Digital quantum simulation and Pseudoquantum Simulation of $\mathbb{Z}_2$ Gauge Higgs Model

TL;DR

This paper introduces a quantum algorithm for simulating the $ ext{Z}_2$ gauge-Higgs model on a small lattice, combining quantum and classical methods to explore its phase diagram and topological properties.

Contribution

It develops a novel digital quantum simulation algorithm for the $ ext{Z}_2$ gauge-Higgs model and demonstrates a pseudoquantum simulation on classical hardware to analyze its phase structure.

Findings

Identification of the topological properties of the deconfined phase

Clarification of the phase diagram and critical points

Observation that the tricritical point lies on the first-order critical line

Abstract

We present a quantum algorithm for digital quantum simulation of the $\mathbb{Z}_2$ gauge-Higgs model on a $3\times 3$ lattice, which is based on Trotter decomposition, the quantum adiabatic algorithm and its circuit realization. Then we perform a classical demonstration, dubbed a pseudoquantum simulation, on a GPU simulator. We obtain useful results on this model, which suggest the topological properties of the deconfined phase and help to clarify the phase diagram. It is suggested that the tricitical point, where the second-order critical lines of deconfinement-confinement transition and of deconfinement-Higgs transition meet, seems to be on the the first-order critical line of confinement-Higgs transition, at a point other than the end of this critical line.