Symmetry Protected and Topological Phases in Quantum Many Body Systems

量子多体系统中的对称保护相和拓扑相

• 批准号: RGPIN-2018-05136
• 负责人: Feder, David
• 金额: $ 4.08万
• 依托单位: University of Calgary
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=762971
• 关键词: Symmetry; Protected; Topological; Phases; Quantum

Standard approaches to quantum computing are not very tolerant to qubit errors and it is not yet clear if the error rates can be made sufficiently low to build a universal fault-tolerant quantum computer. A major focus of my research is to explore an alternative approach to quantum computing, where the quantum information is inherently protected from errors and is manipulated to perform universal quantum logic. The general framework of this work is to exploit the ideas of topological insulator (TI) and symmetry-protected topological (SPT) states of matter that have been of intense recent interest in condensed matter physics. Over the course of the next five years, I will work closely with experimental groups to help develop these new states of matter, and to guide the practical implementation of intrinsically fault-tolerant quantum algorithms. The proposed activities are a unique blend of quantum information and condensed matter physics.Perhaps the best-known example of a TI corresponds to the integer quantum Hall effect, in which the conductance is expressed in terms of the Chern number, a topological quantity. It was subsequently realized that topological states can arise in a variety of settings including three-dimensional (3D) materials with no broken symmetries (the external magnetic field breaks time-reversal symmetry in the quantum Hall effect). Rather, TI phases can follow directly from of the symmetries: SPT phases. A hallmark of the topological order are localized states at the surface; for example, the quantum Hall conductance is due to these 'edge modes.' Quantum information encoded onto these modes is protected by the underlying symmetry / topology, yet remains accessible to external manipulation. Successive measurements of the edge states can yield universal quantum logic.My research will consider several experimental systems which have recently made huge strides toward the realization of SPT and TI states, such as neutral atoms in quantum cavities and optical lattices, and photonic crystals. Emphasis will be placed on systems of particles with spin-orbit coupling, whose ground states can form SPT phases under certain conditions. I will investigate systems of both ideal and interacting particles, with a priority on finding convenient experimental approaches both for the detection of topological order and for the implementation of quantum operations. The theoretical calculations will employ a combination of analytical techniques and state-of-the-art numerical methods, including group theory, algebraic graph theory, matrix-product states and density matrix renormalization group calculations in 1D and more general tensor networks in 2D and 3D, among others. The results should help lead the way toward to development of novel quantum technologies.

量子计算的标准方法对Qubit错误的耐受性不太宽容，尚不清楚是否可以使错误率足够低以构建通用耐故障的量子计算机。我的研究的主要重点是探索量子计算的替代方法，其中量子信息固有地保护了错误，并且被操纵以执行通用量子逻辑。这项工作的一般框架是利用拓扑绝缘子（TI）和对称性保护的拓扑（SPT）状态的概念，这些状态一直对凝结物理学产生强烈的兴趣。在接下来的五年中，我将与实验组紧密合作，以帮助发展这些新的物质状态，并指导实际实施本质上容忍的量子算法。所提出的活动是量子信息和凝结物理物理学的独特混合物。也许最著名的ti示例对应于整数量子霍尔效应，其中电导是用Chern数字表示的，是拓扑数量。随后，人们意识到，拓扑状态可以在各种环境中出现，包括没有损坏对称性的三维（3D）材料（外部磁场会破坏量子霍尔效应中的时间反转对称性）。相反，Ti阶段可以直接来自对称性的：SPT阶段。拓扑顺序的标志是地表处的局部状态。例如，量子大厅电导是由于这些“边缘模式”。编码在这些模式上的量子信息受到基础对称 /拓扑的保护，但外部操作仍然可以访问。边缘状态的连续测量可以产生通用的量子逻辑。我的研究将考虑几种实验系统，这些系统最近朝着实现SPT和TI状态的实现，例如量子腔和光学晶格中的中性原子以及光子晶体。重点将放在具有自旋轨道耦合的颗粒系统上，其基态可以在某些条件下形成SPT阶段。我将研究理想和相互作用的颗粒的系统，并优先寻找方便的实验方法来检测拓扑顺序和实施量子操作。理论计算将采用分析技术和最先进的数值方法的组合，包括组理论，代数图理论，矩阵 - 产物态和1D中的密度矩阵重新归一化组计算以及2D和3D中更多的一般张量网络。结果应有助于引导发展新型量子技术的发展。