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，纠错对于保护脆弱的量子比特免受错误的影响至关重要。量子纠错是量子信息处理的所有应用的核心，从容错量子计算到量子密钥分配、量子传感和可靠光通信中的协调。该项目将通过找到实现量子纠错所带来的好处的结构化方法，为可扩展量子计算和通信的实际实现做出贡献。 该项目将开发一类新的纠错码和容错解码器，并将其应用于量子计算，量子通信和网络的架构中。 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精通量子信息处理的劳动力。这项研究是该团队领导的大学量子工程计划的一个组成部分，其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，让代表性不足的学生参与研究，他们的教育经验将通过国家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、量子密钥分发中的有效协调和保密放大、为长距离纠缠分发网络中的量子中继器构建容错量子存储器以及实现可靠光通信速率的量子极限等方面具有重要意义。量子低密度奇偶校验（QLDPC）码是稳定子族中唯一一种速率渐近非零的量子码，是实现可扩展、容错量子计算的重要环节，但目前还缺乏有效的QLDPC码译码方案。 在这个项目中，该团队将开发采用经典量子消息的高效容错解码器，以充分利用QLDPC码的潜力。 该方法是基于量子解码算法的陷阱集的概念，它允许一个组合，并通过图论表征解码失败。这种知识的陷阱集，然后将用于开发一个框架，系统的解码器设计。由此产生的解码器是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处，并且量子通信发生在解码图上的最近邻边缘上。 该团队将对QLDPC码和容错解码器在最近开发的用于可扩展线性光量子计算的架构中的性能进行表征，以及用于远程量子通信的基于编码传输的全光中继器。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。

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.