Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States.
Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, United States.
J Phys Chem A. 2023 Apr 13;127(14):3246-3255. doi: 10.1021/acs.jpca.2c08993. Epub 2023 Mar 29.
The Hamiltonian of a quantum system governs the dynamics of the system via the Schrodinger equation. In this paper, the Hamiltonian is reconstructed in the Pauli basis using measurables on random states forming a time series data set. The time propagation is implemented through Trotterization and optimized variationally with gradients computed on the quantum circuit. We validate our output by reproducing the dynamics of unseen observables on a randomly chosen state not used for the optimization. Unlike existing techniques that try and exploit the structure/properties of the Hamiltonian, our scheme is general and provides freedom with regard to what observables or initial states can be used while still remaining efficient with regard to implementation. We extend our protocol to doing quantum state learning where we solve the reverse problem of doing state learning given time series data of observables generated against several Hamiltonian dynamics. We show results on Hamiltonians involving , couplings along with transverse field Ising Hamiltonians and propose an analytical method for the learning of Hamiltonians consisting of generators of the (3) group. This paper is likely to pave the way toward using Hamiltonian learning for time series prediction within the context of quantum machine learning algorithms.
量子系统的哈密顿量通过薛定谔方程来支配系统的动力学。在本文中，哈密顿量在保罗i 基中使用随机状态的可测值来重建，这些随机状态形成了时间序列数据集。时间传播通过 Trotterization 实现，并通过在量子电路上计算梯度进行优化。我们通过在未用于优化的随机选择的状态上再现看不见的可观测量的动力学来验证我们的输出。与试图利用哈密顿量的结构/特性的现有技术不同，我们的方案是通用的，并且在使用可观测量或初始状态方面提供了自由度，同时在实现方面仍然有效。我们将我们的协议扩展到进行量子态学习，在给定针对几个哈密顿动力学生成的可观测量的时间序列数据的情况下，我们解决了进行态学习的反向问题。我们展示了涉及 , 耦合以及横向场伊辛哈密顿量的哈密顿量的结果，并提出了一种用于学习由 (3) 群生成器组成的哈密顿量的分析方法。本文可能为在量子机器学习算法的上下文中使用哈密顿量学习进行时间序列预测铺平道路。
