Variational quantum simulation of the quantum critical regime

TL;DR

This paper introduces a variational quantum algorithm to simulate and identify the quantum critical regime at finite temperatures, demonstrating its effectiveness on the Kitaev model with potential for studying complex quantum systems.

Contribution

It proposes a novel variational approach using free energy minimization on quantum computers to explore quantum critical phenomena at finite temperatures.

Findings

Successfully identified the quantum critical regime in the Kitaev model

Evaluated temperature dependence of correlation length and phase coherence time

Demonstrated feasibility on few-qubit quantum devices

Abstract

The quantum critical regime marks a zone in the phase diagram where quantum fluctuation around the critical point plays a significant role at finite temperatures. While it is of great physical interest, simulation of the quantum critical regime can be difficult on a classical computer due to its intrinsic complexity. In this paper, we propose a variational approach, which minimizes the variational free energy, to simulate and locate the quantum critical regime on a quantum computer. The variational quantum algorithm adopts an ansatz by performing an unitary operator on a product of a single-qubit mixed state, in which the entropy can be analytically obtained from the initial state, and thus the free energy can be accessed conveniently. With numeral simulation, we show, using the one-dimensional Kitaev model as a demonstration, the quantum critical regime can be identified by accurately evaluating the temperature crossover line. Moreover, the dependence of both the correlation length and the phase coherence time with the temperature are evaluated for the thermal states. Our work suggests a practical way as well as a first step for investigating quantum critical systems at finite temperatures on quantum devices with few qubits.