Exact spectral gaps of random one-dimensional quantum circuits
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；Department of Applied Physics, Gipuzkoa School of Engineering, University of the Basque Country (UPV/EHU)（巴斯克国立大学吉普斯夸工程学院应用物理系）；Theoretical Division, Los Alamos National Laboratory（洛斯阿拉莫斯国家理论部）；Quantum Science Center, Oak Ridge, TN 37931, USA（橡树岭量子科学中心）
Andrew E. Deneris, Pablo Bermejo, Paolo Braccia, Lukasz Cincio, M. Cerezo
备注：
10 + 6 pages, 3 figures, updated to published version
The spectral gap of local random quantum circuits is a fundamental property that determines how close the moments of the circuit's unitaries match those of a Haar random distribution. When studying spectral gaps, it is common to bound these quantities using tools from statistical mechanics or via quantum information-based inequalities. By focusing on the second moment of one-dimensional unitary circuits where nearest neighboring gates act on sets of qudits (with open and closed boundary conditions), we show that one can exactly compute the associated spectral gaps. Indeed, having access to their functional form allows us to prove several important results, such as the fact that the spectral gap for closed boundary condition is exactly the square of the gap for open boundaries, as well as improve on previously known bounds for approximate design convergence. Finally, we verify our theoretical results by numerically computing the spectral gap for systems of up to 70 qubits, as well as comparing them to gaps of random orthogonal and symplectic circuits.
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Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学与物理学院）；Institute of Mathematics, Physics and Mechanics（数学、物理和力学研究所）；Department of Physics, University of Wuppertal（伍珀塔尔大学物理系）
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Lomonosov Moscow State University（莫斯科国立大学）；University of Science and Technology of China（中国科学技术大学）；Peking University（北京大学）；Southern University of Science and Technology（南方科技大学）
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Key Laboratory of System Software (Chinese Academy of Sciences), Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所系统软件重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）；Beijing Zhongke Arclight Quantum Computing Technology Co., Ltd.（北京中科极光量子计算技术有限公司）；Nanjing Tech University（南京工业大学）；Taizhou University（台州学院）；Ningbo University（宁波大学）
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Computing band gaps of periodic materials via sample-based quantum diagonalization
IBM Research（IBM研究院）；Instituto de Física, Universidade Federal Fluminense（弗鲁米嫩塞联邦大学物理研究所）；Centro Brasileiro de Pesquisas Físicas（巴西物理研究中心）；IBM Research Europe（IBM欧洲研究院）；National Center for Competence in Research-Catalysis (NCCR-Catalysis)（国家卓越研究中心-催化）；IBM Quantum, IBM T.J. Watson Research Center（IBM量子，IBM T.J.沃森研究中心）
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