Random quantum circuits are commonly viewed as hard to simulate classically. In some regimes this has been formally conjectured, and there had been no evidence against the more general possibility that for circuits with uniformly random gates, approximate simulation of typical instances is almost as hard as exact simulation. We prove that this is not the case by exhibiting a shallow circuit family with uniformly random gates that cannot be efficiently classically simulated near-exactly under standard hardness assumptions, but can be simulated approximately for all but a superpolynomially small fraction of circuit instances in time linear in the number of qubits and gates. We furthermore conjecture that sufficiently shallow random circuits are efficiently simulable more generally. To this end, we propose and analyze two simulation algorithms. Implementing one of our algorithms numerically, we give strong evidence that it is efficient both asymptotically and, in some cases, in practice. To argue analytically for efficiency, we reduce the simulation of 2D shallow random circuits to the simulation of a form of 1D dynamics consisting of alternating rounds of random local unitaries and weak measurements -- a type of process that has generally been observed to undergo a phase transition from an efficient-to-simulate regime to an inefficient-to-simulate regime as measurement strength is varied. Using a mapping from quantum circuits to statistical mechanical models, we give evidence that a similar computational phase transition occurs for our algorithms as parameters of the circuit architecture like the local Hilbert space dimension and circuit depth are varied.
The Power of Shallow-depth Toffoli and Qudit Quantum Circuits
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；School of Informatics, University of Edinburgh（爱丁堡大学信息学院）；International Iberian Nanotechnology Laboratory（伊比利亚纳米技术国际实验室）
An unconditional distribution learning advantage with shallow quantum circuits
Technische Universität Berlin（柏林工业大学）；Freie Universität Berlin（柏林自由大学）；Fraunhofer Heinrich Hertz Institute（弗劳恩霍夫海因里希·赫兹研究所）；Helmholtz-Zentrum Berlin für Materialien und Energie（亥姆霍兹柏林材料与能源研究中心）
Sample-efficient benchmarking of shallow all-to-all random quantum circuits
The College of William & Mary（威廉玛丽学院）；The University of Chicago（芝加哥大学）；Joint Center for Quantum Information and Computer Science, University of Maryland and NIST（马里兰大学和NIST联合量子信息与计算中心）；University of Waterloo（滑铁卢大学）
Conditional dependence and Scrooge ensembles in shallow random quantum circuits
University of Waterloo（滑铁卢大学）；TCM Group, Cavendish Laboratory, University of Cambridge（剑桥大学卡文迪许实验室 TCM 组）；Walter Burke Institute for Theoretical Physics and Institute for Quantum Information and Matter, California Institute of Technology（加州理工学院理论物理沃尔特·伯克研究所与量子信息物质研究所）；Google Quantum AI（谷歌量子人工智能）；Perimeter Institute for Theoretical Physics（理论物理珀米特研究所）
California Institute of Technology（加州理工学院）；Massachusetts Institute of Technology（麻省理工学院）；Google Quantum AI（谷歌量子人工智能团队）；University of California, Berkeley（加州大学伯克利分校）；University of California, Davis（加州大学戴维斯分校）；Harvard University（哈佛大学）
Entanglement scaling in matrix product state representation of smooth functions and their shallow quantum circuit approximations
Haiqu, Inc.（海奎公司）；Akhiezer Institute for Theoretical Physics, NSC KIPT（阿赫伊泽尔理论物理研究所，国家核子研究中心基辅物理技术研究所）；V.N. Karazin Kharkiv National University（V.N.卡拉金哈尔科夫国立大学）；HSBC Lab, Emerging Technologies, Innovation & Ventures（汇丰实验室，新兴技术、创新与风险投资部门）；Faculty of Electrical Engineering, Czech Technical University in Prague（捷克布拉格工业大学电气工程学院）；Archimedes Research Unit on AI, Data Science and Algorithms, Athena Research Center（雅典娜研究中心人工智能、数据科学与算法研究组）；HSBC Service Delivery Sp. z o.o.（汇丰服务交付有限公司）；Department of Physics, University of Zürich（苏黎世大学物理系）
Ensemble-learning error mitigation for variational quantum shallow-circuit classifiers
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科技大学基础与前沿研究院）；The Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology（香港科技大学电子与计算机工程学系）；Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生院）
Noise-induced shallow circuits and absence of barren plateaus
Freie Universität Berlin（柏林自由大学）；Sorbonne Université（索邦大学）；Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；University of Chicago（芝加哥大学）；Fraunhofer Heinrich Hertz Institute（弗劳恩霍夫海因里希赫兹研究所）；University of Copenhagen（哥本哈根大学）；Massachusetts Institute of Technology（麻省理工学院）
