Quantum error correction allows to actively correct errors occurring in a quantum computation when the noise is weak enough. To make this error correction competitive information about the specific noise is required. Traditionally, this information is obtained by benchmarking the device before operation. We address the question of what can be learned from only the measurements done during decoding. Such estimation of noise models was proposed for surface codes, exploiting their special structure, and in the limit of low error rates also for other codes. However, so far it has been unclear under what general conditions noise models can be estimated from the syndrome measurements. In this work, we derive a general condition for identifiability of the error rates. For general stabilizer codes, we prove identifiability under the assumption that the rates are small enough. Without this assumption we prove a result for perfect codes. Finally, we propose a practical estimation method with linear runtime for concatenated codes. We demonstrate that it outperforms other recently proposed methods and that the estimation is optimal in the sense that it reaches the Cramér-Rao Bound. Our method paves the way for practical calibration of error corrected quantum devices during operation.
QMCtwin: Master-Equation Simulation of Syndrome Statistics Beyond Pauli Noise
University of Southern California（南加州大学）；Center for Quantum Information Science & Technology, University of Southern California（南加州大学量子科学与技术中心）；Quantum Elements, Inc.（量子元素公司）；Harvard University（哈佛大学）；AWS Worldwide Specialist Organization（亚马逊云科技全球专家组织）
Logical error estimation from syndrome data of surface-code experiments
Duke Quantum Center, Duke University（杜克量子中心，杜克大学）；Department of Electrical and Computer Engineering, Duke University（电气与计算机工程系，杜克大学）；Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid（马德里自治大学-西班牙国家科研委员会理论物理研究所，马德里自治大学）；Department of Electrical & Computer Engineering, University of Southern California（电气与计算机工程系，南加州大学）；Center for Quantum Information Science & Technology, University of Southern California（量子信息与科技中心，南加州大学）；Quantum Elements, Inc.（量子元素公司）；Department of Physics & Astronomy, University of Southern California（物理与天文学系，南加州大学）；Department of Chemistry, University of Southern California（化学系，南加州大学）；Department of Physics, Duke University（物理系，杜克大学）；Department of Chemistry, Duke University（化学系，杜克大学）
Error Mitigation From a Single Unmodified Error-Corrected Circuit
Qedma Quantum Computing（Qedma量子计算）；The Benin School of Computer Science and Engineering, Hebrew University（希伯来大学本计算机科学与工程学院）；Faculty of Mathematics and Computer Science, Weizmann Institute of Science（魏茨曼科学研究所数学与计算机科学系）；Department of Physics, Technion（以色列理工学院物理系）
Differentiable Maximum Likelihood Noise Estimation for Quantum Error Correction
Singapore University of Technology and Design（新加坡科技设计大学）；CAS Key Laboratory for Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
Qedma Quantum Computing（Qedma 量子计算）；The Benin School of Computer Science and Engineering, Hebrew University（希伯来大学本因计算机科学与工程学院）；Faculty of Mathematics and Computer Science, Weizmann Institute of Science（魏茨曼科学研究所数学与计算机科学系）；Department of Physics, Technion（以色列理工学院物理系）
In-situ benchmarking of fault-tolerant quantum circuits. I. Clifford circuits
Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（量子信息与计算机联合中心，美国国家标准与技术研究院/马里兰大学）；Simons Institute for the Theory of Computing, University of California at Berkeley（西蒙斯计算理论研究所，加州大学伯克利分校）；Institute for Theoretical Physics, ETH Zürich（理论物理研究所，苏黎世联邦理工学院）；Department of Physics, Harvard University（物理学系，哈佛大学）；National Institute of Standards and Technology（美国国家标准与技术研究院）
Iterative Decoding of Stabilizer Codes under Radiation-Induced Correlated Noise
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Brookhaven National Laboratory（布鲁克海文国家实验室）；Tufts University（塔夫茨大学）；Texas A&M University（德克萨斯农工大学）；Stony Brook University（石溪大学）
Adaptive decoding of quantum LDPC codes through decoder disagreement
Centre for Computational Science, University College London（计算科学中心，伦敦大学学院）；Advanced Research Computing Centre, University College London（高级研究计算中心，伦敦大学学院）
Fusion-assisted decoding of non-Abelian topological order
Harvard University（哈佛大学）；Purdue University（普渡大学）；New York University（纽约大学）；State University of New York at Stony Brook（纽约州立大学石溪分校）；University of Oklahoma（俄克拉荷马大学）；NIST/University of Maryland（美国国家标准与技术研究院/马里兰大学）；University of British Columbia（不列颠哥伦比亚大学）
DGR: Tackling Drifted and Correlated Noise in Quantum Error Correction via Decoding Graph Re-weighting
Massachusetts Institute of Technology（麻省理工学院）；Carnegie Mellon University（卡内基梅隆大学）；Cornell University（康奈尔大学）；Arizona State University（亚利桑那州立大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of Chicago（芝加哥大学）
Maximum Likelihood Decoding of Quantum Error Correction Codes
Science, Mathematics and Technology Cluster, Singapore University of Technology and Design（新加坡科技设计大学科技、数学与技术集群）；College of Computing and Data Science, Nanyang Technological University（南洋理工大学计算机与数据科学学院）；School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学科学学院）
