To break, or not to break: translation symmetry in adaptive quantum simulations of the lattice Schwinger model

Adaptive variational quantum simulation algorithms have been shown to be highly successful in efficiently finding the ground-state properties of small molecules. Some adaptive algorithms find paths to the target state in which certain problem symmetries, such as the particle-number preservation, are broken along the way but regained at the end; however, studies have found that preserving problem symmetries in the ansatz improves the convergence of the algorithm. This motivates the question: is symmetry-breaking beneficial or not? Moreover, do all symmetries (e.g., particle-number conservation, point-group, translation-invariance) behave similarly, or is the algorithm more sensitive to breaking some particular symmetries? We address these questions in the context of translation symmetry and particle-number conservation in the lattice Schwinger model, a discretized model of quantum electrodynamics in 1+1 dimensions.