Collaborative Research: Statistical Mechanics of Non-local Disordered Models Associated with Quantum LDPC Codes

合作研究：与量子 LDPC 码相关的非局域无序模型的统计力学

• 批准号: 1415600
• 负责人: Alexey Kovalev
• 金额: $ 25.5万
• 依托单位: University of Nebraska-Lincoln
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-09-15 至 2018-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1415600&HistoricalAwards=false
• 关键词: Collaborative; Research; Statistical; Mechanics; Non

Quantum low-density-parity-check (LDPC) codes is the only class of quantum error correcting codes where an asymptotically finite rate isknown to coexist with a finite fault-tolerant error-correction threshold. In simple terms, using these codes for coherence protection, a large quantum computer can in principle be built, and compared to other existing schemes, it would require fewer redundant qubits. Good finite-rate quantum LDPC codes are preciously few: the firstanalytical examples have only been constructed a few years ago. These codes will be used as a scaffold to construct novel non-local statistical mechanical models with unusual properties. Studying these models will improve our understanding of the quantum theoretical problems related to quantum computation.These studies will also offer an insight in general properties of non-local models. Many studies of such models concentrated on caseswhere interactions between particles are chosen randomly; these tend to produce generic mean-field behavior which is well understood. In contrast, in this work models will be constructed with features never seen before and even proved to be impossible in a local setting. At the same time, because of the connection to the original quantum codes, these models can be guaranteed to have some highlysought-after qualifications, e.g., several distinct thermodynamical phases and non-trivial "duality" mappings between them, "topological"phases where different ground states cannot be distinguished by a local measurement, etc. Among the more ambitious potential applications is a consistent theory of quantum gravity where the universe itself would emerge from chaos via some quantum code.The award supports theoretical research on physics of non-local discrete and continuous statistical-mechanical models associated with quantum error correcting codes. An important feature of such codes is the existence of the decoding threshold, where a sufficiently largecode can deal effectively with any noise level below the threshold, but not above it.Disordered spin models associated with decoding transition (these models have exact Wegner's self-duality), related models with large gauge groups associated with fault-tolerant decoding, as well as models with extensive ground state entropy, including U(1) gauge theories which generalize Wen's mutual Chern-Simons theory describing the ground state of Kitaev's toric code will be constructed and studied. Models associated with quantum LDPC codes are expected to be particularly interesting since their interaction terms involve a limited number of participating particles. The low-energy sectors of these models are expected to be dominated by non-trivial extended defects which generalize the notion of topological defects like domain walls, vortices, etc. New physics includes a phase transition driven by an extensive entropy of defectclasses, coming from the exponentially large number of dimensions describing the original quantum code. Results will be relevant toseveral established fields of physics traditionally dealing with similar models: statistical mechanics of spin glasses, phase transition theory, etc., with potential applications extending to many other fields.

量子低密度奇偶校验（LDPC）码是唯一一类速率渐近有限且纠错门限有限的量子纠错码。 简而言之，使用这些代码进行相干保护，原则上可以构建大型量子计算机，与其他现有方案相比，它需要更少的冗余量子位。 好的有限速率量子LDPC码是非常少的：第一个分析的例子仅仅是在几年前构造的。 这些代码将被用来作为一个支架，以构建新的非局部统计力学模型与不寻常的属性。对这些模型的研究将有助于加深我们对量子计算相关量子理论问题的理解，也有助于我们对非定域模型的一般性质的了解。 许多研究集中在这样的模型caseswhere粒子之间的相互作用是随机选择的，这些往往会产生通用的平均场行为，这是很好地理解。 相比之下，在这项工作中，模型将使用以前从未见过的特征来构建，甚至被证明在当地环境中是不可能的。 同时，由于与原始量子码的联系，这些模型可以保证具有一些备受追捧的资格，例如，几个不同的几何相位和它们之间的非平凡“对偶”映射，其中不同基态不能通过局部测量区分的“拓扑“相位，等等。更雄心勃勃的潜在应用之一是量子引力的一致性理论，其中宇宙本身将通过某种量子代码从混乱中出现。该奖项支持非局域离散和连续统计物理学的理论研究-与量子纠错码相关的机械模型。 这种码的一个重要特征是存在解码阈值，其中足够大的码可以有效地处理低于阈值的任何噪声电平，但不能处理高于阈值的任何噪声电平。（这些模型具有精确的Wegner自对偶性），具有与容错解码相关联的大规范群的相关模型，以及具有广泛基态熵的模型，包括U（1）规范理论，它推广了描述Kitaev复曲面码基态的Wen的相互Chern-Simons理论。与量子LDPC码相关的模型预计将特别有趣，因为它们的相互作用项涉及有限数量的参与粒子。 这些模型的低能量部门预计将占主导地位的非平凡的扩展缺陷，概括了拓扑缺陷的概念，如域壁，涡流等新物理包括一个相变驱动的广泛的熵defectclasses，来自指数级的大量的维度描述原始的量子代码。 结果将与传统上处理类似模型的几个已建立的物理学领域相关：自旋玻璃的统计力学，相变理论等，其潜在应用扩展到许多其它领域。

项目成果

Stability of skyrmion lattices and symmetries of quasi-two-dimensional chiral magnets

• DOI: 10.1103/physrevb.93.064428
• 发表时间: 2016-02-24
• 期刊: PHYSICAL REVIEW B
• 影响因子: 3.7
• 作者: Guengoerdue, Utkan;Nepal, Rabindra;Kovalev, Alexey A.
• 通讯作者: Kovalev, Alexey A.

Magnetization pumping and dynamics in a Dzyaloshinskii-Moriya magnet

Dzyaloshinskii-Moriya 磁体中的磁化泵浦和动力学

• DOI: 10.1209/0295-5075/109/67008
• 发表时间: 2015
• 期刊: EPL (Europhysics Letters
• 作者: Kovalev, Alexey A.;Güngördü, Utkan
• 通讯作者: Güngördü, Utkan

Spin torque and Nernst effects in Dzyaloshinskii-Moriya ferromagnets

• DOI: 10.1103/physrevb.93.161106
• 发表时间: 2015-09
• 期刊: Physical Review B
• 影响因子: 3.7
• 作者: A. Kovalev;V. Zyuzin

Parafermion stabilizer codes

• DOI: 10.1103/physreva.90.042326
• 发表时间: 2014-09
• 期刊: Physical Review A
• 影响因子: 2.9
• 作者: Utkan Gungordu;Rabindra Nepal;A. Kovalev

Numerical and analytical bounds on threshold error rates for hypergraph-product codes

超图积代码阈值错误率的数值和分析界限

• DOI: 10.1103/physreva.97.062320
• 发表时间: 2018
• 期刊: Physical Review A
• 影响因子: 2.9
• 作者: Kovalev, Alexey A.;Prabhakar, Sanjay;Dumer, Ilya;Pryadko, Leonid P.
• 通讯作者: Pryadko, Leonid P.