Collaborative Research: CIF: Medium: QODED: Quantum codes Optimized for the Dynamics between Encoded Computation and Decoding using Classical Coding Techniques

协作研究：CIF：中：QODED：针对使用经典编码技术的编码计算和解码之间的动态进行优化的量子代码

基本信息

批准号：
2106213
负责人：
Henry Pfister
金额：
$ 50万
依托单位：
Duke University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-10-01 至 2024-09-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2106213&HistoricalAwards=false
关键词：
Collaborative Research CIF Medium QODED

项目摘要

Leveraging quantum phenomena in nature for processing information promises exciting gains and advantages in several tasks such as computing and communications. At the minute scale where such phenomena occur, however, the information carriers, such as atoms, are fragile and highly susceptible to noise. In order to build scalable and reliable quantum systems, one needs to mitigate noise through error-correction techniques. A quantum error correcting code (QECC) encodes data in a larger mathematical space so that the redundancy can be use to detect and correct errors. For quantum computation, one needs to regularly do such error correction, which tries to preserve data as it is, while also performing active computation to process the data, which keeps altering it. In order to be fault-tolerant, such a quantum computer needs to find ways of carefully balancing computation and decoding (error correction) while keeping resource requirements at a minimum. This is a very challenging task, and this project develops methods to study modern QECCs that are optimized for the dynamics between encoded computation and decoding using techniques from classical error-correction theory. The team will also nurture young talent in these areas and inspire underrepresented groups to join the growing quantum workforce.The celebrated threshold theorem of QEC established that quantum information can be protected indefinitely as long as each hardware component meets a fidelity threshold that is a function of the specific QECC. This project will provide a concrete understanding of desirable code structure, motivated by practical constraints, and hence address both thresholds and computational overhead as a function of this structure. Specifically, the intellectual contributions of the proposed research plan can be summarized as follows: (1) Recent results of investigators have produced systematic methods to synthesize logical operations on stabilizer codes. The team of researchers will begin by applying such methods to quantum low-density parity-check (QLDPC) codes in order to understand their utility for logical computation. (2) The team will explore strategies such as concatenation and lifting algebraic protographs to combine the best aspects of QLDPC codes and algebraic codes such as quantum Reed-Muller codes. (3) For QEC, it has been observed that iterative decoders with symmetric message updates fail on QLDPC codes due to cycles and "quantum" trapping sets related to error degeneracy. The team will leverage their classical expertise to develop single-shot algorithms based on message-passing with noisy syndromes, understand the effect of non-linear message updates, and analyze error floors. (4) The investigators will also determine how the desirable graph structure for such methods interplay with realizing logical operations on these hybrid QECCs. Finally, the team will combine these insights with other promising approaches such as measurement-based quantum computation, which will make the results apply across a wide array of technologies.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.

利用自然界中的量子现象来处理信息有望在计算和通信等多项任务中带来令人兴奋的收益和优势。然而，在发生这种现象的微小尺度上，信息载体（例如原子）是脆弱的并且极易受到噪声的影响。为了构建可扩展且可靠的量子系统，需要通过纠错技术来减轻噪声。量子纠错码（QECC）在更大的数学空间中对数据进行编码，以便可以使用冗余来检测和纠正错误。对于量子计算，需要定期进行这种纠错，试图保留数据原样，同时还执行主动计算来处理数据，从而不断改变数据。为了实现容错，这样的量子计算机需要找到仔细平衡计算和解码（纠错）的方法，同时将资源需求保持在最低限度。这是一项非常具有挑战性的任务，该项目开发了研究现代 QECC 的方法，这些方法使用经典纠错理论的技术针对编码计算和解码之间的动态进行了优化。该团队还将培养这些领域的年轻人才，并激励代表性不足的群体加入不断增长的量子劳动力队伍。QEC 著名的阈值定理规定，只要每个硬件组件满足保真度阈值，量子信息就可以无限期地受到保护，该保真度阈值是具体QECC。该项目将在实际约束的推动下，提供对所需代码结构的具体理解，从而解决作为该结构函数的阈值和计算开销。具体来说，所提出的研究计划的智力贡献可以概括如下：（1）研究人员的最新成果产生了综合稳定器代码逻辑运算的系统方法。研究人员团队将首先将此类方法应用于量子低密度奇偶校验（QLDPC）码，以了解它们在逻辑计算中的效用。 (2) 该团队将探索级联和提升代数原图等策略，以结合 QLDPC 码和代数码（例如量子 Reed-Muller 码）的最佳方面。 (3) 对于 QEC，已经观察到，由于与错误简并相关的循环和“量子”陷阱集，具有对称消息更新的迭代解码器在 QLDPC 代码上失败。该团队将利用他们的经典专业知识来开发基于带有噪声综合症的消息传递的单次算法，了解非线性消息更新的影响，并分析错误层。 (4) 研究人员还将确定此类方法的理想图结构如何与在这些混合 QECC 上实现逻辑运算相互作用。最后，该团队将这些见解与其他有前途的方法（例如基于测量的量子计算）相结合，这将使结果适用于广泛的技术。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准。