We introduce a new primitive, called welding, for combining two stabilizer codes to produce a new stabilizer code. We apply welding to construct surface codes and then use the surface codes to construct solid codes, a variant of a 3-d toric code with rough and smooth boundaries. Finally, we weld solid codes together to produce a $(O(L^3),1,O(L^{4/3}))$ stabilizer code with an energy barrier of $O(L^{2/3})$, which solves an open problem of whether a power law energy barrier is possible for local stabilizer code Hamiltonians in three-dimensions. The previous highest energy barrier is $O(\log L)$. Previous no-go results are avoided by breaking translation invariance.
Entanglement of superpositions in zero-energy subspace: insights from stabilizer theory
Faculty of Physics, M.V. Lomonosov Moscow State University（莫斯科国立大学物理系）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；Artificial Intelligence Research Institute (AIRI)（人工智能研究院）
Invariant Measures and Weak-Magic-Injection Asymptotics in Random Monitored Quantum Circuits
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；QudeLeap Research（酷跃研究）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area（粤港澳大湾区量子科学中心）
Post-Quantum Cryptography from Quantum Stabilizer Decoding
Massachusetts Institute of Technology（麻省理工学院）；Boston University（波士顿大学）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；California Institute of Technology（加州理工学院）
Neural Quantum States in Non-Stabilizer Regimes: Benchmarks with Atomic Nuclei
Universität Bielefeld（比勒费尔德大学）；Argonne National Laboratory（阿贡国家实验室）；INFN-TIFPA Trento Institute for Fundamental Physics and Applications（特伦托基础物理与应用研究所）；GSI Helmholtzzentrum für Schwerionenforschung（重离子研究中心）
Binary Gauss Stabilizers for Abelian Lattice Gauge Theories
Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院）；PQI – Portuguese Quantum Institute（葡萄牙量子研究所）；Centro de Física e Engenharia de Materiais Avançados (CeFEMA)（先进材料与工程物理中心）；University of Trento（特伦托大学）；INFN-TIFPA Trento Institute of Fundamental Physics and Applications（特伦托基础物理与应用研究所）
Quantum advantage unlocked: Charging quantum batteries with K-regular graph stabilizers
Harish-Chandra Research Institute（哈立什-昌德拉研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Mark Kac Complex Systems Research Center, Jagiellonian University in Kraków（雅盖隆大学马克·卡克复杂系统研究中心）；Dipartimento di Fisica e Astronomia, Università di Padova（帕多瓦大学物理与天文学系）；Department of Physics, Indian Institute of Technology Palakkad（印度理工学院帕拉卡德分校物理系）
Entanglement Barriers from Computational Complexity: Matrix-Product-State Approach to Satisfiability
Technische Universität Dresden（德累斯顿工业大学）；Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Max Planck Institute for the Physics of Complex Systems（马普复杂系统物理研究所）
Layer codes as partially self-correcting quantum memories
Yale Quantum Institute & Department of Applied Physics, Yale University（耶鲁大学应用物理系与耶鲁量子研究所）；School of Computation, Information and Technology, Technical University of Munich（慕尼黑工业大学计算、信息与技术学院）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）；IQM Quantum Computers（IQM量子计算机公司）；Department of Mathematics, Massachusetts Institute of Technology（麻省理工学院数学系）；Departments of Mathematics & Physics, Northeastern University（东北大学数学与物理系）
Nonstabilizerness of quantum tensor network states is intractable in two dimensions
Scuola Superiore Meridionale（南方高等学院）；Istituto Nazionale di Fisica Nucleare, Sezione di Napoli（意大利国家核物理研究所那不勒斯分部）；Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与工程中心）
Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与工程中心）；Department of Physics, Duke University（杜克大学物理系）；Institut für Theoretische Physik, Universität Regensburg（雷根斯堡大学理论物理研究所）；Department of Physics, National Taiwan University（台湾大学物理系）；Department of Physics and Arnold Sommerfeld Center for Theoretical Physics (ASC), Ludwig Maximilian University of Munich（慕尼黑大学物理系与阿诺德·索末菲理论物理中心）；InQubator for Quantum Simulation, Department of Physics, University of Washington（华盛顿大学物理系量子模拟创新中心）
Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom
