AF: Medium: Quantum Hamiltonian Complexity: Through the Computational Lens

AF：介质：量子哈密顿复杂性：通过计算镜头

• 批准号: 1410022
• 负责人: Umesh Vazirani
• 金额: $ 120万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-09-01 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1410022&HistoricalAwards=false
• 关键词: AF; Medium; Quantum; Hamiltonian; Complexity

Quantum computation has taught us that, in general, quantum systems are exponentially powerful. This is a double-edged sword: while making quantum computers possible, it is also an enormous obstacle to analyzing and understanding physical systems. Indeed, this is not just an abstract concern; with the major push in condensed matter physics towards studying and creating highly entangled states of matter, the computational complexity of these systems has moved to the fore as a major issue, and this is the main focus of the emerging area of Quantum Hamiltonian Complexity. Here is a list of three basic questions in this area:1. Can "typical" states of ?naturally occurring? quantum systems be described succinctly (i.e. polynomial rather than exponential in the number of particles)?2. Does the exponential complexity of general quantum systems persist at high temperature?3. Is the scientific method sufficiently powerful to be applicable to general quantum systems?Each of these can be formulated as a precise computational question -- the first is a natural generalization of a question about the complexity class NP, the second about the celebrated PCP theorem and the third about interactive proof systems. Over the last few years the outline of remarkable positive answers to some of these questions has emerged, and there are in place some of the basic techniques necessary to tackle these questions. This project aims to pursue this line of inquiry.This project is interdisciplinary at the deepest level. It brings a computational lens to bear on some of the most basic issues in condensed matter physics and in the philosophy of science. Conversely, it extends the core concepts of computational complexity theory in important new directions, at the same time drawing on deep insights from physics to make progress on fundamental questions.

量子计算告诉我们，一般来说，量子系统的威力呈指数级增长。 这是一把双刃剑：在使量子计算机成为可能的同时，它也成为分析和理解物理系统的巨大障碍。 事实上，这不仅仅是一个抽象的问题；而是一个问题。随着凝聚态物理学向研究和创建高度纠缠态物质的重大推动，这些系统的计算复杂性已成为一个主要问题，这也是量子哈密顿复杂性新兴领域的主要焦点。 以下列出了该领域的三个基本问题：1． “典型”状态可以自然发生吗？量子系统可以被简洁地描述（即粒子数量是多项式而不是指数）？2。 一般量子系统的指数复杂性在高温下是否持续存在？3． 科学方法是否足够强大，足以适用于一般的量子系统？每个问题都可以表述为精确的计算问题——第一个是关于复杂性类别 NP 的问题的自然概括，第二个是关于著名的 PCP 定理的问题，第三个是关于交互式证明系统的问题。 在过去的几年里，对其中一些问题的显着积极答案的轮廓已经出现，并且解决这些问题所需的一些基本技术已经到位。 该项目旨在追求这一探究方向。该项目在最深层次上是跨学科的。它带来了计算镜头来解决凝聚态物理和科学哲学中的一些最基本的问题。 相反，它将计算复杂性理论的核心概念扩展到重要的新方向，同时借鉴物理学的深刻见解，在基本问题上取得进展。