CIF: Medium: Iterative Quantum LDPC Decoders

量子信息处理系统比传统的数字计算机更容易出错，而纠错对于保护脆弱的量子位不受错误的影响至关重要。量子纠错是量子信息处理所有应用的核心，从容错量子计算到量子密钥分发、量子传感和可靠的光通信中的协调。该项目将通过寻找实现量子纠错所带来的好处的结构化方法，为实际实现可伸缩的量子计算和通信做出贡献。该项目将开发一类新型的纠错码和容错解码器，并将其应用于量子计算、量子通信和网络的体系结构中。该项目将有助于为不断增长的量子产业和国家实验室的量子信息计划培养熟练的量子信息处理劳动力。这项研究是该团队领导的全大学量子工程计划的组成部分，该计划的目标是在亚利桑那大学建立量子信息科学工程研究生课程。这将有助于亚利桑那大学继续努力让代表不足的学生参与研究，他们的教育经验将通过国内和国际合作得到丰富。纠错是量子信息处理所有应用的核心，例如在实现容错量子计算、量子密钥分发中的高效协调和隐私放大、为用于远距离纠缠分发网络的量子中继器构建容错量子存储器，以及达到可靠光通信速率的量子极限。量子低密度奇偶校验(QLDPC)码是目前已知的唯一一类具有渐近非零码率的稳定子量子码，是实现可扩展、容错量子计算的重要组成部分，但目前还缺乏一种有效的QLDPC码的译码方案。在这个项目中，该团队将开发使用经典量子消息的高效和容错解码器，以充分利用QLDPC码的潜力。该方法基于捕获量子译码算法集的概念，允许人们通过组合和图论来表征译码失败。然后，这些关于陷阱集的知识将被用来开发系统解码器设计的框架。由此产生的解码器是一个使用噪声门构建的小型容错量子计算机，其中所有计算都保持在节点上的本地，量子通信跨解码图上最近邻的边进行。该团队将在最近开发的用于可扩展线性光量子计算的体系结构中表征QLDPC码和容错解码器的性能，以及用于远程量子通信的基于编码传输的全光中继器的性能。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Quantum information processing systems are far more susceptible to making errors than conventional digital computers, and error correcting is vital in protecting fragile qubits from errors. Quantum error-correction is at the heart of all applications of quantum information processing, from fault tolerant quantum computing to reconciliation in quantum key distribution, quantum sensing, and reliable optical communications. This project will contribute to the practical realization of scalable quantum computing and communications by finding structured ways of achieving the benefits afforded by quantum error-correction. This project will develop a novel class of error-correction codes and fault-tolerant decoders and apply them in architectures for quantum computing, quantum communications and networks. The project will contribute to the development of workforce skilled in quantum information processing for the growing quantum industries and quantum information programs in national laboratories. This research is an integral part of the university-wide quantum engineering initiative led by the team with a goal to establish a graduate program in quantum information science engineering at the University of Arizona. It will help the continued effort at the University of Arizona in involving under-represented students into research, whose educational experiences will be enriched by national and international collaboration.Error-correction is at the heart of all applications of quantum information processing, e.g., in realizing fault tolerant quantum computing, efficient reconciliation and privacy amplification in quantum key distribution, building fault-tolerant quantum memories for quantum repeaters used in a long distance entanglement distribution network, and for attaining quantum limits of the rate of reliable optical communications. Quantum low-density parity check (QLDPC) codes are the only known class of quantum codes in the stabilizer family that have asymptotically nonzero rates, and are an important cog in realizing scalable, fault tolerant quantum computation, but an efficient decoding solution for QLDPC codes is still lacking. In this project, the team will develop efficient and fault-tolerant decoders that employ classical-quantum messages, to harness the full potential of QLDPC codes. The approach is based on the concept of a trapping sets of quantum decoding algorithms, which allows one to characterize decoding failures combinatorially and through graph theory. This knowledge of trapping sets will be then used to develop a framework for systematic decoder design. The resulting decoder is a small fault-tolerant quantum computer built using noisy gates wherein all computations remain local at nodes, and quantum communication happens across nearest-neighbor edges on the decoding graph. The team will characterize the performance of the QLDPC codes and fault-tolerant decoders in recently developed architectures for scalable linear optical quantum computing, and coded transmission-based all-optical repeaters for long-range quantum communication.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.