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.

在本质上利用量子现象来处理信息，有望在计算和通信等多个任务中获得令人兴奋的收益和优势。然而，在发生这种现象的分钟尺度上，信息载体（例如原子）是脆弱的，并且高度容易受到噪声的影响。为了构建可扩展且可靠的量子系统，需要通过错误校正技术来减轻噪声。量子错误纠正代码（QECC）在较大的数学空间中编码数据，以便可以使用冗余来检测和纠正错误。对于量子计算，需要定期进行此类误差校正，该纠正试图保留数据，同时还执行主动计算来处理数据，从而不断更改数据。为了使故障耐受性，这种量子计算机需要找到仔细平衡计算和解码（误差校正）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，这些方法是针对编码计算和使用经典错误纠正理论技术解码之间动态的优化的。该团队还将在这些领域培养年轻的人才，并激发代表性不足的团体加入不断增长的量子劳动力。Qec的著名阈值定理确定，只要每个硬件组件都符合富裕性阈值，即量子信息可以无限期地保护量子信息。该项目将对所需的代码结构提供具体的理解，该结构是由实际约束的动机，因此将阈值和计算开销作为该结构的函数。具体而言，提出的研究计划的智力贡献可以总结如下：（1）研究人员的最新结果已经产生了系统的方法，以合成稳定器代码的逻辑操作。研究人员团队将首先将这种方法应用于量子低密度平价检查（QLDPC）代码，以了解其逻辑计算的效用。（2）团队将探索诸如串联和提升代数原质图之类的策略，以结合QLDPC代码的最佳方面和代数代码，例如量子芦苇 - 穆勒代码。（3）对于QEC，已经观察到，由于周期和与错误退化性相关的“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。该团队将利用其经典专业知识来开发基于噪音综合症的消息，了解非线性消息更新的效果并分析错误地板的效果。（4）研究者还将确定此类方法与实现这些混合QECC的逻辑操作相互作用的理想图结构。最后，团队将将这些见解与其他有前途的方法相结合，例如基于测量的量子计算，这将使结果适用于广泛的技术。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的审查标准通过评估来获得支持的。