Concurrent VQE for Simulating Excited States of the Schwinger Model

TL;DR

This paper introduces a concurrent variational quantum eigensolver (cVQE) approach for efficiently computing excited states of the Schwinger model, demonstrating its effectiveness through classical simulations and a proof-of-principle quantum hardware experiment.

Contribution

It presents a novel cVQE method with specialized ansatz circuits for excited states, capable of scaling to large qubit systems and measuring low-lying spectra accurately.

Findings

Successfully computed multiple eigenstates with minimal ancillary qubits.

Classical simulations handled systems with up to 100 qubits.

Experimental demonstration on quantum hardware validated the approach.

Abstract

This work explores the application of the concurrent variational quantum eigensolver (cVQE) for computing excited states of the Schwinger model. By designing suitable ansatz circuits utilizing universal SO(4) or SO(8) qubit gates, we demonstrate how to efficiently obtain the lowest two, four, and eight eigenstates with one, two, and three ancillary qubits for both vanishing and non-vanishing background electric field cases. Simulating the resulting quantum circuits classically with tensor network techniques, we demonstrate the capability of our approach to compute the two lowest eigenstates of systems with up to $\mathcal{O}(100)$ qubits. Given that our method allows for measuring the low-lying spectrum precisely, we also present a novel technique for estimating the additive mass renormalization of the lattice based on the energy gap. As a proof-of-principle calculation, we prepare the ground and first-excited states with one ancillary and four physical qubits on quantum hardware, demonstrating the practicality of using the cVQE to simulate excited states.