Condensed Matter comprises selected papers from the 1st International Conference on Quantum Simulators and Design (QSD2006) held in Hiroshima, Japan, 3-6 December 2006. This conference was organized under the auspices of the Development of New Quantum Simulators and Quantum Design Grant-in-Aid for Scientific Research on Priority Areas, Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT), and Hiroshima University Quantum design is a computational approach to the development of new materials with specified properties and functionalities. The basic ingredient is the use of quantum simulations to design a material that meets a given specification of properties and functionalities. For this to be successful, the quantum simulation should be highly reliable and be applicable to systems of realistic size. A central interest is, therefore, the development of new methods of quantum simulation and quantum design. This includes methods beyond the local density approximation of density functional theory (LDA), order-N methods, methods dealing with excitations and reactions, and so on, as well as the application of these methods to the design of new materials and devices. The field of quantum design has developed rapidly in the past few years and this conference provides an international forum for experimental and theoretical researchers to exchange ideas. A total of 183 delegates from 8 countries participated in the conference. There were 18 invited talks, 16 oral presentations and 100 posters. There were many new ideas and we foresee dramatic progress in the coming years. The 2nd International Conference on Quantum Simulators and Design will be held in Tokyo, Japan, 31 May-3 June 2008.

Superadiabatic holonomic quantum computation in cavity QED

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

Simulation of Quantum Many-Body Dynamics for Generic Strongly-Interacting Systems

NASA Astrophysics Data System (ADS)

Meyer, Gregory; Machado, Francisco; Yao, Norman

2017-04-01

Recent experimental advances have enabled the bottom-up assembly of complex, strongly interacting quantum many-body systems from individual atoms, ions, molecules and photons. These advances open the door to studying dynamics in isolated quantum systems as well as the possibility of realizing novel out-of-equilibrium phases of matter. Numerical studies provide insight into these systems; however, computational time and memory usage limit common numerical methods such as exact diagonalization to relatively small Hilbert spaces of dimension 215 . Here we present progress toward a new software package for dynamical time evolution of large generic quantum systems on massively parallel computing architectures. By projecting large sparse Hamiltonians into a much smaller Krylov subspace, we are able to compute the evolution of strongly interacting systems with Hilbert space dimension nearing 230. We discuss and benchmark different design implementations, such as matrix-free methods and GPU based calculations, using both pre-thermal time crystals and the Sachdev-Ye-Kitaev model as examples. We also include a simple symbolic language to describe generic Hamiltonians, allowing simulation of diverse quantum systems without any modification of the underlying C and Fortran code.

Blind quantum computation with identity authentication

NASA Astrophysics Data System (ADS)

Li, Qin; Li, Zhulin; Chan, Wai Hong; Zhang, Shengyu; Liu, Chengdong

2018-04-01

Blind quantum computation (BQC) allows a client with relatively few quantum resources or poor quantum technologies to delegate his computational problem to a quantum server such that the client's input, output, and algorithm are kept private. However, all existing BQC protocols focus on correctness verification of quantum computation but neglect authentication of participants' identity which probably leads to man-in-the-middle attacks or denial-of-service attacks. In this work, we use quantum identification to overcome such two kinds of attack for BQC, which will be called QI-BQC. We propose two QI-BQC protocols based on a typical single-server BQC protocol and a double-server BQC protocol. The two protocols can ensure both data integrity and mutual identification between participants with the help of a third trusted party (TTP). In addition, an unjammable public channel between a client and a server which is indispensable in previous BQC protocols is unnecessary, although it is required between TTP and each participant at some instant. Furthermore, the method to achieve identity verification in the presented protocols is general and it can be applied to other similar BQC protocols.

Towards a Quantum Computer?

NASA Astrophysics Data System (ADS)

Bellac, Michel Le

2014-11-01

In everyday life, practically all the information which is processed, exchanged or stored is coded in the form of discrete entities called bits, which take two values only, by convention 0 and 1. With the present technology for computers and optical fibers, bits are carried by electrical currents and electromagnetic waves corresponding to macroscopic fluxes of electrons and photons, and they are stored in memories of various kinds, for example, magnetic memories. Although quantum physics is the basic physics which underlies the operation of a transistor (Chapter 6) or of a laser (Chapter 4), each exchanged or processed bit corresponds to a large number of elementary quantum systems, and its behavior can be described classically due to the strong interaction with the environment (Chapter 9). For about thirty years, physicists have learned to manipulate with great accuracy individual quantum systems: photons, electrons, neutrons, atoms, and so forth, which opens the way to using two-state quantum systems, such as the polarization states of a photon (Chapter 2) or the two energy levels of an atom or an ion (Chapter 4) in order to process, exchange or store information. In § 2.3.2, we used the two polarization states of a photon, vertical (V) and horizontal (H), to represent the values 0 and 1 of a bit and to exchange information. In what follows, it will be convenient to use Dirac's notation (see Appendix A.2.2 for more details), where a vertical polarization state is denoted by |V> or |0> and a horizontal one by |H> or |1>, while a state with arbitrary polarization will be denoted by |ψ>. The polarization states of a photon give one possible realization of a quantum bit, or for short a qubit. Thanks to the properties of quantum physics, quantum computers using qubits, if they ever exist, would outperform classical computers for some specific, but very important, problems. In Sections 8.1 and 8.2, we describe some typical quantum algorithms and, in order to do so

Quantum computation based on photonic systems with two degrees of freedom assisted by the weak cross-Kerr nonlinearity.

PubMed

Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong

2016-07-18

Most of previous quantum computations only take use of one degree of freedom (DoF) of photons. An experimental system may possess various DoFs simultaneously. In this paper, with the weak cross-Kerr nonlinearity, we investigate the parallel quantum computation dependent on photonic systems with two DoFs. We construct nearly deterministic controlled-not (CNOT) gates operating on the polarization spatial DoFs of the two-photon or one-photon system. These CNOT gates show that two photonic DoFs can be encoded as independent qubits without auxiliary DoF in theory. Only the coherent states are required. Thus one half of quantum simulation resources may be saved in quantum applications if more complicated circuits are involved. Hence, one may trade off the implementation complexity and simulation resources by using different photonic systems. These CNOT gates are also used to complete various applications including the quantum teleportation and quantum superdense coding.

Quantum computation based on photonic systems with two degrees of freedom assisted by the weak cross-Kerr nonlinearity

PubMed Central

Luo, Ming-Xing; Li, Hui-Ran; Lai, Hong

2016-01-01

Most of previous quantum computations only take use of one degree of freedom (DoF) of photons. An experimental system may possess various DoFs simultaneously. In this paper, with the weak cross-Kerr nonlinearity, we investigate the parallel quantum computation dependent on photonic systems with two DoFs. We construct nearly deterministic controlled-not (CNOT) gates operating on the polarization spatial DoFs of the two-photon or one-photon system. These CNOT gates show that two photonic DoFs can be encoded as independent qubits without auxiliary DoF in theory. Only the coherent states are required. Thus one half of quantum simulation resources may be saved in quantum applications if more complicated circuits are involved. Hence, one may trade off the implementation complexity and simulation resources by using different photonic systems. These CNOT gates are also used to complete various applications including the quantum teleportation and quantum superdense coding. PMID:27424767

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 versus classical machine learning applied to a simplified computational biology problem

NASA Astrophysics Data System (ADS)

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

2018-03-01

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 classify and rank binding affinities. Using simplified data sets 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 data sets, 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.

Two-spectral Yang-Baxter operators in topological quantum computation

NASA Astrophysics Data System (ADS)

Sanchez, William F.

2011-05-01

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

Iterated Gate Teleportation and Blind Quantum Computation.

PubMed

Pérez-Delgado, Carlos A; Fitzsimons, Joseph F

2015-06-05

Blind quantum computation allows a user to delegate a computation to an untrusted server while keeping the computation hidden. A number of recent works have sought to establish bounds on the communication requirements necessary to implement blind computation, and a bound based on the no-programming theorem of Nielsen and Chuang has emerged as a natural limiting factor. Here we show that this constraint only holds in limited scenarios, and show how to overcome it using a novel method of iterated gate teleportations. This technique enables drastic reductions in the communication required for distributed quantum protocols, extending beyond the blind computation setting. Applied to blind quantum computation, this technique offers significant efficiency improvements, and in some scenarios offers an exponential reduction in communication requirements.

Quantum Corrections to the 'Atomistic' MOSFET Simulations

NASA Technical Reports Server (NTRS)

Asenov, Asen; Slavcheva, G.; Kaya, S.; Balasubramaniam, R.

2000-01-01

We have introduced in a simple and efficient manner quantum mechanical corrections in our 3D 'atomistic' MOSFET simulator using the density gradient formalism. We have studied in comparison with classical simulations the effect of the quantum mechanical corrections on the simulation of random dopant induced threshold voltage fluctuations, the effect of the single charge trapping on interface states and the effect of the oxide thickness fluctuations in decanano MOSFETs with ultrathin gate oxides. The introduction of quantum corrections enhances the threshold voltage fluctuations but does not affect significantly the amplitude of the random telegraph noise associated with single carrier trapping. The importance of the quantum corrections for proper simulation of oxide thickness fluctuation effects has also been demonstrated.

Silicon CMOS architecture for a spin-based quantum computer.

PubMed

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

2017-12-15

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

Nonlinear optics quantum computing with circuit QED.

PubMed

Adhikari, Prabin; Hafezi, Mohammad; Taylor, J M

2013-02-08

One approach to quantum information processing is to use photons as quantum bits and rely on linear optical elements for most operations. However, some optical nonlinearity is necessary to enable universal quantum computing. Here, we suggest a circuit-QED approach to nonlinear optics quantum computing in the microwave regime, including a deterministic two-photon phase gate. Our specific example uses a hybrid quantum system comprising a LC resonator coupled to a superconducting flux qubit to implement a nonlinear coupling. Compared to the self-Kerr nonlinearity, we find that our approach has improved tolerance to noise in the qubit while maintaining fast operation.

U(1) Wilson lattice gauge theories in digital quantum simulators

NASA Astrophysics Data System (ADS)

Muschik, Christine; Heyl, Markus; Martinez, Esteban; Monz, Thomas; Schindler, Philipp; Vogell, Berit; Dalmonte, Marcello; Hauke, Philipp; Blatt, Rainer; Zoller, Peter

2017-10-01

Lattice gauge theories describe fundamental phenomena in nature, but calculating their real-time dynamics on classical computers is notoriously difficult. In a recent publication (Martinez et al 2016 Nature 534 516), we proposed and experimentally demonstrated a digital quantum simulation of the paradigmatic Schwinger model, a U(1)-Wilson lattice gauge theory describing the interplay between fermionic matter and gauge bosons. Here, we provide a detailed theoretical analysis of the performance and the potential of this protocol. Our strategy is based on analytically integrating out the gauge bosons, which preserves exact gauge invariance but results in complicated long-range interactions between the matter fields. Trapped-ion platforms are naturally suited to implementing these interactions, allowing for an efficient quantum simulation of the model, with a number of gate operations that scales polynomially with system size. Employing numerical simulations, we illustrate that relevant phenomena can be observed in larger experimental systems, using as an example the production of particle-antiparticle pairs after a quantum quench. We investigate theoretically the robustness of the scheme towards generic error sources, and show that near-future experiments can reach regimes where finite-size effects are insignificant. We also discuss the challenges in quantum simulating the continuum limit of the theory. Using our scheme, fundamental phenomena of lattice gauge theories can be probed using a broad set of experimentally accessible observables, including the entanglement entropy and the vacuum persistence amplitude.

Hamiltonian quantum simulation with bounded-strength controls

NASA Astrophysics Data System (ADS)

Bookatz, Adam D.; Wocjan, Pawel; Viola, Lorenza

2014-04-01

We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians. Each simulation protocol consists of periodic repetitions of a basic control block, constructed as a modification of an ‘Eulerian decoupling cycle,’ that would otherwise implement a trivial (zero) target Hamiltonian. For an open quantum system coupled to an uncontrollable environment, our approach may be employed to engineer an effective evolution that simulates a target Hamiltonian on the system while suppressing unwanted decoherence to the leading order, thereby allowing for dynamically corrected simulation. We present illustrative applications to both closed- and open-system simulation settings, with emphasis on simulation of non-local (two-body) Hamiltonians using only local (one-body) controls. In particular, we provide simulation schemes applicable to Heisenberg-coupled spin chains exposed to general linear decoherence, and show how to simulate Kitaev's honeycomb lattice Hamiltonian starting from Ising-coupled qubits, as potentially relevant to the dynamical generation of a topologically protected quantum memory. Additional implications for quantum information processing are discussed.

Continuous-variable quantum computing in optical time-frequency modes using quantum memories.

PubMed

Humphreys, Peter C; Kolthammer, W Steven; Nunn, Joshua; Barbieri, Marco; Datta, Animesh; Walmsley, Ian A

2014-09-26

We develop a scheme for time-frequency encoded continuous-variable cluster-state quantum computing using quantum memories. In particular, we propose a method to produce, manipulate, and measure two-dimensional cluster states in a single spatial mode by exploiting the intrinsic time-frequency selectivity of Raman quantum memories. Time-frequency encoding enables the scheme to be extremely compact, requiring a number of memories that are a linear function of only the number of different frequencies in which the computational state is encoded, independent of its temporal duration. We therefore show that quantum memories can be a powerful component for scalable photonic quantum information processing architectures.

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.

Experimental Blind Quantum Computing for a Classical Client.

PubMed

Huang, He-Liang; Zhao, Qi; Ma, Xiongfeng; Liu, Chang; Su, Zu-En; Wang, Xi-Lin; Li, Li; Liu, Nai-Le; Sanders, Barry C; Lu, Chao-Yang; Pan, Jian-Wei

2017-08-04

To date, blind quantum computing demonstrations require clients to have weak quantum devices. Here we implement a proof-of-principle experiment for completely classical clients. Via classically interacting with two quantum servers that share entanglement, the client accomplishes the task of having the number 15 factorized by servers who are denied information about the computation itself. This concealment is accompanied by a verification protocol that tests servers' honesty and correctness. Our demonstration shows the feasibility of completely classical clients and thus is a key milestone towards secure cloud quantum computing.

Experimental Blind Quantum Computing for a Classical Client

NASA Astrophysics Data System (ADS)

Huang, He-Liang; Zhao, Qi; Ma, Xiongfeng; Liu, Chang; Su, Zu-En; Wang, Xi-Lin; Li, Li; Liu, Nai-Le; Sanders, Barry C.; Lu, Chao-Yang; Pan, Jian-Wei

2017-08-01

To date, blind quantum computing demonstrations require clients to have weak quantum devices. Here we implement a proof-of-principle experiment for completely classical clients. Via classically interacting with two quantum servers that share entanglement, the client accomplishes the task of having the number 15 factorized by servers who are denied information about the computation itself. This concealment is accompanied by a verification protocol that tests servers' honesty and correctness. Our demonstration shows the feasibility of completely classical clients and thus is a key milestone towards secure cloud quantum computing.

Magnetic resonance: Using computer simulations and visualizations to connect quantum theory with classical concepts

NASA Astrophysics Data System (ADS)

Engelhardt, Larry

2015-12-01

We discuss how computers can be used to solve the ordinary differential equations that provide a quantum mechanical description of magnetic resonance. By varying the parameters in these equations and visually exploring how these parameters affect the results, students can quickly gain insights into the nature of magnetic resonance that go beyond the standard presentation found in quantum mechanics textbooks. The results were generated using an IPython notebook, which we provide as an online supplement with interactive plots and animations.

Secure entanglement distillation for double-server blind quantum computation.