Fermionic approach to variational quantum simulation of Kitaev spin models

TL;DR

This paper introduces a fermionic variational ansatz for simulating Kitaev spin models using VQE, leveraging their exact solvability via fermion mapping, reducing qubit requirements, and extending applicability beyond integrable regimes.

Contribution

The paper presents a novel fermionic variational ansatz tailored for Kitaev models, improving accuracy and efficiency in quantum simulations, especially in non-integrable regimes.

Findings

The fermionic ansatz accurately reproduces ground states in the solvable limit.

It reduces qubit count by a factor of two compared to traditional methods.

The approach extends effectively beyond integrability, outperforming other VQE strategies.

Abstract

We use the variational quantum eigensolver (VQE) to simulate Kitaev spin models with and without integrability breaking perturbations, focusing in particular on the honeycomb and square-octagon lattices. These models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation and is capable of expressing the exact ground state in the solvable limit. We also demonstrate that this ansatz can be extended beyond this limit to provide excellent accuracy when compared to other VQE approaches. In certain cases, this fermionic representation is advantageous because it reduces by a factor of two the number of qubits required to perform the simulation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.