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Quantifying fermionic nonlinearity of quantum circuits

Physical Review Research 2022年第4期4卷 043100-043100页

作者： Shigeo Hakkaku Yuichiro Tashima Kosuke Mitarai Wataru Mizukami Keisuke Fujii Graduate School of Engineering Science Osaka University 1-3 Machikaneyama Toyonaka Osaka 560-8531 Japan NTT Computer and Data Science Laboratories NTT Corporation 3-9-11 Midoricho Musashino 180-8585 Japan Center for Quantum Information and Quantum Biology Osaka University 1-2 Machikaneyama Toyonaka 560-0043 Japan JST PRESTO 4-1-8 Honcho Kawaguchi Saitama 332-0012 Japan RIKEN Center for Quantum Computing (RQC) Hirosawa 2-1 Wako Saitama 351-0198 Japan Fujitsu Quantum Computing Joint Research Division at QIQB Osaka University 1-2 Machikaneyama Toyonaka 560-0043 Japan

Variational quantum algorithms (VQAs) have been proposed as one of the most promising approaches to demonstrate quantum advantage on noisy intermediate-scale quantum (NISQ) devices. However, it has been unclear whether VQAs can maintain quantum advantage under the intrinsic noise of the NISQ devices, which deteriorates the quantumness. Here we propose a measure, called fermionic nonlinearity, to quantify the classical simulatability of quantum circuits designed for simulating fermionic Hamiltonians. Specifically, we construct a Monte Carlo type classical algorithm based on the classical simulatability of fermionic linear optics, whose sampling overhead is characterized by the fermionic nonlinearity. As a demonstration of these techniques, we calculate the upper bound of the fermionic nonlinearity of a rotation gate generated by four fermionic modes under the dephasing noise. Moreover, we estimate the sampling costs of the unitary coupled cluster singles and doubles quantum circuits for hydrogen chains subject to the dephasing noise. We find that, depending on the error probability and atomic spacing, there are regions where the fermionic nonlinearity becomes very small or unity, and hence the circuits are classically simulatable. We believe that our method and results help to design quantum circuits for fermionic systems with potential quantum advantages.

关键词： Quantum algorithms Quantum computation Quantum correlations in quantum information Quantum information processing Quantum simulation Resource theories

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General condition of quantum teleportation by one-dimensional quantum walks

arXiv

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arXiv 2021年

作者： Yamagami, Tomoki Segawa, Etsuo Konno, Norio Department of Information Physics and Computing Graduate School of Information Science and Technology The University of Tokyo Tokyo113-8656 Japan Graduate School of Environment and Information Sciences Yokohama National University Yokohama240-8501 Japan Department of Applied Mathematics Faculty of Engineering Yokohama National University Yokohama240-8501 Japan

We extend the scheme of quantum teleportation by quantum walks introduced by Wang et al. (2017). First, we introduce the mathematical definition of the accomplishment of quantum teleportation by this extended scheme. Secondly, we show a useful necessary and sufficient condition that the quantum teleportation is accomplished rigorously. Our result classifies the parameters of the setting for the accomplishment of quantum teleportation. Copyright © 2021, The Authors. All rights reserved.

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Error Exponent and Strong Converse for Quantum Soft Covering

Error Exponent and Strong Converse for Quantum Soft Covering

引用

IEEE International Symposium on Information Theory

作者： Hao-Chung Cheng Li Gao Department of Electrical Engineering and Graduate Institute of Communication Engineering National Taiwan University Taipei Taiwan (R.O.C.) Department of Mathematics National Taiwan University Taipei Taiwan (R.O.C.) Center for Quantum Science and Engineering National Taiwan University Taipei Taiwan (R.O.C.) Hon Hai (Foxconn) Quantum Computing Research Center New Taipei City Taiwan (R.O.C.) Department of Mathematics University of Houston Houston TX USA

ISBN: (数字)9781665421591

ISBN: (纸本)9781665421607

How well can we approximate a classical-quantum channel output state by using a random codebook with a certain size? In this work, we study the quantum soft covering problem and establish exponential achievability and strong converse bounds on the expected trace distance between the codebook-induced state and the true state. When using independent and identically distributed random codebook or constant composition random codebook with a rate above the quantum mutual information I(X : B) ρ , we prove that the trace distances decay exponentially with error exponents expressed by the sandwiched Rényi and Augustin information. For a rate below I(X : B) ρ , we show that both the trace distances converge to 1 exponentially fast. The full manuscript can be found at [1].

关键词： Quantum mechanics Mutual information Convergence

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EXPLAINABLE ARTIFICIAL INTELLIGENCE (XAI) 2.0: A MANIFESTO OF OPEN CHALLENGES AND INTERDISCIPLINARY RESEARCH DIRECTIONS

arXiv

引用

arXiv 2023年

作者： Longo, Luca Brcic, Mario Cabitza, Federico Choi, Jaesik Confalonieri, Roberto Ser, Javier Del Guidotti, Riccardo Hayashi, Yoichi Herrera, Francisco Holzinger, Andreas Jiang, Richard Khosravi, Hassan Lecue, Freddy Malgieri, Gianclaudio Páez, Andrés Samek, Wojciech Schneider, Johannes Speith, Timo Stumpf, Simone The Artificial Intelligence and Cognitive Load Research Lab Technological University Dublin Ireland University of Zagreb Faculty of Electrical Engineering and Computing Croatia University of Milano-Bicocca Milan Italy IRCCS Ospedale Galeazzi Sant’Ambrogio Milan Italy Kim Jaechul Graduate School of AI Korea Advanced Institute of Science & Technology Korea Republic of INEEJI Corporation Korea Republic of Department of Mathematics University of Padua Italy Derio Spain Bilbao Spain University of Pisa Pisa Italy Department of Computer Science Meiji University Tokyo Japan Department of Computer Science and Artificial Intelligence DaSCI Andalusian Institute in Data Science & Computational Intelligence University of Granada Granada Spain Human-Centered AI Lab University of Natural Resources and Life Sciences Vienna Austria School of Computing and Communications Lancaster University United Kingdom The University of Queensland Brisbane Australia Sophia Antipolis France eLaw Center for Law and Digital Technologies Leiden University Netherlands Department of Philosophy Universidad de los Andes Bogotá Colombia Center for Research & Formation in Artificial Intelligence Universidad de los Andes Bogotá Colombia Technical University of Berlin Berlin Germany Fraunhofer Heinrich Hertz Institute Berlin Germany Berlin Germany Department of Information Systems and Computer Science University of Liechtenstein Liechtenstein Liechtenstein Department of Philosophy University of Bayreuth Bayreuth Germany Center for Perspicuous Computing Saarland University Saarbrücken Germany School of Computing Science University of Glasgow United Kingdom

As systems based on opaque Artificial Intelligence (AI) continue to flourish in diverse real-world applications, understanding these black box models has become paramount. In response, Explainable AI (XAI) has emerged as a field of research with practical and ethical benefits across various domains. This paper not only highlights the advancements in XAI and its application in real-world scenarios but also addresses the ongoing challenges within XAI, emphasizing the need for broader perspectives and collaborative efforts. We bring together experts from diverse fields to identify open problems, striving to synchronize research agendas and accelerate XAI in practical applications. By fostering collaborative discussion and interdisciplinary cooperation, we aim to propel XAI forward, contributing to its continued success. Our goal is to put forward a comprehensive proposal for advancing XAI. To achieve this goal, we present a manifesto of 27 open problems categorized into nine categories. These challenges encapsulate the complexities and nuances of XAI and offer a road map for future research. For each problem, we provide promising research directions in the hope of harnessing the collective intelligence of interested stakeholders. © 2023, CC BY-SA.

关键词： Ethical technology

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Optimal Hamiltonian simulation for time-periodic systems

arXiv

引用

arXiv 2022年

作者： Mizuta, Kaoru Fujii, Keisuke Hirosawa 2-1 Saitama Wako351-0198 Japan Graduate School of Engineering Science Osaka University 1-3 Machikaneyama Osaka Toyonaka560-8531 Japan Center for Quantum Information and Quantum Biology Osaka University Japan Fujitsu Quantum Computing Joint Research Division at QIQB Osaka University 1-2 Machikaneyama Toyonaka560-0043 Japan

The implementation of time-evolution operators U(t), called Hamiltonian simulation, is one of the most promising usage of quantum computers. For time-independent Hamiltonians, qubitization has recently established efficient realization of time-evolution U(t) = e−iHt, with achieving the optimal computational resource both in time t and an allowable error Ε. In contrast, those for time-dependent systems require larger cost due to the difficulty of handling time-dependency. In this paper, we establish optimal/nearly-optimal Hamiltonian simulation for generic time-dependent systems with time-periodicity, known as Floquet systems. By using a so-called Floquet-Hilbert space equipped with auxiliary states labeling Fourier indices, we develop a way to certainly obtain the target time-evolved state without relying on either time-ordered product or Dyson-series expansion. Consequently, the query complexity, which measures the cost for implementing the time-evolution, has optimal and nearly-optimal dependency respectively in time t and inverse error Ε, and becomes sufficiently close to that of qubitization. Thus, our protocol tells us that, among generic time-dependent systems, time-periodic systems provides a class accessible as efficiently as time-independent systems despite the existence of time-dependency. As we also provide applications to simulation of nonequilibrium phenomena and adiabatic state preparation, our results will shed light on nonequilibrium phenomena in condensed matter physics and quantum chemistry, and quantum tasks yielding time-dependency in quantum computation. © 2022, CC BY.

关键词： Hamiltonians

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Strong Converse for Privacy Amplification against Quantum Side Information

Strong Converse for Privacy Amplification against Quantum Si...

引用

IEEE International Symposium on Information Theory

作者： Yu-Chen Shen Li Gao Hao-Chung Cheng Department of Electrical Engineering Graduate Institute of Communication Engineering National Taiwan University Taipei Taiwan (R.O.C.) Department of Mathematics University of Houston Houston USA Department of Mathematics National Taiwan University Taipei Taiwan (R.O.C.) Center for Quantum Science and Engineering National Taiwan University Taipei Taiwan (R.O.C.) Hon Hai (Foxconn) Quantum Computing Research Center New Taipei City Taiwan (R.O.C.)

ISBN: (数字)9781665421591

ISBN: (纸本)9781665421607

We establish a one-shot strong converse bound for privacy amplification against quantum side information with trace distance as a security criterion. Firstly, our result shows that the trace distance converges to 1 exponentially fast for any finite blocklength when the rate of the extractable randomness exceeds the conditional von Neumann entropy of Alice given Eavesdropper. Secondly, we obtain a second-order converse bound for the maximal extractable randomness. Thirdly, our result extends to the moderate deviation regime. Namely, when the rate of the extractable randomness approaches the conditional von Neumann entropy from above with speed slower than $O\left( {1/\sqrt n } \right.$, the trace distance still converges to 1 asymptotically. Lastly, our result yields strong converse to entropy accumulation, which complements the recent result by Dupuis [arXiv:2105.05342]. The full manuscript can be assessed in [1], [2].

关键词： Privacy Protocols Entropy Behavioral sciences Security Information theory Convergence

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Adapting the HHL algorithm to quantum many-body theory

arXiv

引用

arXiv 2022年

作者： Baskaran, Nishanth Rawat, Abhishek Singh Jayashankar, Akshaya Chakravarti, Dibyajyoti Sugisaki, K. Roy, Shibdas Mandal, Sudhindu Bikash Mukherjee, D. Prasannaa, V.S. Centre for Quantum Engineering Research and Education TCG CREST Sector V Salt Lake Kolkata700091 India Graduate School of Science and Technology Keio University 7-1 Shinkawasaki Saiwai-ku Kanagawa Kawasaki212-0032 Japan Quantum Computing Center Keio University 3-14-1 Hiyoshi Kohoku-ku Kanagawa Yokohama223-8522 Japan

Rapid progress in developing near- and long-term quantum algorithms for quantum chemistry has provided us with an impetus to move beyond traditional approaches and explore new ways to apply quantum computing to electronic structure calculations. In this work, we identify the connection between quantum many-body theory and a quantum linear solver, and implement the Harrow-Hassidim-Lloyd (HHL) algorithm to make precise predictions of correlation energies for light molecular systems via the (non-unitary) linearized coupled cluster theory, where the term 'light molecular systems' refer to those molecules whose constituent atoms have low atomic number. For the purposes of practical computations, we make suitable changes to the HHL framework. This entails two aspects- (a) Adapt: prescribing a novel scaling approach that allows one to scale any arbitrary Hermitian matrix, A, that in turn dictates the controlled rotation angles without having to precompute the eigenvalues of A, and yet achieve a reasonably high precision in |x〉, and (b) Lite: we devise techniques that reduce the depth of the relevant quantum circuit. In this context, we introduce the following variants of HHL for different eras of quantum computing-AdaptHHLite in its appropriate forms for noisy intermediate scale quantum (NISQ), late-NISQ, and the early fault-tolerant eras, as well as AdaptHHL for the fault-tolerant quantum computing era. We demonstrate the ability of the NISQ variant of AdaptHHLite to capture correlation energy precisely, while simultaneously being resource-lean, using simulation as well as the 11-qubit IonQ quantum hardware. © 2022, CC BY.

关键词： Quantum chemistry

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Recursive Quantum Eigenvalue/Singular-Value Transformation: Analytic Construction of Matrix Sign Function by Newton Iteration

arXiv

引用

arXiv 2023年

作者： Mizuta, Kaoru Fujii, Keisuke Hirosawa 2-1 Wako Saitama351-0198 Japan Department of Applied Physics The University of Tokyo Hongo 7-3-1 Bunkyo Tokyo113-8656 Japan Graduate School of Engineering Science Osaka University 1-3 Machikaneyama Toyonaka Osaka560-8531 Japan Center for Quantum Information and Quantum Biology Osaka University Japan Fujitsu Quantum Computing Joint Research Division at QIQB Osaka University 1-2 Machikaneyama Toyonaka560-0043 Japan

Quantum eigenvalue transformation (QET) and its generalization, quantum singular value transformation (QSVT), are versatile quantum algorithms that allow us to apply broad matrix functions to quantum states, which cover many of significant quantum algorithms such as Hamiltonian simulation. However, finding a parameter set which realizes preferable matrix functions in these techniques is difficult for large-scale quantum systems: there is no analytical result other than trivial cases as far as we know and we often suffer also from numerical instability. In this Letter, we propose recursive QET or QSVT (r-QET or r-QSVT), in which we can execute complicated matrix functions by recursively organizing block-encoding by low-degree QET or QSVT. Owing to the simplicity of recursive relations, it works only with a few parameters with exactly determining the parameters, while its iteration results in complicated matrix functions. In particular, by exploiting the recursive relation of Newton iteration, we construct the matrix sign function, which can be applied for eigenstate filtering for example, in a tractable way. We show that an analytically-obtained parameter set composed of only 8 different values is sufficient for executing QET of the matrix sign function with an arbitrarily small error Ε. Our protocol will serve as an alternative protocol for constructing QET or QSVT for some useful matrix functions without numerical instability. © 2023, CC BY.

关键词： Hamiltonians

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Local Variational Quantum Compilation of Large-Scale Hamiltonian Dynamics

引用

PRX Quantum 2022年第4期3卷 040302-040302页

作者： Kaoru Mizuta Yuya O. Nakagawa Kosuke Mitarai Keisuke Fujii QunaSys Inc. Aqua Hakusan Building 9F 1-13-7 Hakusan Bunkyo Tokyo 113-0001 Japan Department of Physics Kyoto University Kyoto 606-8502 Japan RIKEN Center for Quantum Computing (RQC) Hirosawa 2-1 Wako Saitama 351-0198 Japan Graduate School of Engineering Science Osaka University 1-3 Machikaneyama Toyonaka Osaka 560-8531 Japan Center for Quantum Information and Quantum Biology Osaka University 1-2 Machikaneyama Toyonaka Osaka 560-0043 Japan Japan Science and Technology Agency (JST) Precursory Research for Embryonic Science and Technology (PRESTO) 4-1-8 Honcho Kawaguchi Saitama 332-0012 Japan Fujitsu Quantum Computing Joint Research Division at QIQB Osaka University 1-2 Machikaneyama Toyonaka 560-0043 Japan

The implementation of time-evolution operators on quantum circuits is important for quantum simulation. However, the standard method, Trotterization, requires a huge number of gates to achieve desirable accuracy. Here, we propose a local variational quantum compilation (LVQC) algorithm, which allows us to accurately and efficiently compile time-evolution operators on a large-scale quantum system by optimization with smaller-size quantum systems. LVQC utilizes a subsystem cost function, which approximates the fidelity of the whole circuit, defined for each subsystem that is as large as the approximate causal cones generated by the Lieb-Robinson (LR) bound. We rigorously derive its scaling property with respect to the subsystem size and show that the optimization conducted on the subsystem size leads to the compilation of whole-system time-evolution operators. As a result, LVQC runs with limited-size quantum computers or classical simulators that can handle such smaller quantum systems. For instance, finite-ranged and short-ranged interacting L-size systems can be compiled with O(L0)- or O(log L)-size quantum systems depending on the observables of interest. Furthermore, since this formalism relies only on the LR bound, it can efficiently construct time-evolution operators of various systems in generic dimensions involving finite-, short-, and long-ranged interactions. We also numerically demonstrate the LVQC algorithm for one-dimensional systems. Through the employment of classical simulation by time-evolving block decimation, we succeed in compressing the depth of the time-evolution operators up to 40 qubits by the compilation for 20 qubits. LVQC not only provides classical protocols for designing large-scale quantum circuits but also sheds light on applications of intermediate-scale quantum devices in implementing algorithms in larger-scale quantum devices.

关键词： Quantum algorithms Quantum repeaters Quantum simulation Quantum many-body systems

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Fermionic quantum approximate optimization algorithm

arXiv

引用

arXiv 2023年

作者： Yoshioka, Takuya Sasada, Keita Nakano, Yuichiro Fujii, Keisuke Strategic Technology Center TIS Inc. 2-2-1 Toyosu Koto-ku Tokyo135-0061 Japan Graduate School of Engineering Science Osaka University 1-3 Machikaneyama Osaka Toyonaka560-8531 Japan Center for Quantum Information and Quantum Biology Institute for Open and Transdisciplinary Research Initiatives Osaka Univrsity 1-2 Machikaneyama Osaka Toyonaka560-0043 Japan Center for Quantum Computing RIKEN 2-1 Hirosawa Saitama Wako351-0198 Japan

Quantum computers are expected to accelerate solving combinatorial optimization problems, including algorithms such as Grover adaptive search and quantum approximate optimization algorithm (QAOA). However, many combinatorial optimization problems involve constraints which, when imposed as soft constraints in the cost function, can negatively impact the performance of the optimization algorithm. In this paper, we propose fermionic quantum approximate optimization algorithm (FQAOA) for solving combinatorial optimization problems with constraints. Specifically FQAOA tackle the constrains issue by using fermion particle number preservation to intrinsically impose them throughout QAOA. We provide a systematic guideline for designing the driver Hamiltonian for a given problem Hamiltonian with constraints. The initial state can be chosen to be a superposition of states satisfying the constraint and the ground state of the driver Hamiltonian. This property is important since FQAOA reduced to quantum adiabatic computation in the large limit of circuit depth p and improved performance, even for shallow circuits with optimizing the parameters starting from the fixed-angle determined by Trotterized quantum adiabatic evolution. We perform an extensive numerical simulation and demonstrates that proposed FQAOA provides substantial performance advantage against existing approaches in portfolio optimization problems. Furthermore, the Hamiltonian design guideline is useful not only for QAOA, but also Grover adaptive search and quantum phase estimation to solve combinatorial optimization problems with constraints. Since software tools for fermionic systems have been developed in quantum computational chemistry both for noisy intermediate-scale quantum computers and fault-tolerant quantum computers, FQAOA allows us to apply these tools for constrained combinatorial optimization problems. Copyright © 2023, The Authors. All rights reserved.

关键词： Hamiltonians

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