Preparing symmetry broken ground states with variational quantum algorithms

TL;DR

This paper explores three variations of the Variational Hamiltonian Ansatz to effectively find symmetry-broken ground states in quantum systems, demonstrating their performance and robustness through simulations of the two-dimensional Hubbard model.

Contribution

It introduces and compares three modified VHA algorithms specifically designed to target symmetry-broken states near phase transitions in quantum simulations.

Findings

Two algorithms match exact solutions across parameter ranges.

One algorithm is more robust against dephasing noise.

Simulations confirm the effectiveness of the proposed methods.

Abstract

One of the most promising applications for near term quantum computers is the simulation of physical quantum systems, particularly many-electron systems in chemistry and condensed matter physics. In solid state physics, finding the correct symmetry broken ground state of an interacting electron system is one of the central challenges. The Variational Hamiltonian Ansatz (VHA), a variational hybrid quantum-classical algorithm especially suited for finding the ground state of a solid state system, will in general not prepare a broken symmetry state unless the initial state is chosen to exhibit the correct symmetry. In this work, we discuss three variations of the VHA designed to find the correct broken symmetry states close to a transition point between different orders. As a test case we use the two-dimensional Hubbard model where we break the symmetry explicitly by means of external fields coupling to the Hamiltonian and calculate the response to these fields. For the calculation we simulate a gate-based quantum computer and also consider the effects of dephasing noise on the algorithms. We find that two of the three algorithms are in good agreement with the exact solution for the considered parameter range. The third algorithm agrees with the exact solution only for a part of the parameter regime, but is more robust with respect to dephasing compared to the other two algorithms.