Variational Quantum Eigensolver for SU($N$) Fermions

TL;DR

This paper applies the variational quantum eigensolver to SU(N) fermions to explore their ground-state properties and quantum phases, proposing a basis for a quantum simulator on noisy intermediate-scale quantum computers.

Contribution

It introduces a method to study SU(N) fermions using VQE, enabling phase mapping and ground-state analysis on NISQ devices.

Findings

Ground-state properties of SU(N) fermions analyzed

Persistent current used to identify quantum phases

Framework for a current-based quantum simulator

Abstract

Variational quantum algorithms aim at harnessing the power of noisy intermediate-scale quantum computers, by using a classical optimizer to train a parameterized quantum circuit to solve tractable quantum problems. The variational quantum eigensolver is one of the aforementioned algorithms designed to determine the ground-state of many-body Hamiltonians. Here, we apply the variational quantum eigensolver to study the ground-state properties of $N$-component fermions. With such knowledge, we study the persistent current of interacting SU($N$) fermions, which is employed to reliably map out the different quantum phases of the system. Our approach lays out the basis for a current-based quantum simulator of many-body systems that can be implemented on noisy intermediate-scale quantum computers.