Simulating gauge theories with variational quantum eigensolvers in superconducting microwave cavities

TL;DR

This paper proposes a bosonic variational quantum eigensolver using superconducting microwave cavities to simulate gauge theories, overcoming qubit limitations and enabling the study of complex models like the U(1) Higgs model with a topological term.

Contribution

It introduces a novel bosonic VQE platform with tunable nonlinearities in microwave cavities for simulating infinite-dimensional gauge theories.

Findings

Allows simulation of models with infinite-dimensional Hilbert spaces.

Enables realization of a wide range of bosonic ansatz states.

Potential to address models with sign problems in Monte Carlo methods.

Abstract

Quantum-enhanced computing methods are promising candidates to solve currently intractable problems. We consider here a variational quantum eigensolver (VQE), that delegates costly state preparations and measurements to quantum hardware, while classical optimization techniques guide the quantum hardware to create a desired target state. In this work, we propose a bosonic VQE using superconducting microwave cavities, overcoming the typical restriction of a small Hilbert space when the VQE is qubit based. The considered platform allows for strong nonlinearities between photon modes, which are highly customisable and can be tuned in situ, i.e. during running experiments. Our proposal hence allows for the realization of a wide range of bosonic ansatz states, and is therefore especially useful when simulating models involving degrees of freedom that cannot be simply mapped to qubits, such as gauge theories, that include components which require infinite-dimensional Hilbert spaces. We thus propose to experimentally apply this bosonic VQE to the U(1) Higgs model including a topological term, which in general introduces a sign problem in the model, making it intractable with conventional Monte Carlo methods.