EAGER: QSA: Eigenstate Thermalization and the Quantum Metropolis Algorithm

EAGER：QSA：本征态热化和量子都会算法

• 批准号: 2037613
• 负责人: Ivan Deutsch
• 金额: $ 20万
• 依托单位: University of New Mexico
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-10-01 至 2023-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2037613&HistoricalAwards=false
• 关键词: EAGER; QSA; Eigenstate; Thermalization; Quantum

Systems of strongly interacting quantum particles are capable of realizing novel phases of quantum matter, which can exhibit astonishing emergent macroscopic properties like superfluidity, superconductivity, and long-termstorage of quantum information. Despite significant effort in simulating these systems using conventional supercomputers, progress has been limited by a fundamental barrier of computational complexity which veils an unexplored frontier of physics called the entanglement frontier. Quantum computers are naturally able to probe this frontier because they harness entanglement in their elementary operations, and so the eventual development of mature quantum computing technology will greatly advance our understanding of quantum phase transitions and enable the discovery of new phases of quantum matter with potentially transformative properties for technology and society. All of this depends on the development of efficient quantum algorithms for simulating the thermodynamic properties of quantum systems. This project investigates the quantum Metropolis algorithm, which is a quantum algorithm that directly generalizes one of the most successful 20th century paradigms for simulating classical statistical physics. By paralleling developments that occurred in the corresponding classical algorithm, this project seeks to determine general conditions which imply that a quantum computer can efficiently simulate quantum thermal properties.The main new perspective used in this project is based on a connection between physical thermalization - the process by which a physical quantum system comes into thermal equilibrium with its environment - and the behavior and convergence of the quantum Metropolis algorithm. The eigenstate thermalization hypothesis (ETH) is a prominent explanation for how physical quantum systems approach thermal equilibrium, despite their dynamical behavior being time-reversible in principle. This project connects mathematical inequalities developed in the context of the ETH directly to the transition probabilities that govern the behavior of the quantum Metropolis algorithm. This quantitative characterization of transition probabilities opens the door to establishing the first non-trivial cases of rigorously efficient (polynomial-time) quantum algorithms for simulating thermal states of some class of quantum systems that is strongly suspected to be beyond the range of efficient classical simulation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

强相互作用的量子粒子系统能够实现量子物质的新相，它可以表现出惊人的宏观特性，如超流性、超导性和量子信息的长期存储。 尽管在使用传统超级计算机模拟这些系统方面付出了巨大努力，但进展仍受到计算复杂性的基本障碍的限制，该障碍掩盖了称为纠缠前沿的未探索的物理学前沿。 量子计算机自然能够探索这一前沿领域，因为它们在基本运算中利用了纠缠，因此成熟的量子计算技术的最终发展将极大地增进我们对量子相变的理解，并能够发现具有潜在变革性的量子物质新相。技术和社会的属性。 所有这一切都取决于用于模拟量子系统热力学性质的高效量子算法的开发。 该项目研究量子 Metropolis 算法，这是一种量子算法，直接概括了 20 世纪模拟经典统计物理的最成功范式之一。 通过与相应经典算法中发生的并行发展，该项目试图确定意味着量子计算机可以有效模拟量子热性质的一般条件。该项目中使用的主要新视角是基于物理热化与过程之间的联系通过它，物理量子系统与其环境达到热平衡，以及量子大都会算法的行为和收敛。 本征态热化假说（ETH）是对物理量子系统如何接近热平衡的一个重要解释，尽管它们的动力学行为原则上是时间可逆的。 该项目将 ETH 背景下开发的数学不等式直接与控制量子 Metropolis 算法行为的转移概率联系起来。 这种跃迁概率的定量表征为建立严格有效（多项式时间）量子算法的第一个非平凡案例打开了大门，该算法用于模拟某些类量子系统的热状态，这些系统被强烈怀疑超出了有效经典模拟的范围该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。