  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.
