Multi-state quantum simulations via model-space quantum imaginary time evolution

TL;DR

This paper presents a novel model space quantum imaginary time evolution (MSQITE) framework that enables stable, multi-state quantum simulations, including excited states, with improved convergence and spin state control on quantum computers.

Contribution

The authors introduce MSQITE, extending QITE with a model space approach and quantum Lanczos acceleration, outperforming previous methods in simulating multiple quantum states.

Findings

MSQITE accurately estimates ground and excited states.

The scheme outperforms standard QLanczos and folded-spectrum QITE.

Spin contamination can be effectively mitigated.

Abstract

We introduce the framework of model space into quantum imaginary time evolution (QITE) to enable stable estimation of ground and excited states using a quantum computer. Model-space QITE (MSQITE) propagates a model space to the exact one by retaining its orthogonality, and hence is able to describe multiple states simultaneously. The quantum Lanczos (QLanczos) algorithm is extended to MSQITE to accelerate the convergence. The present scheme is found to outperform both the standard QLanczos and the recently proposed folded-spectrum QITE in simulating excited states. Moreover, we demonstrate that spin contamination can be effectively removed by shifting the imaginary time propagator, and thus excited states with a particular spin quantum number are efficiently captured without falling into the different spin states that have lower energies. We also investigate how different levels of the unitary approximation employed in MSQITE can affect the results. The effectiveness of the algorithm over QITE is demonstrated by noise simulations for the H4 model system.