论文标题
用于哈密顿对角线化的差异量子算法
A variational quantum algorithm for Hamiltonian diagonalization
论文作者
论文摘要
哈密顿对角线化是了解量子系统的物理特性和实际应用的核心。非常希望设计可以加速哈密顿对角线化的量子算法，尤其是可以在近期量子设备上实现的量子算法。在这项工作中，我们提出了一种量子系统的汉密尔顿对角线化（VQHD）的变分算法，该算法探讨了系统的重要物理特性，例如温度，位置和相关性。关键的想法是，系统的热状态编码了哈密顿系统系统的特征值和特征态的信息。为了获得Hamiltonian的全光谱，我们使用具有高温的量子假想时间演化算法，该算法准备了相关长度较小的热状态。通过Trotterization，这使我们能够通过仅在少数站点上进行局部统一转换来实现假想时间演变的每个步骤。对角度化这些热状态会导致对哈密顿特征系统的全部知识。我们应用算法将当地的哈密顿人对角线化，并以很高的精度返回结果。我们的VQHD算法为近期量子计算机的应用提供了新的启示。
Hamiltonian diagonalization is at the heart of understanding physical properties and practical applications of quantum systems. It is highly desired to design quantum algorithms that can speedup Hamiltonian diagonalization, especially those can be implemented on near-term quantum devices. In this work, we propose a variational algorithm for Hamiltonians diagonalization (VQHD) of quantum systems, which explores the important physical properties, such as temperature, locality and correlation, of the system. The key idea is that the thermal states of the system encode the information of eigenvalues and eigenstates of the system Hamiltonian. To obtain the full spectrum of the Hamiltonian, we use a quantum imaginary time evolution algorithm with high temperature, which prepares a thermal state with a small correlation length. With Trotterization, this then allows us to implement each step of imaginary time evolution by a local unitary transformation on only a small number of sites. Diagonalizing these thermal states hence leads to a full knowledge of the Hamiltonian eigensystem. We apply our algorithm to diagonalize local Hamiltonians and return results with high precision. Our VQHD algorithm sheds new light on the applications of near-term quantum computers.
