CIF: Small: Quantum LDPC codes: structure and logical operations

CIF：小：量子 LDPC 码：结构和逻辑运算

• 批准号: 2330909
• 负责人: Alexander Barg
• 金额: $ 60万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-12-01 至 2026-11-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2330909&HistoricalAwards=false
• 关键词: CIF; Small; Quantum; LDPC; codes

Quantum computer algorithms hold significant promise in tackling fundamental search problems that lack efficient classical solutions. The general challenge of constructing functioning quantum computers is thus currently pursued by engineers in academia and industry worldwide, and it is also supported by theoretical research in the physics and computer science communities. Since quantum states, irrespective of the specific architecture, are inevitably exposed to inherent noise, the reliability of quantum computations hinges on incorporating noise-controlling procedures directly into computational processes. This challenge gives rise to various issues concerning the construction, analysis, and implementation of quantum error-correcting codes. This project specifically delves into the study of a class of quantum codes known as low-density parity-check codes, which are considered promising contenders for facilitating fault-tolerant computations. The anticipated outcomes of this project include constructions and analysis of new methods of noise mitigation in the computation process, as well as development and teaching of undergraduate courses covering quantum information science.Recent advances in quantum coding theory have focussed on the construction and decoding of quantum stabilizer codes, whose generators act on a small number of qubits. Such codes, termed low-density parity-check codes, have been the primary candidate for supporting fault-tolerant operation of quantum computers. Several related code families, designed in the last few years, attain parameters that were previously thought impossible for this class of codes. Relying on methods of homological algebra, balanced product codes and, in particular, lifted product codes, new designs were shown to have distance proportional to the block length of the code, resulting in asymptotically good code families. One problem area that this project will analyze is constructions of logical operators for balanced product codes that act locally, for instance, on a single physical qubit or a small group of such qubits. Logical operators of this type are preferable for implementing the codes, and constitute an active, developing research area. This project will also study common underlying structures in the two prominent families of quantum low-density codes, namely, lifted product codes and quantum Tanner codes. A key goal of this study is to advance constructions of quantum locally testable codes, which are important in quantum complexity theory. This project also will address constructions of lifted product codes based on specific graphs and group actions, aiming at constructing new stabilizer codes of small or moderate length with improved parameters.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.

量子计算机算法在解决缺乏有效经典解决方案的基本搜索问题方面具有重大前景。因此，构建功能量子计算机的普遍挑战目前是全世界学术界和工业界工程师所追求的，并且也得到了物理学和计算机科学界理论研究的支持。由于无论具体架构如何，量子态都不可避免地会受到固有噪声的影响，因此量子计算的可靠性取决于将噪声控制程序直接纳入计算过程。这一挑战引发了有关量子纠错码的构造、分析和实现的各种问题。该项目专门深入研究一类被称为低密度奇偶校验码的量子码，它们被认为是促进容错计算的有希望的竞争者。该项目的预期成果包括计算过程中噪声抑制新方法的构建和分析，以及涵盖量子信息科学的本科课程的开发和教学。量子编码理论的最新进展集中在量子编码的构建和解码上。稳定器代码，其生成器作用于少量量子位。此类代码被称为低密度奇偶校验码，是支持量子计算机容错操作的主要候选代码。过去几年设计的几个相关代码系列获得了以前认为此类代码不可能实现的参数。依靠同调代数、平衡乘积码以及特别是提升乘积码的方法，新设计被证明具有与代码的块长度成比例的距离，从而产生渐近良好的代码族。该项目将分析的一个问题领域是平衡乘积代码的逻辑运算符的构造，这些代码在本地起作用，例如，作用于单个物理量子位或一小组此类量子位。这种类型的逻辑运算符更适合实现代码，并且构成了一个活跃的、发展中的研究领域。该项目还将研究两个著名的量子低密度码家族的共同基础结构，即提升乘积码和量子坦纳码。这项研究的一个关键目标是推进量子局部可测试代码的构造，这在量子复杂性理论中很重要。该项目还将解决基于特定图表和群体行为的提升产品代码的构建，旨在构建具有改进参数的小或中等长度的新稳定器代码。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。