Stabilizer states, which are also known as the Clifford states, have been commonly utilized in quantum information, quantum error correction, and quantum circuit simulation due to their simple mathematical structure. In this work, we apply stabilizer states to tackle quantum many-body ground state problems and introduce the concept of stabilizer ground states. We establish an equivalence formalism for identifying stabilizer ground states of general Pauli Hamiltonians. Moreover, we develop an exact and linear-scaled algorithm to obtain stabilizer ground states of 1D local Hamiltonians and thus free from discrete optimization. This proposed equivalence formalism and linear-scaled algorithm are not only applicable to finite-size systems, but also adaptable to infinite periodic systems. The scalability and efficiency of the algorithms are numerically benchmarked on different Hamiltonians. Finally, we demonstrate that stabilizer ground states are promising tools for not only qualitative understanding of quantum systems, but also cornerstones of more advanced classical or quantum algorithms.
Selected Stabilizer Subspaces for Compact Many-Body Wave Functions
Yusuf Hamied Department of Chemistry, University of Cambridge（剑桥大学尤素夫·哈米德化学系）；Department of Physics and Thomas Young Centre, King’s College London（伦敦国王学院物理系及托马斯·杨中心）
Simulating general noise nearly as cheaply as Pauli noise
National University of Singapore（新加坡国立大学）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；University of Chicago（芝加哥大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Entropica Labs（熵实验室）；Department of Physics, National University of Singapore（新加坡国立大学物理系）
MPStab: an hybrid stabilizers tensor-network quantum circuit simulator
University of Trieste（的里雅斯特大学）；Istituto Nazionale di Fisica Nucleare, Trieste Section（意大利国家核物理研究所的里雅斯特分部）；University of Helsinki（赫尔辛基大学）；European Organization for Nuclear Research (CERN)（欧洲核子研究组织（日内瓦））；Chalmers University of Technology（查尔姆斯理工大学）
Non-stabilizerness and U(1) symmetry in chaotic many-body quantum systems
Scuola Superiore Meridionale（南方高等学院）；INFN Sezione di Napoli（那不勒斯 INFN 分部）；SISSA（的里雅斯特国际高等研究学校）；INFN Sezione di Trieste（的里雅斯特 INFN 分部）；Dipartimento di Fisica ‘Ettore Pancini’, Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学物理系）
Dismagicker: Unitary Gate for Non-Stabilizerness Reduction
Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院人工结构与量子控制教育部重点实验室）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Hefei National Laboratory（合肥国家实验室）
Phase-sensitive representation of Majorana stabilizer states
Institute of Physical and Theoretical Chemistry, University of Würzburg（维尔茨堡大学物理与理论化学研究所）；Division of Chemistry and Chemical Engineering, California Institute of Technology（加州理工学院化学与化学工程系）
Measurement-free Preparation of Surface-Code States with Digital-Analog Counterdiabatic Drivings
Intelligent Data Analysis Laboratory (IDAL), Departament d’Enginyeria Electrònica, ETSE-UV, Universitat de València（瓦伦西亚大学电子工程系智能数据分析实验室）；Kipu Quantum（基普量子）
Stabilizer Statistical Mechanics: A Framework for Efficient Quantification and Classification of Magic States
LG Electronics Toronto AI Lab（LG电子多伦多人工智能实验室）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, UMI 3654（MajuLab，CNRS-UNS-NUS-NTU国际联合研究单元，UMI 3654）；National Institute of Education, Nanyang Technological University（南洋理工大学国立教育学院）
Stabilizer-based quantum simulation of fermion dynamics with local qubit encodings
IBM Quantum, IBM Research Europe - Zurich（IBM量子，IBM欧洲苏黎世研究中心）；Institute for Theoretical Physics, ETH Zürich（苏黎世联邦理工学院理论物理研究所）；Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所）
Slow growth of quantum magic in disorder-free Stark many-body localization
Institute for Quantum Science and Technology, Shanghai University（上海大学量子科学与技术研究院）；Department of Physics, National University of Singapore（新加坡国立大学物理系）；School of Physics and Optoelectronics, Xiangtan University（湘潭大学物理与光电工程学院）
Many-body chirality of topological stabilizer states
Purdue University（普渡大学）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；University of Waterloo（滑铁卢大学）；IBM Quantum, T.J. Watson Research Center（IBM量子，T.J.沃森研究中心）；University of Toronto（多伦多大学）
