Weaving Stability from Dissipation: Fixed-Point Engineering for Quantum Information Processing

耗散的编织稳定性：量子信息处理的定点工程

• 批准号: 1620541
• 负责人: Lorenza Viola
• 金额: $ 27万
• 依托单位: Dartmouth College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-15 至 2021-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1620541&HistoricalAwards=false
• 关键词: Weaving; Stability; Dissipation; Fixed; Point

Understanding how physical systems approach equilibrium is a central question in statistical physics, and this topic is all the more profound when systems behave according to the laws of quantum mechanics. As a familiar example, consider how a hot cup of tea or a cold glass of water equilibrate to room temperature. One cools down while the other warms up; but in each case individual molecular interactions affect the rate and the fluctuations with which these systems approach equilibrium. A more nuanced example comes from the field of quantum computing, where information can be encoded in the quantum mechanical spin states of individual molecules. One compelling motivation for this is to produce more powerful computers with memory and information processing capabilities far superior to today's classical computers. However, since relaxation towards equilibrium can disorganize the quantum information stored in molecules, equilibration is normally considered an obstacle or a hindrance for quantum computing. The goal of this project is to find ways to utilize the stability of states near equilibrium in order to improve quantum computing protocols. Methods to characterize and influence the stability of multi-particle quantum states will be developed. Techniques to "attract" or nudge any given initial state towards a set of stable equilibrium states that contain genuinely non-classical multi-particle correlations ("entanglement") needed for quantum computing will be explored. This research will address fundamental questions about the conditions under which stabilization to a desired quantum state may be achieved, and it will expand the toolkit and of methods to characterize and control dissipative quantum systems. This project also provides education and training for students working on subjects at the cross-disciplinary boundaries between quantum information science, quantum control theory, applied mathematics, and many-body and statistical physics. Over the last few years, the principal investigator has established rigorous conditions for a general quantum state of interest to be the unique fixed point of a class of continuous-time "frustration-free" Markovian dynamics, subject to realistic locality constraints. Building on these results, this project aims to explore quantum stabilization problems in physical settings that remain largely uncharted as yet -- for instance: (i) Continuous-time Markovian dynamics under more general constraints than imposed by locality, including sensitivity to perturbations and periodically time-varying Floquet-Markov generators; (ii) Constrained discrete-time Markovian dynamics, for which the intriguing possibilities of exact dissipative state preparation and dissipative encoding in finite time arise; (iii) Randomized open-system dynamics, which may shed light on the stabilizability properties of generic (random) target states or subspaces. The methods to be employed will be both analytical and numerical, and will draw on a diverse range of tools from applied mathematics and quantum control theory (including operator algebras, Lyapunov stability techniques, and semi-definite programming), to quantum information theory and many-body physics (notably, entanglement theory, information-preserving structures, and tensor-network techniques). Theoretically, a central theme will be to clarify the extent to which core features from many-body and statistical mechanics -- in particular, the complexity of quantum correlations in the equilibrium state, the lack of frustration, the gapped nature or the commutativity of the underlying "parent" Hamiltonians -- may be brought to bear on the feasibility and efficiency of stabilization tasks for quantum information processing. From a practical standpoint, the goal of these investigations is to improve protocols for dissipative quantum state preparation and quantum information encoding.

理解物理系统如何接近平衡是统计物理学的一个中心问题，当系统根据量子力学定律运行时，这个主题就更加深刻了。 作为一个熟悉的例子，考虑一杯热茶或一杯冷水如何平衡到室温。 一个冷却，而另一个升温;但在每种情况下，单个分子的相互作用都会影响这些系统接近平衡的速率和波动。 一个更微妙的例子来自量子计算领域，信息可以编码在单个分子的量子力学自旋状态中。 一个令人信服的动机是生产更强大的计算机，其内存和信息处理能力远远上级今天的经典计算机。 然而，由于向平衡态的弛豫会破坏存储在分子中的量子信息，平衡态通常被认为是量子计算的障碍或阻碍。 该项目的目标是找到利用接近平衡态的稳定性的方法，以改进量子计算协议。 将开发表征和影响多粒子量子态稳定性的方法。 将探索“吸引”或推动任何给定的初始状态朝向一组稳定的平衡状态的技术，这些平衡状态包含量子计算所需的真正非经典的多粒子关联（“纠缠”）。 这项研究将解决有关稳定到所需量子态的条件的基本问题，并将扩展表征和控制耗散量子系统的工具包和方法。 该项目还为从事量子信息科学，量子控制理论，应用数学以及多体和统计物理学之间的跨学科边界的学生提供教育和培训。 在过去的几年里，首席研究员已经建立了严格的条件，使感兴趣的一般量子态成为一类连续时间“无挫折”马尔可夫动力学的唯一不动点，并受到现实的局部性约束。在这些结果的基础上，该项目旨在探索在物理环境中的量子稳定问题，这些问题在很大程度上仍然是未知的-例如：㈠在比局部性更一般的限制下的连续时间马尔可夫动力学，包括对扰动的敏感性和周期性时变Floquet-Markov生成器;（ii）受约束的离散时间马尔可夫动力学，在有限时间内出现精确耗散态制备和耗散编码的有趣可能性;（iii）随机开放系统动力学，它可能揭示一般（随机）目标状态或子空间的稳定性属性。将采用的方法将是分析和数值，并将利用各种工具，从应用数学和量子控制理论（包括算子代数，李雅普诺夫稳定性技术和半定规划），量子信息理论和多体物理学（特别是纠缠理论，信息保存结构和张量网络技术）。从理论上讲，一个中心主题将是澄清多体和统计力学的核心特征-特别是平衡态量子相关性的复杂性、缺乏挫折感、基本“父”哈密顿量的间隙性质或交换性-在多大程度上可能影响量子信息处理稳定任务的可行性和效率。 从实用的角度来看，这些研究的目标是改进耗散量子态制备和量子信息编码的协议。