Variational simulation of quantum phase transitions induced by boundary fields

TL;DR

This paper demonstrates the use of variational quantum algorithms to simulate and analyze quantum phase transitions in a spin chain with boundary fields, combining theoretical, simulation, and experimental approaches.

Contribution

It introduces a variational quantum simulation method for studying boundary-induced quantum phase transitions in a spin chain, including experimental validation on superconducting hardware.

Findings

Successfully simulated phase transitions using VQE

Predicted critical boundary field values for different transitions

Experimental results align with noiseless simulations

Abstract

The characterization of quantum phase transitions is a fundamental task for the understanding of quantum phases of matter, with a number of potential applications in quantum technologies. In this work, we use digital quantum simulation as a resource to theoretically and experimentally study quantum phase transitions. More specifically, we implement the variational quantum eigensolver (VQE) algorithm to the one-dimensional spin-$1/2$ transverse-field Ising chain in the presence of boundary magnetic fields. Such fields can induce a rich phase diagram, including a first-order line and also a continuous wetting transition, which is a quantum version of the classical wetting surface phenomenon. We present results for noiseless simulations of the associated quantum circuits as well as hardware results taken from a superconducting quantum processor. For different regions of the phase diagram, the quantum algorithm allows us to predict the critical value of the magnetic fields responsible for either the first or second-order transitions occurring in the system.