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We use the variational quantum eigensolver (VQE) to simulate Kitaev spinmodels with and without integrability breaking perturbations, focusing inparticular on the honeycomb and square-octagon lattices. These models are wellknown for being exactly solvable in a certain parameter regime via a mapping tofree fermions. We use classical simulations to explore a novel variationalansatz that takes advantage of this fermionic representation and is capable ofexpressing the exact ground state in the solvable limit. We also demonstratethat this ansatz can be extended beyond this limit to provide excellentaccuracy when compared to other VQE approaches. In certain cases, thisfermionic representation is advantageous because it reduces by a factor of twothe number of qubits required to perform the simulation. We also comment on theimplications of our results for simulating non-Abelian anyons on quantumcomputers.

Fermionic approach to variational quantum simulation of Kitaev spin models