Quantum algorithms for Hamiltonian simulation

量子系统的哈密顿量完全决定了它的动力学。在特定的哈密顿量下计算这些动力学称为哈密顿模拟问题，它允许预测系统行为。尽管在过去的世纪中经典计算机上的哈密顿模拟取得了重大进展，但由于维数灾难，哈密顿模拟问题在过去的世纪中仍然是一项极具挑战性的任务，因为计算成本随着系统大小呈指数级增长。费曼1982年提出量子计算机设计的动机之一就是为了解决这个问题。这个博士项目的目的是开发用于哈密顿模拟的量子算法。这些包括经典分裂方法启发的算法，以及涉及量子电路优化的变分量子算法。

The Hamiltonian of a quantum system dictates its dynamics completely. The computation of these dynamics under a particular Hamiltonian is called the Hamiltonian simulation problem, and it allows prediction of the system behavior. Despite significant progress in Hamiltonian simulation on classical computers over the past century, the Hamiltonian simulation problem has remained an extremely challenging task over the past century due to the curse of dimensionality as the computation costs grow exponentially with system size. One of the motivations for Feynman's 1982 proposal for the design of quantum computers was in response to this problem. The aim of this PhD project is to develop quantum algorithms for Hamiltonian simulation. These include algorithms inspired by classical splitting methods, as well as variational quantum algorithms involving quantum circuit optimization.