CCF: AF: Small: Simulating Hamiltonian dynamics: Algorithms and applications

CCF：AF：小：模拟哈密顿动力学：算法和应用

• 批准号: 1526380
• 负责人: Andrew Childs
• 金额: $ 50万
• 依托单位: University of Maryland, College Park
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-08-01 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1526380&HistoricalAwards=false
• 关键词: CCF; AF; Small; Simulating; Hamiltonian

Simulating the dynamics of quantum systems is a major potential application of quantum computers. Quantum simulation can be applied, for example, to model chemical reactions and to predict the behavior of materials. It can also be used as a tool to develop other quantum algorithms, and its study sheds light on the power of quantum computers. This project focuses on two related aspects of quantum simulation: developing improved quantum algorithms for basic simulation problems and studying applications of quantum simulation to other computational tasks.While the state of the art in quantum simulation algorithms is fairly advanced, the ultimate limits for this fundamental task remain unclear. Operating within a broadly applicable framework of quantum systems described by sparse matrices, the project aims to develop optimal tradeoffs among all relevant simulation parameters. It also studies quantum algorithms for simulating open quantum systems, leveraging algorithmic ideas from the well-studied scenario of noiseless systems to give new algorithms for the more realistic setting of noisy quantum systems that interact with their environments. Furthermore, the project studies applications of quantum simulation algorithms. Quantum simulation is the core component of a quantum algorithm for extracting information about the solutions of large systems of linear equations. The project applies recent improvements to quantum simulation algorithms to give improved quantum algorithms for linear systems. It also studies the computational power of particular types of linear systems, such as those that arise in the computation of effective resistances in electrical networks. Finally, the project investigates how algorithmic ideas from advanced quantum simulation algorithms can be applied outside the context of simulation, e.g., in computational number theory.

模拟量子系统的动力学是量子计算机的一个主要潜在应用。 例如，量子模拟可用于模拟化学反应和预测材料的行为。 它还可以用作开发其他量子算法的工具，其研究揭示了量子计算机的强大功能。 该项目重点关注量子模拟的两个相关方面：开发用于基本模拟问题的改进量子算法以及研究量子模拟在其他计算任务中的应用。虽然量子模拟算法的最新技术相当先进，但这一基本模拟的最终限制任务仍不明确。 该项目在稀疏矩阵描述的广泛适用的量子系统框架内运行，旨在在所有相关模拟参数之间进行最佳权衡。 它还研究用于模拟开放量子系统的量子算法，利用经过充分研究的无噪声系统场景中的算法思想，为与环境交互的噪声量子系统的更真实设置提供新算法。 此外，该项目还研究量子模拟算法的应用。 量子模拟是量子算法的核心组成部分，用于提取大型线性方程组解的信息。 该项目应用了量子模拟算法的最新改进，为线性系统提供改进的量子算法。 它还研究特定类型线性系统的计算能力，例如在计算电网有效电阻时出现的系统。 最后，该项目研究了如何将先进量子模拟算法的算法思想应用于模拟环境之外，例如计算数论。