Quantum error correction suppresses noise in quantum systems to allow for high-precision computations. In this work, we introduce Multivariate Bicycle (MB) Quantum Low-Density Parity-Check (QLDPC) codes, via an extension of the framework developed by Bravyi et al. [Nature, 627, 778-782 (2024)] and particularly focus on Trivariate Bicycle (TB) codes. Unlike the weight-6 codes proposed in their study, we offer concrete examples of weight-5 TB-QLDPC codes which promise to be more amenable to near-term experimental setups. We show that TB-QLDPC codes up to weight-6 have a bi-planar structure and often posses a two-dimensional toric layout. Under circuit level noise, we find substantially better encoding rates than comparable surface codes while offering similar error suppression capabilities. For example, we can encode $4$ logical qubits with distance $5$ into $60$ physical qubits using weight-5 check measurements of circuit depth 7, while a surface code with these parameters requires $200$ physical qubits. The high encoding rate and compact layout make our codes highly suitable candidates for near-term hardware implementations, paving the way for a realizable quantum error correction protocol.
Yale University（耶鲁大学）；Yale Quantum Institute, Yale University（耶鲁量子研究所，耶鲁大学）；IBM Quantum, T. J. Watson Research Center（IBM 量子，T.J.沃森研究中心）；School of Physics, University of Sydney（悉尼大学物理学院）；IBM Quantum, IBM Almaden Research Center（IBM 量子，IBM阿尔马登研究中心）；IBM Denmark（IBM丹麦）
Towards self-correcting quantum codes for neutral atom arrays
Department of Physics, University of Colorado, Boulder（科罗拉多大学博尔德分校物理系）；Center for Theory of Quantum Matter, University of Colorado, Boulder（科罗拉多大学博尔德分校量子物质理论中心）；Joint Quantum Institute & Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park（马里兰大学帕克分校与国家标准与技术研究院联合量子研究所及联合量子信息与计算科学中心）；JILA, University of Colorado and National Institute of Standards and Technology, Boulder（科罗拉多大学与国家标准与技术研究院联合JILA实验室）
Machine Learning Decoding of Circuit-Level Noise for Bivariate Bicycle Codes
Massachusetts Institute of Technology（麻省理工学院）；Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系）；Department of Mathematics, Massachusetts Institute of Technology（麻省理工学院数学系）；Physics & Informatics Laboratories, NTT Research（NTT研究院物理与信息实验室）
Multivariate Multicycle Codes for Complete Single-Shot Decoding
Manning College of Information and Computer Sciences, University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校曼宁信息与计算机科学学院）；Department of Mathematics and Statistics, University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校数学与统计系）；Department of Physics, University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校物理系）
University of California, Riverside（加州大学河滨分校）；Google Quantum AI（谷歌量子人工智能）；Department of Physics & Astronomy, University of California, Riverside（加州大学河滨分校物理与天文学系）
Metachecks in Bivariate Bicycle Codes: Syndrome Distance, Measurement Faults, and Repair Limits
Centre for Quantum Software and Information (QSI), School of Computer Science, University of Technology Sydney（悉尼科技大学计算机科学学院量子软件与信息中心）；School of Electrical Engineering and Telecommunications, University of New South Wales (UNSW)（新南威尔士大学电气与电信学院）
Breaking the bicycle frame: Coset-based quantum LDPC codes
University of Maryland, College Park（马里兰大学帕克分校）；Tel Aviv University（特拉维夫大学）；Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park（量子信息与计算机科学联合中心，美国国家标准与技术研究院/马里兰大学帕克分校）
Translation-invariant quantum low-density parity-check codes from compactified fracton models
University of California, Davis（加州大学戴维斯分校）；Joint Center for Quantum Information and Computer Science, NIST/University of Maryland（量子信息与计算科学联合中心，美国国家标准与技术研究院/马里兰大学）；School of Physics, The University of Sydney（悉尼大学物理学院）
Demonstration of low-overhead quantum error correction codes
Zhejiang University（浙江大学）；Shanghai Qi Zhi Institute（上海人工智能实验室）；Tsinghua University（清华大学）；Harvard University（哈佛大学）；Xi'an Jiaotong University（西安交通大学）；Institute of Physics, Polish Academy of Sciences（波兰科学院物理研究所）；Hefei National Laboratory（合肥国家实验室）
