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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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Subspace variational quantum simulator

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Physical Review Research 2023年第2期5卷 023078-023078页

作者： Kentaro Heya Ken M. Nakanishi Kosuke Mitarai Zhiguang Yan Kun Zuo Yasunari Suzuki Takanori Sugiyama Shuhei Tamate Yutaka Tabuchi Keisuke Fujii Yasunobu Nakamura RIKEN Center for Quantum Computing (RQC) Wako Saitama 351-0198 Japan Institute for Physics of Intelligence The University of Tokyo Tokyo 113-0033 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 Japan JST PRESTO 4-1-8 Honcho Kawaguchi Saitama 332-0012 Japan NTT Computer and Data Science Laboratories NTT Corporation Musashino 180-8585 Japan Research Center for Advanced Science and Technology (RCAST) The University of Tokyo Meguro-ku Tokyo 153-8904 Japan Department of Applied Physics Graduate School of Engineering The University of Tokyo Bunkyo-ku Tokyo 113-8656 Japan

Quantum simulation is one of the key applications of quantum computing, which accelerates research and development in the fields such as chemistry and material science. The recent development of noisy intermediate-scale quantum (NISQ) devices urges the exploration of applications without the necessity of quantum error correction. In this paper, we propose an efficient method to simulate quantum dynamics driven by a static Hamiltonian on NISQ devices, named subspace variational quantum simulator (SVQS). SVQS employs the subspace-search variational quantum eigensolver (SSVQE) [Phys. Rev. Res. 1, 033062 (2019)] to find a low-lying eigensubspace and extends it to simulate dynamics within the subspace with lower overhead compared to the existing schemes. We experimentally simulate the time-evolution operator in a low-lying eigensubspace of a hydrogen molecule. We also define the subspace process fidelity as a measure between two quantum processes in a subspace. The subspace time evolution mimicked by SVQS shows the subspace process fidelity of 0.896–0.989.

关键词： Quantum algorithms Quantum algorithms for chemical calculations Quantum computation Quantum control Quantum gates Quantum simulation Quantum tomography

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Noise propagation in hybrid tensor networks

arXiv

引用

arXiv 2023年

作者： Harada, Hiroyuki Suzuki, Yasunari Yang, Bo Tokunaga, Yuuki Endo, Suguru Department of Applied Physics and Physico-Informatics Keio University Hiyoshi 3-14-1 Kohoku Yokohama223-8522 Japan NTT Computer and Data Science Laboratories NTT Corporation 3-9-11 Midori-cho Musashino-shi Tokyo180-8585 Japan LIP6 Sorbonne Université 4 Place Jussieu Paris75005 France Graduate School of Information Science and Technology The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-8656 Japan JST PRESTO 4-1-8 Honcho Kawaguchi Saitama332-0012 Japan

The hybrid tensor network (HTN) method is a general framework allowing for the construction of an effective wavefunction with the combination of classical tensors and quantum tensors, i.e., amplitudes of quantum states. In particular, hybrid tree tensor networks (HTTNs) are very useful for simulating larger systems beyond the available size of the quantum hardware. However, while the realistic quantum states in NISQ hardware are highly likely to be noisy, this framework is formulated for pure states. In this work, as well as discussing the relevant methods, i.e., Deep VQE and entanglement forging under the framework of HTTNs, we investigate the noisy HTN states by introducing the expansion operator for providing the description of the expansion of the size of simulated quantum systems and the noise propagation. This framework enables the general tree HTN states to be explicitly represented and their physicality to be discussed. We also show that the expectation value of a measured observable exponentially vanishes with the number of contracted quantum tensors. Our work will lead to providing the noise-resilient construction of HTN states. Copyright © 2023, The Authors. All rights reserved.

关键词： Tensors

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Generalized Quantum Subspace Expansion

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Physical Review Letters 2022年第2期129卷 020502-020502页

作者： Nobuyuki Yoshioka Hideaki Hakoshima Yuichiro Matsuzaki Yuuki Tokunaga Yasunari Suzuki Suguru Endo Department of Applied Physics University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo 113-8656 Japan Theoretical Quantum Physics Laboratory RIKEN Cluster for Pioneering Research (CPR) Wako-shi Saitama 351-0198 Japan Research Center for Emerging Computing Technologies National Institute of Advanced Industrial Science and Technology (AIST) 1-1-1 Umezono Tsukuba Ibaraki 305-8568 Japan Center for Quantum Information and Quantum Biology Osaka University 1-2 Machikaneyama Toyonaka 560-0043 Japan NEC-AIST Quantum Technology Cooperative Research Laboratory National Institute of Advanced Industrial Science and Technology (AIST) Tsukuba Ibaraki 305-8568 Japan NTT Computer and Data Science Laboratories NTT Corporation Musashino 180-8585 Japan JST PRESTO 4-1-8 Honcho Kawaguchi Saitama 332-0012 Japan

One of the major challenges for erroneous quantum computers is undoubtedly the control over the effect of noise. Considering the rapid growth of available quantum resources that are not fully fault tolerant, it is crucial to develop practical hardware-friendly quantum error mitigation (QEM) techniques to suppress unwanted errors. Here, we propose a novel generalized quantum subspace expansion method which can handle stochastic, coherent, and algorithmic errors in quantum computers. By fully exploiting the substantially extended subspace, we can efficiently mitigate the noise present in the spectra of a given Hamiltonian, without relying on any information of noise. The performance of our method is discussed under two highly practical setups: the quantum subspaces are mainly spanned by powers of the noisy state ρm and a set of error-boosted states, respectively. We numerically demonstrate in both situations that we can suppress errors by orders of magnitude, and show that our protocol inherits the advantages of previous error-agnostic QEM techniques as well as overcoming their drawbacks.

关键词： Quantum algorithms Quantum computation Quantum error correction Quantum information processing Variational approach

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Quantifying fermionic nonlinearity of quantum circuits

arXiv

引用

arXiv 2021年

作者： Hakkaku, Shigeo Tashima, Yuichiro Mitarai, Kosuke Mizukami, Wataru Fujii, Keisuke Graduate School of Engineering Science Osaka University 1-3 Machikaneyama Osaka Toyonaka560-8531 Japan NTT Computer and Data Science Laboratories NTT Corporation 3-9-11 Midoricho Musashino180-8585 Japan Center for Quantum Information and Quantum Biology Osaka University 1-2 Machikaneyama Toyonaka560-0043 Japan JST PRESTO 4-1-8 Honcho Saitama Kawaguchi332-0012 Japan Hirosawa 2-1 Saitama Wako351-0198 Japan Fujitsu Quantum Computing Joint Research Division QIQB Osaka University 1-2 Machikaneyama Toyonaka560-0043 Japan

关键词： Timing circuits

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Generalized quantum subspace expansion

arXiv

引用

arXiv 2021年

作者： Yoshioka, Nobuyuki Hakoshima, Hideaki Matsuzaki, Yuichiro Tokunaga, Yuuki Suzuki, Yasunari Endo, Suguru Department of Applied Physics University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-8656 Japan Wako-shi Saitama351-0198 Japan 1-1-1 Umezono Ibaraki Tsukuba305-8568 Japan Center for Quantum Information and Quantum Biology Osaka University 1-3 Machikaneyama Toyonaka Osaka560-8531 Japan Ibaraki Tsukuba305-8568 Japan NTT Computer and Data Science Laboratories NTT Corporation Musashino180-8585 Japan JST PRESTO 4-1-8 Honcho Kawaguchi Saitama332-0012 Japan

One of the major challenges for erroneous quantum computers is undoubtedly the control over the effect of noise. Considering the rapid growth of available quantum resources that are not fully fault-tolerant, it is crucial to develop practical hardware-friendly quantum error mitigation (QEM) techniques to suppress unwanted errors. Here, we propose a novel generalized quantum subspace expansion method which can handle stochastic, coherent, and algorithmic errors in quantum computers. By fully exploiting the substantially extended subspace, we can efficiently mitigate the noise present in the spectra of a given Hamiltonian, without relying on any information of noise. The performance of our method is discussed under two highly practical setups: the quantum subspaces are mainly spanned by powers of the noisy state ρm and a set of error-boosted states, respectively. We numerically demonstrate in both situations that we can suppress errors by orders of magnitude, and show that out protocol inherits the advantages of previous error-agnostic QEM techniques as well as overcoming their drawbacks. © 2021, CC BY.

关键词： Errors

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Localized Virtual Purification

arXiv

引用

arXiv 2023年

作者： Hakoshima, Hideaki Endo, Suguru Yamamoto, Kaoru Matsuzaki, Yuichiro Yoshioka, Nobuyuki Graduate School of Engineering Science Osaka University 1-3 Machikaneyama Osaka Toyonaka560-8531 Japan Center for Quantum Information and Quantum Biology Osaka University 1-2 Machikaneyama Osaka Toyonaka560-0043 Japan NTT Computer and Data Science Laboratories NTT Corporation Musashino180-8585 Japan JST PRESTO 4-1-8 Honcho Saitama Kawaguchi332-0012 Japan Department of Electrical Electronic and Communication Engineering Faculty of Science and Engineering Chuo University Bunkyo-ku 1-13-27 Kasuga Tokyo112-8551 Japan Department of Applied Physics University of Tokyo Bunkyo-ku 7-3-1 Hongo Tokyo113-8656 Japan Saitama Wako-shi351-0198 Japan

Analog and digital quantum simulators can efficiently simulate quantum many-body systems that appear in natural phenomena. However, experimental limitations of near-term devices still make it challenging to perform the entire process of quantum simulation. The purification-based quantum simulation methods can alleviate the limitations in experiments such as the cooling temperature and noise from the environment, while this method has the drawback that it requires global entangled measurement with a prohibitively large number of measurements that scales exponentially with the system size. In this Letter, we propose that we can overcome these problems by restricting the entangled measurements to the vicinity of the local observables to be measured, when the locality of the system can be exploited. We provide theoretical guarantees that the global purification operation can be replaced with local operations under some conditions, in particular for the task of cooling and error mitigation. We furthermore give a numerical verification that the localized purification is valid even when conditions are not satisfied. Our method bridges the fundamental concept of locality with quantum simulators, and therefore expected to open a path to unexplored quantum many-body phenomena. Copyright © 2023, The Authors. All rights reserved.

关键词： Purification

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Quantum Circuits for Exact Unitary t-Designs and Applications to Higher-Order Randomized Benchmarking

引用

PRX Quantum 2021年第3期2卷 030339-030339页

作者： Yoshifumi Nakata Da Zhao Takayuki Okuda Eiichi Bannai Yasunari Suzuki Shiro Tamiya Kentaro Heya Zhiguang Yan Kun Zuo Shuhei Tamate Yutaka Tabuchi Yasunobu Nakamura Photon Science Center Graduate School of Engineering The University of Tokyo Bunkyo-ku Tokyo 113–8656 Japan JST PRESTO 4–1–8 Honcho Kawaguchi Saitama 332–0012 Japan School of Mathematical Sciences Shanghai Jiao Tong University Shanghai 400240 China Department of Mathematics Hiroshima University 1-3-1 Kagamiyama Higashihiroshima 739-8562 Japan Faculty of Mathematics Kyushu University (emeritus) Fukuoka 819-0385 Japan Mathematics Division National Center for Theoretical Sciences National Taiwan University Taipei 10617 Taiwan NTT Computer and Data Science Laboratories NTT Corporation Musashino 180-8585 Japan Department of Applied Physics Graduate School of Engineering The University of Tokyo 7-3-1 Hongo Bynkyo-ku Tokyo 113-8656 Japan Research Center for Advanced Science and Technology (RCAST) The University of Tokyo Meguro-ku Tokyo 153-8904 Japan RIKEN Center for Quantum Computing (RQC) Wako Saitama 351-0198 Japan

A unitary t-design is a powerful tool in quantum information science and fundamental physics. Despite its usefulness, only approximate implementations were known for general t. In this paper, we provide quantum circuits that generate exact unitary t-designs for any t on an arbitrary number of qubits. Our construction is inductive and is of practical use in small systems. We then introduce a tth-order generalization of randomized benchmarking (t-RB) as an application of exact 2t-designs. We particularly study the 2-RB in detail and show that it reveals self-adjointness of quantum noise, a metric related to the feasibility of quantum error correction (QEC). We numerically demonstrate that the 2-RB in one- and two-qubit systems is feasible, and experimentally characterize background noise of a superconducting qubit by the 2-RB. It is shown from the experiment that interactions with adjacent qubits induce the noise that may result in an obstacle toward a realization of QEC.

关键词： Quantum algorithms Quantum benchmarking Quantum gates Quantum protocols

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Leveraging hardware-control imperfections for error mitigation via generalized quantum subspace

arXiv

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arXiv 2023年

作者： Ohkura, Yasuhiro Endo, Suguru Satoh, Takahiko Van Meter, Rodney Yoshioka, Nobuyuki Graduate School of Media and Governance Keio University SFC Kanagawa Fujisawa252-0882 Japan NTT Computer and Data Science Laboratories NTT Corporation Musashino180-8585 Japan Keio University Quantum Computing Center Kanagawa Yokohama223-8522 Japan Graduate School of Science and Technology Keio University Kanagawa Yokohama223-8522 Japan Faculty of Environment and Information Studies Keio University SFC Kanagawa Fujisawa252-0882 Japan Department of Applied Physics University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-8656 Japan Wako-shi Saitama351-0198 Japan JST PRESTO 4-1-8 Honcho Kawaguchi Saitama332-0012 Japan

In the era of quantum computing without full fault-tolerance, it is essential to suppress noise effects via the quantum error mitigation techniques to enhance the computational power of the quantum devices. One of the most effective noise-agnostic error mitigation schemes is the generalized quantum subspace expansion (GSE) method, which unifies various mitigation algorithms under the framework of the quantum subspace expansion. Specifically, the fault-subspace method, a subclass of GSE method, constructs an error-mitigated quantum state with copies of quantum states with different noise levels. However, from the experimental aspect, it is nontrivial to determine how to reliably amplify the noise so that the error in the simulation result is efficiently suppressed. In this work, we explore the potential of the fault-subspace method by leveraging the hardware-oriented noise: intentional amplification of the decoherence, noise boost by insertion of identity, making use of crosstalk, and probabilistic implementation of noise channel. We demonstrate the validity of our proposals via both numerical simulations with the noise parameters reflecting those in quantum devices available via IBM Quantum, and also experiments performed therein. Copyright © 2023, The Authors. All rights reserved.

关键词： Errors

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Qulacs: A fast and versatile quantum circuit simulator for research purpose

arXiv

引用

arXiv 2020年

作者： Suzuki, Yasunari Kawase, Yoshiaki Masumura, Yuya Hiraga, Yuria Nakadai, Masahiro Chen, Jiabao Nakanishi, Ken M. Mitarai, Kosuke Imai, Ryosuke Tamiya, Shiro Yamamoto, Takahiro Yan, Tennin Kawakubo, Toru Nakagawa, Yuya O. Ibe, Yohei Zhang, Youyuan Yamashita, Hirotsugu Yoshimura, Hikaru Hayashi, Akihiro Fujii, Keisuke NTT Computer and Data Science Laboratories NTT Corporation Musashino180-8585 Japan JST PRESTO Saitama Kawaguchi332-0012 Japan Graduate School of Engineering Science Osaka University 1-3 Machikaneyama Osaka Toyonaka560-8531 Japan Graduate School of Information Science and Technology Osaka University 1-1 Yamadaoka Osaka Suita565-0871 Japan Graduate School of Information and Science Nara Institute of Science and Technology Ikoma Nara Takayama630-0192 Japan Graduate School of Science Kyoto University Yoshida-Ushinomiya Sakyo Kyoto606-8302 Japan QunaSys Inc. Aqua Hakusan Building 9F 1-13-7 Hakusan Bunkyo Tokyo113-0001 Japan Graduate School of Science The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-0033 Japan Center for Quantum Information and Quantum Biology Institute for Open and Transdisciplinary Research Initiatives Osaka University Japan Graduate School of Engineering The University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-0033 Japan School of Computer Science Georgia Institute of Technology AtlantaGA30332 United States Center for Emergent Matter Science RIKEN Saitama Wako351-0198 Japan

To explore the possibilities of a near-term intermediate-scale quantum algorithm and long-term fault-tolerant quantum computing, a fast and versatile quantum circuit simulator is needed. Here, we introduce Qulacs, a fast simulator for quantum circuits intended for research purpose. We show the main concepts of Qulacs, explain how to use its features via examples, describe numerical techniques to speed-up simulation, and demonstrate its performance with numerical benchmarks. © 2020, CC BY.

关键词： Timing circuits

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