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Recovery map for fermionic gaussian channels

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arXiv 2018年

作者： Swingle, Brian G. Wang, Yixu Condensed Matter Theory Center Maryland Center for Fundamental Physics Joint Center for Quantum Information and Computer Science Department of Physics University of Maryland College ParkMD20742 United States Kavli Institute for Theoretical Physics Santa BarbaraCA93106 United States Institute for Advanced Studies PrincetonNJ08540 United States Maryland Center for Fundamental Physics Department of Physics University of Maryland College ParkMD20742 United States

A recovery map effectively cancels the action of a quantum operation to a partial or full extent. We study the Petz recovery map in the case where the quantum channel and input states are fermionic and Gaussian. Gaussian states are convenient because they are totally determined by their covariance matrix and because they form a closed set under so-called Gaussian channels. Using a Grassmann representation of fermionic Gaussian maps, we show that the Petz recovery map is also Gaussian and determine it explicitly in terms of the covariance matrix of the reference state and the data of the channel. As a by-product, we obtain a formula for the fidelity between two fermionic Gaussian states. We also discuss subtleties arising from the singularities of the involved matrices. Copyright © 2018, The Authors. All rights reserved.

关键词： Recovery

quantum error correction decoheres noise

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arXiv 2018年

作者： Beale, Stefanie J. Wallman, Joel J. Gutiérrez, Mauricio Brown, Kenneth R. Laflamme, Raymond Institute for Quantum Computing Department of Physics and Astronomy University of Waterloo WaterlooONN2L 3G1 Canada Institute for Quantum Computing Department of Applied Mathematics University of Waterloo WaterlooONN2L 3G1 Canada Department of Physics College of Science Swansea University Singleton Park SwanseaSA2 8PP United Kingdom Escuela de Química Universidad de Costa Rica San José2060 Costa Rica Department of Electrical and Computer Engineering Chemistry and Physics Duke University DurhamNC27708 United States Perimeter Institute for Theoretical Physics WaterlooONN2L 2Y5 Canada

Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively unknown. Here, we prove that encoding a system in a stabilizer code and measuring error syndromes decoheres errors, that is, causes coherent errors to converge toward probabilistic Pauli errors, even when no recovery operations are applied. Two practical consequences are that the error rate in a logical circuit is well quantified by the average gate fidelity at the logical level and that essentially optimal recovery operators can be determined by independently optimizing the logical fidelity of the effective noise per syndrome. Copyright © 2018, The Authors. All rights reserved.

关键词： Error correction

Extrapolated quantum states, void states, and a huge novel class of distillable entangled states

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arXiv 2017年

作者： Boyer, Michel Brodutch, Aharon Mor, Tal DIRO Université de Montréal Canada Department of Physics & Astronomy Institute for Quantum Computing University of Waterloo Canada Computer Science Department Technion Israel

A nice and interesting property of any pure tensor-product state is that each such state has distillable entangled states at an arbitrarily small distance Ε in its neighbourhood. We say that such nearby states are Ε-entangled, and we call the tensor product state in that case, a "boundary separable state", as there is entanglement at any distance from this "boundary". Here we find a huge class of separable states that also share that property mentioned above – they all have Εentangled states at any small distance in their neighbourhood. Furthermore, the entanglement they have is proven to be distillable. We then extend this result to the discordant/classical cut and show that all classical states (correlated and uncorrelated) have discordant states at distance Ε, and provide a constructive method for finding Ε-discordant states. Copyright © 2017, The Authors. All rights reserved.

关键词： quantum optics

Indefinite causal order enables perfect quantum communication with zero capacity channels

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arXiv 2018年

作者： Chiribella, Giulio Banik, Manik Bhattacharya, Some Sankar Guha, Tamal Alimuddin, Mir Roy, Arup Saha, Sutapa Agrawal, Sristy Kar, Guruprasad QICI Quantum Information and Computation Initiative Department of Computer Science The University of Hong Kong Pokfulam Road Hong Kong Department of Computer Science University of Oxford Wolfson Building Parks Road United Kingdom Perimeter Institute for Theoretical Physics WaterlooN2L 2Y5 Canada School of Physics IISER Thiruvanathapuram Kerala Vithura695551 India Physics and Applied Mathematics Unit Indian Statistical Institute 203 B.T. Road Kolkata700108 India Department of Physics A B N Seal College Cooch Behar West Bengal 736101 India Department of Physics Center for Theory of Quantum Matter University of Colorado BoulderCO80309 United States National Institute of Standards and Technology BoulderCO80305 United States

quantum mechanics is compatible with scenarios where the relative order between two events can be indefinite. Here we show that two independent instances of a noisy process can behave as a perfect quantum communication channel when used in a coherent superposition of two alternative orders. This phenomenon occurs even if the original process has zero capacity to transmit quantum information. In contrast, perfect quantum communication does not occur when the message is sent directly from the sender to the receiver through a superposition of alternative paths, with an independent noise process acting on each path. The possibility of perfect quantum communication through independent noisy channels highlights a fundamental difference between the superposition of orders in time and the superposition of paths in space. Copyright © 2018, The Authors. All rights reserved.

关键词： quantum communication

A universal training algorithm for quantum deep learning

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arXiv 2018年

作者： Verdon, Guillaume Pye, Jason Broughton, Michael Department of Applied Mathematics University of Waterloo WaterlooONN2L 3G1 Canada Institute for Quantum Computing University of Waterloo WaterlooONN2L 3G1 Canada School of Computer Science University of Waterloo WaterlooONN2L 3G1 Canada Perimeter Institute for Theoretical Physics WaterlooONN2L 2Y5 Canada

We introduce the Backwards quantum Propagation of Phase errors (Baqprop) principle, a central theme upon which we construct multiple universal optimization heuristics for training both parametrized quantum circuits and classical deep neural networks on a quantum computer. Baqprop encodes error information in relative phases of a quantum wavefunction defined over the space of network parameters;it can be thought of as the unification of the phase kickback principle of quantum computation and of the backpropagation algorithm from classical deep learning. We propose two core heuristics which leverage Baqprop for quantum-enhanced optimization of network parameters: quantum Dynamical Descent (QDD) and Momentum Measurement Gradient Descent (MoMGrad). QDD uses simulated quantum coherent dynamics for parameter optimization, allowing for quantum tunneling through the hypothesis space landscape. MoMGrad leverages Baqprop to estimate gradients and thereby perform gradient descent on the parameter landscape;it can be thought of as the quantum-classical analogue of QDD. In addition to these core optimization strategies, we propose various methods for parallelization, regularization, and meta-learning as augmentations to MoMGrad and QDD. We introduce several quantum-coherent adaptations of canonical classical feedforward neural networks, and study how Baqprop can be used to optimize such networks. We develop multiple applications of parametric circuit learning for quantum data, and show how to perform Baqprop in each case. One such application allows for the training of hybrid quantum-classical neural-circuit networks, via the seamless integration of Baqprop with classical backpropagation. Finally, for a representative subset of these proposed applications, we demonstrate the training of these networks via numerical simulations of implementations of QDD and MoMGrad. Copyright © 2018, The Authors. All rights reserved.

关键词： Gradient methods

NWChem: Past, present, and future

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arXiv 2020年

作者： Aprà, E. Bylaska, E.J. de Jong, W.A. Govind, N. Kowalski, K. Straatsma, T.P. Valiev, M. van Dam, H.J.J. Alexeev, Y. Anchell, J. Anisimov, V. Aquino, F.W. Atta-Fynn, R. Autschbach, J. Bauman, N.P. Becca, J.C. Bernholdt, D.E. Bhaskaran-Nair, K. Bogatko, S. Borowski, P. Boschen, J. Brabec, J. Bruner, A. Cauët, E. Chen, Y. Chuev, G.N. Cramer, C.J. Daily, J. Deegan, M.J.O. Dunning, T.H. Dupuis, M. Dyall, K.G. Fann, G.I. Fischer, S.A. Fonari, A. Früchtl, H. Gagliardi, L. Garza, J. Gawande, N. Ghosh, S. Glaesemann, K. Götz, A.W. Hammond, J. Helms, V. Hermes, E.D. Hirao, K. Hirata, S. Jacquelin, M. Jensen, L. Johnson, B.G. Jónsson, H. Kendall, R.A. Klemm, M. Kobayashi, R. Konkov, V. Krishnamoorthy, S. Krishnan, M. Lin, Z. Lins, R.D. Littlefield, R.J. Logsdail, A.J. Lopata, K. Ma, W. Marenich, A.V. Martin del Campo, J. Mejia-Rodriguez, D. Moore, J.E. Mullin, J.M. Nakajima, T. Nascimento, D.R. Nichols, J.A. Nichols, P.J. Nieplocha, J. Otero-de-la-Roza, A. Palmer, B. Panyala, A. Pirojsirikul, T. Peng, B. Peverati, R. Pittner, J. Pollack, L. Richard, R.M. Sadayappan, P. Schatz, G.C. Shelton, W.A. Silverstein, D.W. Smith, D.M.A. Soares, T.A. Song, D. Swart, M. Taylor, H.L. Thomas, G.S. Tipparaju, V. Truhlar, D.G. Tsemekhman, K. van Voorhis, T. Vázquez-Mayagoitia, Á. Verma, P. Villa, O. Vishnu, A. Vogiatzis, K.D. Wang, D. Weare, J.H. Williamson, M.J. Windus, T.L. Woliński, K. Wong, A.T. Wu, Q. Yang, C. Yu, Q. Zacharias, M. Zhang, Z. Zhao, Y. Harrison, R.J. Pacific Northwest National Laboratory RichlandWA99352 United States Lawrence Berkeley National Laboratory BerkeleyCA94720 United States National Center for Computational Sciences Oak Ridge National Laboratory Oak RidgeTN37831 United States Brookhaven National Laboratory UptonNY11973 United States Argonne Leadership Computing Facility Argonne National Laboratory ArgonneIL60439 United States Intel Corporation Santa ClaraCA95054 United States QSimulate CambridgeMA02139 United States Department of Physics University of Texas at Arlington ArlingtonTX76019 United States Department of Chemistry University at Buffalo State University of New York BuffaloNY14260 United States Department of Chemistry Pennsylvania State University University ParkPA16802 United States Oak Ridge National Laboratory Oak RidgeTN37831 United States Washington University St. LouisMO63130 United States 4G Clinical WellesleyMA02481 United States Faculty of Chemistry Maria Curie-Sklodowska University in Lublin Lublin20-031 Poland Department of Chemistry Iowa State University AmesIA50011 United States J. Heyrovský Institute of Physical Chemistry Academy of Sciences of the Czech Republic Prague 818223 Czech Republic Department of Chemistry and Physics University of Tennessee at Martin MartinTN38238 United States Université libre de Bruxelles BrusselsB-1050 Belgium Facebook Menlo ParkCA94025 United States Institute of Theoretical and Experimental Biophysics Russian Academy of Science Pushchino Moscow142290 Russia Department of Chemistry Chemical Theory Center Supercomputing Institute University of Minnesota MinneapolisMN55455 United States SKAO Jodrell Bank Observatory MacclesfieldSK11 9DL United Kingdom Department of Chemistry University of Washington SeattleWA98195 United States Dirac Solutions PortlandOR97229 United States Chemistry Division U. S. Naval Research Laboratory WashingtonDC20375 United States School of Chemistry and Biochemis

Specialized computational chemistry packages have permanently reshaped the landscape of chemical and materials science by providing tools to support and guide experimental efforts and for the prediction of atomistic and electronic properties. In this regard, electronic structure packages have played a special role by using first-principle-driven methodologies to model complex chemical and materials processes. Over the last few decades, the rapid development of computing technologies and the tremendous increase in computational power have offered a unique chance to study complex transformations using sophisticated and predictive many-body techniques that describe correlated behavior of electrons in molecular and condensed phase systems at different levels of theory. In enabling these simulations, novel parallel algorithms have been able to take advantage of computational resources to address the polynomial scaling of electronic structure methods. In this paper, we briefly review the NWChem computational chemistry suite, including its history, design principles, parallel tools, current capabilities, outreach and outlook. Copyright © 2020, The Authors. All rights reserved.

关键词： Computational chemistry

Topological insulators in twisted transition metal dichalcogenide homobilayers

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arXiv 2018年

作者： Wu, Fengcheng Lovorn, Timothy Tutuc, Emanuel Martin, Ivar MacDonald, A.H. Materials Science Division Argonne National Laboratory ArgonneIL60439 United States Condensed Matter Theory Center Joint Quantum Institute Department of Physics University of Maryland College ParkMD20742 United States Department of Physics University of Texas at Austin AustinTX78712 United States Department of Electrical and Computer Engineering Microelectronics Research Center University of Texas at Austin AustinTX78758 United States

We show that moiré bands of twisted homobilayers can be topologically nontrivial, and illustrate the tendency by studying valence band states in ±K valleys of twisted bilayer transition metal dichalcogenides, in particular, bilayer MoTe2. Because of the large spin-orbit splitting at the monolayer valence band maxima, the low energy valence states of the twisted bilayer MoTe2at +K (-K) valley can be described using a two-band model with a layer-pseudospin magnetic field Δ(r) that has the moiré period. We show that Δ(r) has a topologically non-trivial skyrmion lattice texture in real space, and that the topmost moiré valence bands provide a realization of the Kane-Mele quantum spin-Hall model, i.e., the two-dimensional time-reversal-invariant topological insulator. Because the bands narrow at small twist angles, a rich set of broken symmetry insulating states can occur at integer numbers of electrons per moiré cell. Copyright © 2018, The Authors. All rights reserved.

关键词： Textures

Universal structure of objective states in all fundamental causal theories

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arXiv 2018年

作者： Scandolo, Carlo Maria Salazar, Roberto Korbicz, Jaroslaw K. Horodecki, Pawel Department of Mathematics & Statistics University of Calgary CalgaryABT2N 1N4 Canada Institute for Quantum Science and Technology University of Calgary CalgaryABT2N 1N4 Canada Institute of Informatics National Quantum Information Centre Faculty of Mathematics Physics and Informatics University of Gdańsk Gdańsk80-308 Poland Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University Kraków30-348 Poland Center for Theoretical Physics Polish Academy of Sciences Warsaw02-668 Poland International Centre for Theory of Quantum Technologies University of Gdańsk Gdańsk80-308 Poland Faculty of Applied Physics and Mathematics National Quantum Information Centre Gdańsk University of Technology Gdańsk80-233 Poland

A crucial question is how objective and classical behavior arises from a fundamental physical theory. Here we provide a natural definition of a decoherence process valid in all causal theories, and show how its behavior can be extremely different from the quantum one. Remarkably, despite this, we prove that the so-called spectrum broadcast structure characterizes all objective states in every fundamental causal theory, exactly as in quantum mechanics. Our results show a stark contrast between the extraordinarily diverse decoherence behavior and the universal features of objectivity. Copyright © 2018, The Authors. All rights reserved.

关键词：

quantum Lyapunov spectrum

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arXiv 2018年

作者： Gharibyan, Hrant Hanada, Masanori Swingle, Brian Tezuka, Masaki Stanford Institute for Theoretical Physics Stanford University StanfordCA94305 United States Department of Physics University of Colorado BoulderCO80309 United States Condensed Matter Theory Center Maryland Center for Fundamental Physics Joint Center for Quantum Information and Computer Science Department of Physics University of Maryland College ParkMD20742 United States Department of Physics Kyoto University Kyoto606-8502 Japan

We introduce a simple quantum generalization of the spectrum of classical Lyapunov exponents. We apply it to the SYK and XXZ models, and study the Lyapunov growth and entropy production. Our numerical results suggest that a black hole is not just the fastest scrambler, but also the fastest entropy generator. We also study the statistical features of the quantum Lyapunov spectrum and find universal random matrix behavior, which resembles the recently-found universality in classical chaos. The random matrix behavior is lost when the system is deformed away from chaos, towards integrability or a many-body localized phase. We propose that quantum systems holographically dual to gravity satisfy this universality in a strong form. We further argue that the quantum Lyapunov spectrum contains important additional information beyond the largest Lyapunov exponent and hence provides us with a better characterization of chaos in quantum systems. Copyright © 2018, The Authors. All rights reserved.

关键词： Lyapunov functions