Surrogate-constructed scalable-circuits adaptive variational quantum eigensolver in the Schwinger model

Inspired by recent advancements in simulating periodic systems on quantum computers, we develop an approach to further advance the simulation of these systems, named (SC)${}^{2}$-ADAPT-VQE. Our approach extends the scalable-circuits ADAPT-VQE framework, which builds an ansatz from a pool of coordinate-invariant operators defined for arbitrarily large, though not arbitrarily small, volumes. Our method uses a classically tractable ``surrogate constructed'' method to remove irrelevant operators from the pool, reducing the minimum size for which the scalable circuits are defined. Bringing together the scalable circuits and the surrogate constructed approaches forms the core of the (SC)${}^{2}$ methodology. Our approach allows for a wider set of classical computations on small volumes, which can be used for a more robust extrapolation protocol. While developed in the context of lattice models, the surrogate construction portion is applicable to a wide variety of problems where information about the relative importance of operators in the pool is available. As an example, we use it to compute the properties of the Schwinger model---quantum electrodynamics for a single, massive fermion in $1+1$ dimensions---and show that our method can be used to accurately extrapolate to the continuum limit.