Quantum error correction (QEC) for generic errors is challenging due to the demanding threshold and resource requirements. Interestingly, when physical noise is biased, we can tailor our QEC schemes to the noise to improve performance. Here we study a family of codes having XZZX-type stabilizer generators, including a set of cyclic codes generalized from the five-qubit code and a set of topological codes that we call generalized toric codes (GTCs). We show that these XZZX codes are highly qubit efficient if tailored to biased noise. To characterize the code performance, we use the notion of effective distance, which generalizes code distance to the case of biased noise and constitutes a proxy for the logical failure rate. We find that the XZZX codes can achieve a favorable resource scaling by this metric under biased noise. We also show that the XZZX codes have remarkably high thresholds that reach what is achievable by random codes, and furthermore they can be efficiently decoded using matching decoders. Finally, by adding only one flag qubit, the XZZX codes can realize fault-tolerant QEC while preserving their large effective distance. In combination, our results show that tailored XZZX codes give a resource-efficient scheme for fault-tolerant QEC against biased noise.
Quantum non-demolition measurements as a practical primitive for fault-tolerant computation against biased noise
Alice & Bob（爱丽丝与鲍勃公司）；Laboratoire de Physique de l’École Normale Supérieure, École Normale Supérieure, Centre Automatique et Systèmes, Mines Paris, Université PSL, CNRS, Inria（巴黎高等师范学院物理实验室，巴黎高等师范学院，自动系统与矿业学院，巴黎高等矿业学院，PSL大学，法国国家科学研究中心，法国国家信息与自动化研究所）
Duke Quantum Center, Duke University（杜克大学量子中心）；Department of Physics, Duke University（杜克大学物理系）；Department of Electrical and Computer Engineering, Duke University（杜克大学电气与计算机工程系）；Department of Chemistry, Duke University（杜克大学化学系）
Surface-Code Thresholds and Qubit Footprints in Shuttling-Based Spin-Qubit Railways
Donostia International Physics Center（多诺斯蒂亚国际物理中心）；Department of Basic Sciences, Tecnun - University of Navarra（纳瓦拉大学特库恩基础科学系）；Research and Development Group, Hitachi, Ltd.（日立有限公司研发集团）；Hitachi Cambridge Laboratory（日立剑桥实验室）
Hardware-Tailored Resource Estimation for Magic-State Distillation on Silicon Spin Qubits
Cavendish Lab., Department of Physics, Univ. of Cambridge（剑桥大学卡文迪什实验室物理系）；Hitachi Cambridge Lab.（日立剑桥实验室）；Department of Computer Science and Technology, Univ. of Cambridge（剑桥大学计算机科学与技术系）
Discovery of Optimal Quantum Error Correcting Codes via Reinforcement Learning
Center for Theoretical Physics & Department of Physics, University of California, Berkeley, CA 94720, USA（加州大学伯克利分校理论物理中心及物理系）；Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD, 20742, USA（马里兰大学量子信息与计算机科学联合中心）；Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, 91125, USA（加州理工学院量子信息与物质研究所）；Department of Physics, Virginia Tech, Blacksburg, VA, 24060, USA（弗吉尼亚理工学院物理系）；Department of Physics, University of California San Diego, La Jolla, CA 92093, USA（加州大学圣地亚哥分校物理系）；Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA（哈佛大学物理系）；Harvard Quantum Initiative, Harvard University, 17 Oxford Street, Cambridge, MA 02138, USA（哈佛大学量子倡议）；Laboratory for Physical Sciences, 8050 Greenmead Dr., College Park, MD 20740, USA（物理科学实验室）；Department of Physics, Brandeis University, Waltham, Massachusetts 02453, USA（布兰迪大学物理系）
Dynamical Decoupling of Nonclassical States in a Biased-Noise Spin Qudit
School of Electrical Engineering and Telecommunications, UNSW Sydney（新南威尔士大学电气与电信工程学院）；HPE Quantum, Emergent Machine Intelligence, Hewlett Packard Labs（惠普实验室）；Quantum Artificial Intelligence Laboratory (QuAIL), NASA Ames Research Center（NASA艾姆斯研究中心量子人工智能实验室）；KBR, Inc.（KBR公司）；ARC Centre of Excellence for Quantum Computer Performance & Integration (QPI)（量子计算机性能与集成卓越中心）；School of Engineering, RMIT University（皇家墨尔本理工大学工程学院）；USRA Research Institute for Advanced Computer Science（美国大学空间研究协会高级计算机科学研究所）
