Hamiltonian learning from time dynamics using variational algorithms

TL;DR

This paper introduces a general variational algorithm for learning quantum Hamiltonians from time series data, enabling flexible and efficient reconstruction of system dynamics without relying on specific Hamiltonian structures.

Contribution

The paper presents a novel, general variational method for Hamiltonian learning from time dynamics, applicable to various observables and initial states, and extends to quantum state learning.

Findings

Successfully reconstructs Hamiltonians with XX, ZZ couplings and transverse field Ising models.

Validates the method by reproducing dynamics of unseen observables.

Proposes an analytical approach for SU(3) Hamiltonian learning.

Abstract

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 dataset. 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 the 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 XX, ZZ couplings along with transverse field Ising Hamiltonians and propose an analytical method for the learning of Hamiltonians consisting of generators of the SU(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.