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arXiv 2022年

作者： Yoshioka, Nobuyuki Okubo, Tsuyoshi Suzuki, Yasunari Koizumi, Yuki Mizukami, Wataru Department of Applied Physics University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-8656 Japan Saitama Wako-shi351-0198 Japan JST PRESTO 4-1-8 Honcho Saitama Kawaguchi332-0012 Japan Institute for Physics of Intelligence University of Tokyo 7-3-1 Hongo Bunkyo-ku Tokyo113-0033 Japan NTT Computer and Data Science Laboratories Musashino180-8585 Japan Center for Quantum Information and Quantum Biology Osaka University 1-2 Machikaneyama Osaka Toyonaka560-0043 Japan Graduate School of Engineering Science Osaka University 1-3 Machikaneyama Osaka Toyonaka560-8531 Japan

The intensive pursuit for quantum advantage in terms of computational complexity has further led to a modernized crucial question: When and how will quantum computers outperform classical computers? The next milestone is undoubtedly the realization of quantum acceleration in practical problems. Here we provide a clear evidence and arguments that the primary target is likely to be condensed matter physics. Our primary contributions are summarized as follows: 1) Proposal of systematic error/runtime analysis on state-of-the-art classical algorithm based on tensor networks;2) Dedicated and high-resolution analysis on quantum resource performed at the level of executable logical instructions;3) Clarification of quantum-classical crosspoint for ground-state simulation to be within runtime of hours using only a few hundreds of thousand physical qubits for 2d Heisenberg and 2d Fermi-Hubbard models, assuming that logical qubits are encoded via the surface code with the physical error rate of p = 10−3. To our knowledge, we argue that condensed matter problems offer the earliest platform for demonstration of practical quantum advantage that is order-of-magnitude more feasible than ever known candidates, in terms of both qubit counts and total runtime. Copyright © 2022, The Authors. All rights reserved.

关键词： Condensed matter physics

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Dual-GSE: Resource-efficient Generalized Quantum Subspace Expansion

arXiv

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arXiv 2023年

作者： Yang, Bo Yoshioka, Nobuyuki Harada, Hiroyuki Hakkaku, Shigeo Tokunaga, Yuuki Hakoshima, Hideaki Yamamoto, Kaoru Endo, Suguru 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 Department of Applied Physics School of Engineering 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 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 Center for Quantum Information and Quantum Biology Osaka University 1-3 Machikaneyama Toyonaka Osaka560-8531 Japan

There are considerable obstacles against realizing practical quantum computing: a significant amount of computation errors and the restricted qubit count. As a unified method of noise-agnostic quantum error mitigation (QEM) methods, i.e., the quantum subspace expansion and virtual purification, a generalized quantum subspace expansion (GSE) has recently been proposed that is significantly robust against stochastic and coherent errors. However, GSE requires entangled measurements between copies of the quantum states, which is a significant drawback under the current situation of the restricted number of qubits and their connectivity. In this work, we propose a resource-efficient implementation of GSE, which we name "Dual-GSE", circumventing significant overheads of state copies by constructing an ansatz of error-mitigated quantum states via dual-state purification. Remarkably, Dual-GSE can further simulate larger quantum systems beyond the size of available quantum hardware with a suitable ansatz construction inspired by divide-and-conquer methods that forge entanglement classically. This also significantly reduces the measurement overhead because we only need to measure subsystems’ Pauli operators. The proposed method is demonstrated by a numerical simulation of the eight-qubit transverse-field Ising model, showing that our method estimates the ground state energy with high precision under gate noise with low mitigation overhead and practical sampling cost. Copyright © 2023, The Authors. All rights reserved.

关键词： Ground state

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Quantum circuits for exact unitary t-designs and applications to higher-order randomized benchmarking

arXiv

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arXiv 2021年

作者： Nakata, Yoshifumi Zhao, Da Okuda, Takayuki Bannai, Eiichi Suzuki, Yasunari Tamiya, Shiro Heya, Kentaro Yan, Zhiguang Zuo, Kun Tamate, Shuhei Tabuchi, Yutaka Nakamura, Yasunobu Photon Science Center Graduate School of Engineering University of Tokyo Bunkyo-ku Tokyo113–8656 Japan JST PRESTO 4–1–8 Honcho Kawaguchi Saitama332–0012 Japan School of Mathematical Sciences Shanghai Jiao Tong University Shanghai400240 China Department of Mathematics Hiroshima University 1-3-1 Kagamiyama Higashihiroshima739-8562 Japan Fukuoka819-0385 Japan Mathematics Division National Center for Theoretical Sciences National Taiwan University Taipei10617 Taiwan NTT Computer and Data Science Laboratories NTT Corporation Musashino180-8585 Japan Department of Applied Physics Graduate School of Engineering University of Tokyo 7-3-1 Hongo Bynkyo-ku Tokyo113-8656 Japan University of Tokyo Meguro-ku Tokyo153-8904 Japan Wako Saitama351-0198 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 for the first time 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 t-th 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 new 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. © 2021, CC BY.

关键词： Benchmarking

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