Sketching phase diagrams using low-depth variational quantum algorithms

TL;DR

This paper explores using low-depth variational quantum algorithms, specifically VQE, to sketch phase diagrams of quantum systems, potentially reducing resource requirements compared to classical simulations.

Contribution

It demonstrates that low-fidelity VQE states can effectively identify phase transitions and introduces a model-agnostic predictor based on energy improvement speed.

Findings

VQE can predict phase transition locations with reasonable accuracy.

Low-depth VQE states are sufficient for phase diagram sketching.

Energy improvement rate can serve as a phase transition indicator.

Abstract

Mapping out phase diagrams of quantum systems using classical simulations can be challenging or intractable due to the computational resources required to simulate even small quantum systems far away from the thermodynamic limit. We investigate using quantum computers and the Variational Quantum Eigensolver (VQE) for this task. In contrast to the task of preparing the exact ground state using VQE, sketching phase diagrams might require less quantum resources and accuracy, because low fidelity approximations to the ground state may be enough to correctly identify different phases. We used classical numerical simulations of low-depth VQE circuits to compute order parameters for four well-studied spin and fermion models which represent a mix of 1D and 2D, and exactly-solvable and classically hard systems. We find that it is possible to predict the location of phase transitions up to reasonable accuracy using states produced by VQE even when their overlap with the true ground state is small. Further, we introduce a model-agnostic predictor of phase transitions based on the speed with which the VQE energy improves with respect to the circuit depth, and find that in some cases this is also able to predict phase transitions.