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Every quantum helps: Operational advantage of quantum resources beyond convexity

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arXiv 2023年

作者： Kuroiwa, Kohdai Takagi, Ryuji Adesso, Gerardo Yamasaki, Hayata Institute for Quantum Computing Department of Combinatorics and Optimization University of Waterloo ONN2L 3G1 Canada Perimeter Institute for Theoretical Physics ONN2L 2Y5 Canada Department of Basic Science The University of Tokyo 3-8-1 Komaba Meguro-ku Tokyo153-8902 Japan School of Mathematical Sciences Centre for the Mathematical and Theoretical Physics of Quantum Non-Equilibrium Systems University of Nottingham University Park NottinghamNG7 2RD United Kingdom Department of Physics Graduate School of Science The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-0033 Japan

Identifying what quantum-mechanical properties are useful to untap a superior performance in quantum technologies is a pivotal question. quantum resource theories provide a unified framework to analyze and understand such properties, as successfully demonstrated for entanglement and coherence. While these are examples of convex resources, for which quantum advantages can always be identified, many physical resources are described by a non-convex set of free states and their interpretation has so far remained elusive. Here we address the fundamental question of the usefulness of quantum resources without convexity assumption, by providing two operational interpretations of the generalized robustness measure in general resource theories. First, we characterize the generalized robustness in terms of a non-linear resource witness and reveal that any state is more advantageous than a free one in some multi-copy channel discrimination task. Next, we consider a scenario where a theory is characterized by multiple constraints and show that the generalized robustness coincides with the worst-case advantage in a single-copy channel discrimination setting. Based on these characterizations, we conclude that every quantum resource state shows a qualitative and quantitative advantage in discrimination problems in a general resource theory even without any specification on the structure of the free states. Copyright © 2023, The Authors. All rights reserved.

关键词： Set theory

Information-Theoretic Equilibration: The Appearance of Irreversibility under Complex quantum Dynamics

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Physical Review Letters 2013年第8期111卷 080403-080403页

作者： Cozmin Ududec Nathan Wiebe Joseph Emerson Department of Physics and Astronomy University of Waterloo Waterloo Ontario N2L3G1 Canada Institute for Quantum Computing 200 University Avenue West Waterloo Ontario N2L3G1 Canada Department of Combinatics and Optimization University of Waterloo Waterloo Ontario N2L3G1 Canada Department of Applied Math University of Waterloo Waterloo Ontario N2L3G1 Canada

The question of how irreversibility can emerge as a generic phenomenon when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the appearance of irreversibility that applies to coherent, isolated systems in a pure quantum state. This equilibration mechanism requires only an assumption of sufficiently complex internal dynamics and natural information-theoretic constraints arising from the infeasibility of collecting an astronomical amount of measurement data. Remarkably, we are able to prove that irreversibility can be understood as typical without assuming decoherence or restricting to coarse-grained observables, and hence occurs under distinct conditions and time scales from those implied by the usual decoherence point of view. We illustrate the effect numerically in several model systems and prove that the effect is typical under the standard random-matrix conjecture for complex quantum systems.

关键词： quantum mechanics CLASSICAL mechanics quantum states ISOLATED systems (Thermodynamics) DECOHERENCE (quantum mechanics)

Robustness- and weight-based resource measures without convexity restriction: Multi-copy witness and operational advantage in static and dynamical quantum resource theories

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arXiv 2023年

quantum resource theories (QRTs) provide a unified framework to analyze quantum properties as resources for achieving advantages in quantum information processing. The generalized robustness and the weight of resource have been gaining increasing attention as useful resource quantifiers. However, the existing analyses of these measures were restricted to the cases where convexity of the set of free states is assumed, and physically motivated resources do not necessarily satisfy this restriction. In this paper, we give characterizations of robustness- and weight-based measures in general QRTs without convexity restriction through two different yet related approaches. On the one hand, we characterize the generalized robustness and the weight of resource by introducing a non-linear witness. We show a general construction of new witness observables that detect the resourcefulness of a given state from multiple copies of the state and, using these witnesses, we provide operational interpretations of the above resource measures even without any convexity assumption. On the other hand, we find that the generalized robustness and the weight of resource can also be interpreted as the worst-case maximum advantage in variants of channel-discrimination and channel-exclusion tasks, respectively, where the set of free states consists of several convex subsets corresponding to multiple restrictions. We further extend these results to QRTs for quantum channels and quantum instruments. These characterizations show that every quantum resource exhibits an advantage for the corresponding tasks, even in general QRTs without convexity assumption. Thus, we establish the usefulness of robustness-based and weight-based techniques beyond the conventional scope of convex QRTs, leading to a better understanding of the general structure of QRTs. Copyright © 2023, The Authors. All rights reserved.

关键词： quantum optics

Neural ensemble decoding for topological quantum error-correcting codes

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Physical Review A 2020年第3期101卷 032338-032338页

作者： Milap Sheth Sara Zafar Jafarzadeh Vlad Gheorghiu Institute for Quantum Computing University of Waterloo Waterloo Ontario Canada N2L 3G1 Department of Combinatorics and Optimization University of Waterloo Waterloo Ontario Canada N2L 3G1 David R. Cheriton School of Computer Science University of Waterloo Waterloo Ontario Canada N2L 3G1 Department of Computer Science and Operations Research Université de Montreal Montreal Quebec Canada H3T 1J4 softwareQ Inc. Kitchener Ontario Canada N2M 0A9

Topological quantum error-correcting codes are a promising candidate for building fault-tolerant quantum computers. Decoding topological codes optimally, however, is known to be a computationally hard problem. Various decoders have been proposed that achieve approximately optimal error thresholds. Due to practical constraints, it is not known if there exists an obvious choice for a decoder. In this paper, we introduce a framework which can combine arbitrary decoders for any given code to significantly reduce the logical error rates. We rely on the crucial observation that two different decoding techniques, while possibly having similar logical error rates, can perform differently on the same error syndrome. We classify each error syndrome to the decoder which is more likely to decode it correctly using machine learning techniques. We apply our framework to an ensemble of minimum-weight perfect matching (MWPM) and hard-decision re-normalization-group decoders for the surface code in the depolarizing noise model. Our simulations show an improvement of 38.4%, 14.6%, and 7.1% over the pseudothreshold of MWPM in the instance of distance 5, 7, and 9 codes, respectively. Lastly, we discuss the advantages and limitations of our framework and applicability to other error-correcting codes. Our framework can provide a significant boost to error correction by combining the strengths of various decoders. In particular, it may allow for combining very fast decoders with moderate error-correcting capability to create a very fast ensemble decoder with high error-correcting capability.

关键词： Machine learning quantum computation quantum memories Surface code quantum computing Topological quantum computing

ALKPU: an active learning method for the DeePMD model with Kalman filter

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arXiv 2024年

作者： Li, Haibo Wu, Xingxing Liu, Liping Wang, Lin-Wang Wang, Long Tan, Guangming Jia, Weile School of Mathematics and Statistics The University of Melbourne MelbourneVIC3010 Australia Technology Department Longxun Quantum Inc. Beijing100192 China Institute of Semiconductors Chinese Academy of Sciences Beijing100083 China Computing System Optimization Lab Huawei Technologies Co. Ltd. Beijing100094 China State Key Lab of Processors Institute of Computing Technology Chinese Academy of Sciences Beijing100190 China University of Chinese Academy of Sciences Beijing101408 China

Neural network force field models such as DeePMD have enabled highly efficient large-scale molecular dynamics simulations with ab initio accuracy. However, building such models heavily depends on the training data obtained by costly electronic structure calculations, thereby it is crucial to carefully select and label the most representative configurations during model training to improve both extrapolation capability and training efficiency. To address this challenge, based on the Kalman filter theory we propose the Kalman Prediction Uncertainty (KPU) to quantify uncertainty of the model’s prediction. With KPU we design the Active Learning by KPU (ALKPU) method, which can efficiently select representative configurations that should be labelled during model training. We prove that ALKPU locally leads to the fastest reduction of model’s uncertainty, which reveals its rationality as a general active learning method. We test the ALKPU method using various physical system simulations and demonstrate that it can efficiently coverage the system’s configuration space. Our work demonstrates the benefits of ALKPU as a novel active learning method, enhancing training efficiency and reducing computational resource demands. © 2024, CC BY.

关键词：

Entanglement cost for infinite-dimensional physical systems

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arXiv 2024年

作者： Yamasaki, Hayata Kuroiwa, Kohdai Hayden, Patrick Lami, Ludovico Department of Physics Graduate School of Science The Univerisity of Tokyo 7–3–1 Hongo Bunkyo-ku Tokyo113–0033 Japan Institute for Quantum Computing Department of Combinatorics and Optimization University of Waterloo ONN2L 3G1 Canada Perimeter Institute for Theoretical Physics ONN2L 2Y5 Canada Stanford Institute for Theoretical Physics Stanford University StanfordCA94305 United States QuSoft Science Park 123 Amsterdam1098 XG Netherlands Korteweg–de Vries Institute for Mathematics University of Amsterdam Science Park 105–107 Amsterdam1098 XG Netherlands Institute for Theoretical Physics University of Amsterdam Science Park 904 Amsterdam1098 XH Netherlands

We prove that the entanglement cost equals the regularized entanglement of formation for any infinite-dimensional quantum state pAB with finite quantum entropy on at least one of the subsystems A or B. This generalizes a foundational result in quantum information theory that was previously formulated only for operations and states on finite-dimensional systems. The extension to infinite dimensions is nontrivial because the conventional tools for establishing both the direct and converse bounds, i.e., strong typically, monotonicity, and asymptotic continuity, are no longer directly applicable. To address this problem, we construct a new entanglement dilution protocol for infinite-dimensional states implementable by local operations and a finite amount of one-way classical communication (one-way LOCC), using weak and strong typicality multiple times. We also prove the optimality of this protocol among all protocols even under infinite-dimensional separable operations by developing an argument based on alternative forms of monotonicity and asymptotic continuity of the entanglement of formation for infinite-dimensional states. Along the way, we derive a new integral representation for the quantum entropy of infinite-dimensional states, which we believe to be of independent interest. Our results allow us to fully characterize an important operational entanglement measure — the entanglement cost — for all infinite-dimensional physical systems. Copyright © 2024, The Authors. All rights reserved.

关键词： quantum optics

Solving an Industrially Relevant quantum Chemistry Problem on quantum Hardware

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arXiv 2024年

作者： Nützel, Ludwig Gresch, Alexander Hehn, Lukas Marti, Lucas Freund, Robert Steiner, Alex Marciniak, Christian D. Eckstein, Timo Stockinger, Nina Wolf, Stefan Monz, Thomas Kühn, Michael Hartmann, Michael J. Department of Physics Friedrich-Alexander Universität Erlangen-Nürnberg Erlangen Germany Heinrich Heine University Düsseldorf Faculty of Mathematics and Natural Sciences Germany Institute for Quantum Inspired and Quantum Optimization Hamburg University of Technology Germany BASF SE Next Generation Computing Pfalzgrafenstr. 1 Ludwigshafen67061 Germany Universität Innsbruck Institut für Experimentalphysik Innsbruck Austria Max Planck Institute for the Science of Light Staudtstraße 2 Erlangen91058 Germany Department of Chemistry Technical University of Munich Garching Germany Alpine Quantum Technologies GmbH Innsbruck Austria

quantum chemical calculations are among the most promising applications for quantum computing. Implementations of dedicated quantum algorithms on available quantum hardware were so far, however, mostly limited to comparatively simple systems without strong correlations. As such, they can also be addressed by classically efficient single-reference methods. In this work, we calculate the lowest energy eigenvalue of active space Hamiltonians of industrially relevant and strongly correlated metal chelates on trapped ion quantum hardware, and integrate the results into a typical industrial quantum chemical workflow to arrive at chemically meaningful properties. We are able to achieve chemical accuracy by training a variational quantum algorithm on quantum hardware, followed by a classical diagonalization in the subspace of states measured as outputs of the quantum circuit. This approach is particularly measurement-efficient, requiring 600 single-shot measurements per cost function evaluation on a ten qubit system, and allows for efficient post-processing to handle erroneous runs. © 2024, CC BY-NC-ND.

关键词： Cost functions

Novel technique for robust optimal algorithmic cooling

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arXiv 2019年

作者： Raeisi, Sadegh Kieferová, Mária Mosca, Michele Department of Physics Sharif University of Technology Tehran Iran Institute for Quantum Computing University of Waterloo OntarioN2L 3G1 Canada Department of Physics and Astronomy University of Waterloo OntarioN2L 3G1 Canada Department of Physics and Astronomy Macquarie University SydneyNSW2109 Australia Department of Combinatorics and Optimization University of Waterloo OntarioN2L 3G1 Canada Perimeter Institute for Theoretical Physics WaterlooONN2L 2Y5 Canada Canadian Institute for Advanced Research TorontoONM5G 1Z8 Canada

Heat-bath algorithmic cooling (HBAC) provides algorithmic ways to improve the purity of quantum states. These techniques are complex iterative processes that change from each iteration to the next and this poses a significant challenge to implementing these algorithms. Here, we introduce a new technique that on a fundamental level, shows that it is possible to do algorithmic cooling and even reach the cooling limit without any knowledge of the state and using only a single fixed operation, and on a practical level, presents a more feasible and robust alternative for implementing HBAC. We also show that our new technique converges to the asymptotic state of HBAC and that the cooling algorithm can be efficiently implemented;however, the saturation could require exponentially many iterations and remains impractical. This brings HBAC to the realm of feasibility and makes it a viable option for realistic application in quantum technologies. Copyright © 2019, The Authors. All rights reserved.

关键词： Cooling

Exploring the unexpected: Disharmonized harmonic pulsation modes in high-amplitude δ Scuti stars

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arXiv 2024年

作者： Xue, Hui-Fang Niu, Jia-Shu Department of Physics Taiyuan Normal University Jinzhong030619 China Institute of Computational and Applied Physics Taiyuan Normal University Jinzhong030619 China Shanxi Key Laboratory for Intelligent Optimization Computing and Blockchain Technology Jinzhong030619 China Institute of Theoretical Physics Shanxi University Taiyuan030006 China State Key Laboratory of Quantum Optics and Quantum Optics Devices Shanxi University Taiyuan030006 China Collaborative Innovation Center of Extreme Optics Shanxi University Taiyuan Shanxi030006 China

Harmonics are a ubiquitous feature across various pulsating stars. They are traditionally viewed as mere replicas of the independent primary pulsation modes and have thus been excluded from asteroseismological models. Recent research, however, has uncovered a significant discrepancy: in high-amplitude δ Scuti (HADS) stars, harmonics exhibit uncorrelated variations in amplitude and frequency relative to their independent primary pulsation modes. The nature of these disharmonized harmonics is a question of critical importance. In our study we analysed five triple-mode HADS stars observed by the Transiting Exoplanet Survey Satellite (TESS) and discovered some pervasive patterns of disharmonized harmonics in both the fundamental ( f0) and first overtone ( f1) pulsation modes. Intriguingly, through an in-depth frequency interaction analysis of V1393 Cen, we identified 2 f1as an independent pulsation mode, distinct from f1, and identified it as the progenitor of the frequency variations observed in 3 f1, 4 f1, 5 f1, and 6 f1. Similar behaviour can be found in DO CMi and GSC 06047-00749, in which 2 f1and 3 f1are the independent pulsation modes, respectively. Notably, we found an interesting pattern when decomposing the harmonics that might suggest a generation process of harmonics. These findings serve as a new window on the research of harmonics, which remains a hidden corner of contemporary asteroseismology. © 2024, CC BY.

关键词： Stars