Variational-Cartan Quantum Dynamics Simulations of Excitation Dynamics

TL;DR

This paper introduces a hybrid variational-Cartan quantum simulation method that enables fixed-depth quantum circuits for studying time-dependent excitation dynamics in spin and molecular systems, improving practicality on near-term quantum hardware.

Contribution

It generalizes Cartan decomposition-based Hamiltonian simulation to time-dependent systems by combining it with variational techniques, maintaining fixed circuit depth and high accuracy.

Findings

Accurately simulates excitation spectra of spin systems.

Successfully models molecular response to electric fields.

Demonstrates fixed-depth circuits are feasible for time-dependent quantum dynamics.

Abstract

Quantum dynamics simulations (QDSs) are one of the most highly anticipated applications of quantum computing. Quantum circuit depth for implementing Hamiltonian simulation algorithms is commonly time dependent so that long time dynamics simulations become impratical on near-term quantum processors. The Hamiltonian simulation algorithm based on Cartan decomposition (CD) provides an appealing scheme for QDSs with fixed-depth circuits while limited to time-independent case. In this work, we generalize this CD-based Hamiltonian simulation algorithm for studying time-dependent systems by combining it with variational Hamiltonian simulation. The time-dependent and time-independent parts of the Hamiltonian are treated with the variational approach and the CD-based Hamiltonian simulation algorithms, respectively. As such, only fixed-depth quantum circuits are required in this hybrid Hamiltonian simulation algorithm while still maintaining high accuracy. We apply this new algorithm to study the response of spin and molecular systems to $\delta$-kick electric fields and obtain accurate spectra for these excitation processes.