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Hybrid quantum-classical algorithms have been proposed to circumvent noiselimitations in quantum computers. Such algorithms delegate only a calculationof the expectation value to the quantum computer. Among them, the VariationalQuantum Eigensolver (VQE) has been implemented to study molecules and condensedmatter systems on small size quantum computers. Condensed matter systemsdescribed by the Hubbard model exhibit a rich phase diagram alongside exoticstates of matter. In this manuscript, we try to answer the question: how muchof the underlying physics of a 1D Hubbard chain is described by aproblem-inspired Variational Hamiltonian Ansatz (VHA) in a broad range ofparameter values ? We start by probing how much does the solution increasesfidelity with increasing ansatz complexity. Our findings suggest that even lowfidelity solutions capture energy and number of doubly occupied sites well,while spin-spin correlations are not well captured even when the solution is ofhigh fidelity. Our powerful simulation platform allows us to incorporate arealistic noise model and shows a successful implementation of noise-mitigationstrategies - post-selection and the Richardson extrapolation. Finally, wecompare our results with an experimental realization of the algorithm on IBMQuantum's ibmq_quito device.

Simulating strongly interacting Hubbard chains with the Variational Hamiltonian Ansatz on a quantum computer