Abstract
Hybrid classical-quantum algorithms aim at variationally solving optimisation
problems, using a feedback loop between a classical computer and a quantum
co-processor, while benefitting from quantum resources. Here we present
experiments demonstrating self-verifying, hybrid, variational quantum
simulation of lattice models in condensed matter and high-energy physics.
Contrary to analog quantum simulation, this approach forgoes the requirement of
realising the targeted Hamiltonian directly in the laboratory, thus allowing
the study of a wide variety of previously intractable target models. Here, we
focus on the Lattice Schwinger model, a gauge theory of 1D quantum
electrodynamics. Our quantum co-processor is a programmable, trapped-ion analog
quantum simulator with up to 20 qubits, capable of generating families of
entangled trial states respecting symmetries of the target Hamiltonian. We
determine ground states, energy gaps and, by measuring variances of the
Schwinger Hamiltonian, we provide algorithmic error bars for energies, thus
addressing the long-standing challenge of verifying quantum simulation.
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