AF: Small: Ground State Complexity in Quantum Many-Body Systems

AF：小：量子多体系统中的基态复杂性

• 批准号: 0916181
• 负责人: Sandra Irani
• 金额: $ 49.89万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-07-01 至 2014-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0916181&HistoricalAwards=false
• 关键词: AF; Small; Ground; State; Complexity

One of the central goals of quantum information theory is to understand quantum systems from the standpoint of computational complexity. Physicists have been using computers for decades to understand various aspects of quantum systems, but these methods are typically heuristic and achieve success on only limited classes of systems. Understanding quantum systems through the lens of computational and information-theoretic complexity has already lead to new powerful computational methods in physics and deeper insight into what causes these methods to fail once we step outside specific classes. Meanwhile hardness results often have important implications for quantum computation. If computing a property of a system is shown to be as difficult as computing the output of an arbitrary quantum circuit, that system becomes a candidate for a quantum computer.This proposal focuses specifically on the complexity of ground states, the lowest energy state of a system. How hard is it to compute the ground energy of a quantum system? What are the properties of a system that give rise to provably efficient algorithms to compute the ground state? What is the structure of the ground state? Under what circumstances does the ground state have a succinct representation? The PI will pursue these questions in the context of one-dimensional systems and will begin work on two-dimensional systems about which much less is known.

量子信息理论的核心目标之一是从计算复杂性的角度来理解量子系统。几十年来，物理学家一直在使用计算机来理解量子系统的各个方面，但这些方法通常是启发式的，只能在有限的系统类别上取得成功。通过计算和信息论复杂性的透镜来理解量子系统，已经带来了物理学中新的强大计算方法，以及更深入地了解一旦我们走出特定的课程，是什么导致这些方法失败。同时，硬度的结果往往对量子计算有重要的意义。如果计算一个系统的一个属性被证明和计算一个任意量子电路的输出一样困难，那么这个系统就成为量子计算机的候选者。这个提议特别关注基态的复杂性，基态是系统的最低能量状态。计算量子系统的基态能量有多难？一个系统的什么性质会产生可证明有效的算法来计算基态？基态的结构是什么？在什么情况下基态有一个简洁的表示？PI将在一维系统的背景下继续研究这些问题，并将开始对二维系统的研究，因为对二维系统的了解要少得多。