A hybrid method for quantum dynamics simulation

TL;DR

This paper introduces a hybrid quantum-classical method combining Trotter algorithms and dynamic mode decomposition to efficiently predict long-term quantum observables from short-term measurements.

Contribution

It presents a novel hybrid approach that leverages classical data analysis to extend quantum simulation capabilities for many-body dynamics.

Findings

Accurately predicts long-term observables with limited quantum data

Error scales as O(t^{3/2}) with fixed measurements

Effective in Hubbard and spin systems simulations

Abstract

We propose a hybrid approach to simulate quantum many body dynamics by combining Trotter based quantum algorithm with classical dynamic mode decomposition. The interest often lies in estimating observables rather than explicitly obtaining the wave function's form. Our method predicts observables of a quantum state in the long time by using data from a set of short time measurements from a quantum computer. The upper bound for the global error of our method scales as $O(t^{3/2})$ with a fixed set of the measurement. We apply our method to quench dynamics in Hubbard model and nearest neighbor spin systems and show that the observable properties can be predicted up to a reasonable error by controlling the number of data points obtained from the quantum measurements.