qecGPT: decoding Quantum Error-correcting Codes with Generative Pre-trained Transformers
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）；School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS（中国科学院大学杭州高等研究院基础物理与数学科学学院）；International Centre for Theoretical Physics Asia-Pacific（国际理论物理中心亚太地区）
We propose a general framework for decoding quantum error-correcting codes with generative modeling. The model utilizes autoregressive neural networks, specifically Transformers, to learn the joint probability of logical operators and syndromes. This training is in an unsupervised way, without the need for labeled training data, and is thus referred to as pre-training. After the pre-training, the model can efficiently compute the likelihood of logical operators for any given syndrome, using maximum likelihood decoding. It can directly generate the most-likely logical operators with computational complexity $\mathcal O(2k)$ in the number of logical qubits $k$, which is significantly better than the conventional maximum likelihood decoding algorithms that require $\mathcal O(4^k)$ computation. Based on the pre-trained model, we further propose refinement to achieve more accurately the likelihood of logical operators for a given syndrome by directly sampling the stabilizer operators. We perform numerical experiments on stabilizer codes with small code distances, using both depolarizing error models and error models with correlated noise. The results show that our approach provides significantly better decoding accuracy than the minimum weight perfect matching and belief-propagation-based algorithms. Our framework is general and can be applied to any error model and quantum codes with different topologies such as surface codes and quantum LDPC codes. Furthermore, it leverages the parallelization capabilities of GPUs, enabling simultaneous decoding of a large number of syndromes. Our approach sheds light on the efficient and accurate decoding of quantum error-correcting codes using generative artificial intelligence and modern computational power.
AI-Enabled Decoding of Qubit Loss for Quantum Error-Correcting Codes
Tsinghua University（清华大学）；Intelligent Quantum Inception Co., Ltd.（智量量子创新有限公司）；Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；iFLYTEK Research（科大讯飞研究院）
Optimal Decoder for the Error Correcting Parity Code
Parity Quantum Computing Germany GmbH（Parity量子计算德国有限公司）；Institute for Theoretical Physics, University of Innsbruck（因斯布鲁克大学理论物理研究所）；Parity Quantum Computing GmbH（Parity量子计算有限公司）
Homological Thresholds in Randomly Monitored Quantum Error-Correcting Codes
Institute for Theoretical Physics, University of Cologne（科隆大学理论物理研究所）；Department of Physics, Graduate School of Science, Tohoku University（东北大学理学研究科物理学系）
Simplified circuit-level decoding using Knill error correction
Inria Paris（巴黎国家信息与自动化研究所）；Quandela（夸当德拉）；Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）
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）
Linear-Time Encodable and Decodable Quantum Error-Correcting Codes
Massachusetts Institute of Technology（麻省理工学院）；Hon Hai (Foxconn) Research Institute（鸿海（富士康）研究院）；University of California at San Diego（加州大学圣地亚哥分校）；CSAIL, Massachusetts Institute of Technology（麻省理工学院计算机科学与人工智能实验室）
Quantum Error Correction beyond the Bounded Distance Decoding Limit
在本文中，我们考虑在去极化信道上的量子纠错与非二进制低密度奇偶校验码定义在有限域的大小$2^p$。提出的量子纠错码是基于二进制准循环CSS（Calderbank，Shor and Steane）码。由此产生的量子码优于已知的最好的量子码，并超过了有界距离解码器的性能极限。通过增加底层伽罗瓦域的大小，即，$2^p$，错误平层得到显著改善。
