Gauging a global symmetry of a system amounts to introducing new degrees of freedom whose transformation rule makes the overall system observe a local symmetry. In quantum systems there can be obstructions to gauging a global symmetry. When this happens the symmetry is dubbed anomalous. Such obstructions are related to the fact that the global symmetry cannot be written as a tensor product of local operators. In this manuscript we study non-local symmetries that have an additional structure: they take the form of a matrix product operator (MPO). We exploit the tensor network structure of the MPOs to construct local operators from them satisfying the same group relations, that is, we are able to localize even anomalous MPOs. For non-anomalous MPOs, we use these local operators to explicitly gauge the MPO symmetry of a one-dimensional quantum state obtaining non-trivial gauged states. We show that our gauging procedure satisfies all the desired properties as the standard on-site case does. We also show how this procedure is naturally represented in matrix product states protected by MPO symmetries. In the case of anomalous MPOs, we shed light on the obstructions to gauging these symmetries.
Gauging Modulated Symmetries via Multiple Gauge Symmetry Operators and Adaptive Quantum Circuits
Sungkyunkwan University（成均馆大学）；Institute of Basic Science, Sungkyunkwan University（成均馆大学基础科学研究院）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Symmetry defects and gauging for quantum states with matrix product unitary symmetries
Max-Planck-Institut für Quantenoptik（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）；University of Vienna, Faculty of Physics（维也纳大学物理学院）
There and Back Again: A Gauging Nexus between Topological and Fracton Phases
University of Chicago（芝加哥大学）；Princeton University（普林斯顿大学）；Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；Bard College（巴德学院）；Institute for Advanced Study（高等研究院）；Stony Brook University（石溪大学）；California Institute of Technology（加州理工学院）；The University of Sydney（悉尼大学）
The City College of the CUNY（纽约市立学院）；The Graduate School and University Center, The City University of New York（纽约市立大学研究生院与大学中心）；Universidad de Oviedo（奥维耶多大学）；Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA)（阿斯图里亚斯空间科学与技术大学研究所）
Lattice 2-group symmetries: operators, defects, and gauging
Department of Physics, Harvard University（哈佛大学物理系）；Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系）；School of Natural Sciences, Institute for Advanced Study（高等研究院自然科学学院）
Type-IV 't Hooft Anomalies on the Lattice: Emergent Higher-Categorical Symmetries and Applications to LSM Systems
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS) RIKEN（理化学研究所交叉理论与数学科学项目）
Symmetry protected quantum many body scars through half-gauging
Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；National Tsing Hua University（国立清华大学）；National Center for Theoretical Sciences（国家理论科学中心）；Academia Sinica（中央研究院）
Non-Abelian qLDPC: TQFT Formalism, Addressable Gauging Measurement and Application to Magic State Fountain on 2D Product Codes
IBM Quantum, IBM T.J. Watson Research Center（IBM量子，IBM托马斯·J·沃森研究中心）；School of Natural Sciences, Institute for Advanced Study（自然科学院，高等研究院）；Department of Mathematics, King’s College London（数学系，伦敦国王学院）
(2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
Mathematical Institute, University of Oxford（牛津大学数学研究所）；Rudolf Peierls Centre for Theoretical Physics, University of Oxford（牛津大学鲁道夫·派尔斯理论物理中心）；Center for Quantum Mathematics at IMADA, Southern Denmark University（南丹麦大学IMADA量子数学中心）
