Sparse identification of quantum Hamiltonian dynamics via quantum circuit learning

TL;DR

This paper introduces SIQHDy, a quantum circuit learning method inspired by SINDy, for accurately estimating quantum Hamiltonian dynamics from measurement data, demonstrating robustness and extensions for limited observables.

Contribution

It presents a novel quantum Hamiltonian identification framework based on sparse circuit parameter estimation, extending SINDy principles to quantum systems.

Findings

Accurately reconstructs dynamics of multi-spin systems.

Robust to measurement noise in quantum data.

Effective with limited observable access.

Abstract

Sparse identification of nonlinear dynamics (SINDy) is a data-driven framework for estimating classical nonlinear dynamical systems from time-series data. In this approach, system dynamics is represented as a linear combination of a predefined set of basis functions, and the corresponding coefficients are sparsely estimated from observed time-series data. In this study, we propose sparse identification of quantum Hamiltonian dynamics (SIQHDy), a SINDy-inspired quantum circuit learning framework for estimating quantum Hamiltonian dynamics from time-series data of quantum measurement outcomes. In SIQHDy, the unitary evolution of a quantum Hamiltonian system is expressed as a product of basis quantum circuits, and the corresponding circuit parameters are estimated through sparsity-promoting optimization. We numerically demonstrate that SIQHDy accurately reconstructs the dynamics of single-, three-, and five-spin systems, and exhibits robustness to measurement noise in the three-spin case. Furthermore, we propose an extension of SIQHDy for scenarios with limited accessible observables and evaluate its performance in identifying two-spin systems and in network-structure identification for five-spin systems.