F. Pastawski和J. Preskill讨论了基于奇偶校验编码自旋系统（称为Sourlas-Lechner-Hauke-Zoller (SLHZ)系统）的量子退火（QA）纠错。他们指出，SLHZ系统与经典低密度奇偶校验（LDPC）码密切相关，并通过假设独立随机自旋翻转错误的置信传播（BP）算法证明了其纠错能力。相反，Ablash等人认为SLHZ系统并未从读出后解码中获益。原因在于，无论是在封闭还是开放系统情况下，独立随机自旋翻转并不是退火过程中对激发态进行采样时产生的最相关错误。在这项工作中，我们重新审视了这个问题：我们提出了一种非常简单的解码算法来消除SLHZ系统读出中的错误，并展示了表明SLHZ系统在解码退火读出时具有纠错能力的实验证据。我们的新算法可以看作是LDPC码的比特翻转算法。假设独立同分布的噪声模型，我们发现我们的算法性能与BP算法相当。我们使用模拟QA最终时间分布的Monte Carlo计算研究了采样读出的纠错能力。结果表明，在没有采样到无错误状态甚至码字状态的情况下，该算法成功消除了采样读出中的错误。我们的模拟表明，如果退火能够采样到可纠正状态，那么退火读出的解码将会成功，并且退火可以被认为扮演了经典解码过程的前处理角色。这一知识对于在不久的将来设计和开发基于SLHZ系统的实用QA将是有用的。
英文摘要：
F. Pastawski and J. Preskill discussed error correction of quantum annealing (QA) based on a parity-encoded spin system, known as the Sourlas-Lechner-Hauke-Zoller (SLHZ) system. They pointed out that the SLHZ system is closely related to a classical low-density parity-check (LDPC) code and demonstrated its error-correcting capability through a belief propagation (BP) algorithm assuming independent random spin-flip errors. In contrast, Ablash et al. suggested that the SLHZ system does not receive the benefits of post-readout decoding. The reason is that independent random spin-flips are not the most relevant error arising from sampling excited states during the annealing process, whether in closed or open system cases. In this work, we revisit this issue: we propose a very simple decoding algorithm to eliminate errors in the readout of SLHZ systems and show experimental evidence suggesting that SLHZ system exhibits error-correcting capability in decoding annealing readouts. Our new algorithm can be thought of as a bit-flipping algorithm for LDPC codes. Assuming an independent and identical noise model, we found that the performance of our algorithm is comparable to that of the BP algorithm. The error correcting-capability for the sampled readouts was investigated using Monte Carlo calculations that simulate the final time distribution of QA. The results show that the algorithm successfully eliminates errors in the sampled readouts under conditions where error-free state or even code state is not sampled at all. Our simulation suggests that decoding of annealing readouts will be successful if the correctable states can be sampled by annealing, and annealing can be considered to play a role as a pre-process of the classical decoding process. This knowledge will be useful for designing and developing practical QA based on the SLHZ system in the near future.
Practical hybrid decoding scheme for parity-encoded spin systems
NEC-AIST Quantum Technology Cooperative Research Laboratory（NEC-AIST量子技术联合研究实验室）；National Institute of Advanced Industrial Science and Technology（产业技术综合研究所）
Solving Differential Equations Using Continuous-Variable Quantum Annealing
Chuo University（中央大学）；The University of Tokyo（东京大学）；Ochanomizu University（御茶水女子大学）；National Institute of Advanced Industrial Science and Technology（产业技术综合研究所）
Benchmarking simulation of hybrid decoding scheme for parity-encoded spin systems
NEC-AIST Quantum Technology Cooperative Research Laboratory（NEC-AIST量子技术联合研究实验室）；National Institute of Advanced Industrial Science and Technology（国立产业技术综合研究所）
Continuous black-box optimization with quantum annealing and random subspace coding
The University of Tokyo（东京大学）；Keio University（庆应义塾大学）；Waseda University（早稻田大学）；National Institute for Materials Science（国立材料科学研究所）；RIKEN Center for Advanced Intelligence Project（理化学研究所革新智能研究中心）
QAMA: Scalable Quantum Annealing Multi-Head Attention Operator for Deep Learning
School of Electronic Information, Central South University（中南大学电子信息学院）；School of Computer Science and Engineering, Central South University（中南大学计算机科学与工程学院）；Beijing QBoson Quantum Technology Co. Ltd.（北京QBoson量子科技有限公司）；Institute of Artificial Intelligence (TeleAI) of China Telecom（中国电信人工智能研究院（TeleAI））
Enhanced analogue quantum computation with a logically-encoded XX gadget
University College London（伦敦大学学院）；Indian Institute of Technology, Bhubaneswar（布巴内斯瓦尔印度理工学院）；Jülich Supercomputing Centre, Institute for Advanced Simulation, Forschungszentrum Jülich（于利希超级计算中心，先进模拟研究所，于利希研究中心）；Universität zu Köln（科隆大学）
Exclusive-or encoded algebraic structure for efficient quantum dynamics
University of Hamburg（汉堡大学）；Center for Optical Quantum Technologies, University of Hamburg（汉堡大学光学量子技术中心）；Institute for Quantum Physics, University of Hamburg（汉堡大学量子物理研究所）；The Hamburg Center for Ultrafast Imaging（汉堡超快成像中心）
