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A key goal of digital quantum computing is the simulation of fermionicsystems such as molecules or the Hubbard model. Unfortunately, for present andnear-future quantum computers the use of quantum error correction schemes isstill out of reach. Hence, the finite error rate limits the use of quantumcomputers to algorithms with a low number of gates. The variational Hamiltonianansatz (VHA) has been shown to produce the ground state in good approximationin a manageable number of steps. Here we study explicitly the effect of gateerrors on its performance. The VHA is inspired by the adiabatic quantumevolution under the influence of a time-dependent Hamiltonian, where the -ideally short - fixed Trotter time steps are replaced by variationalparameters. The method profits substantially from quantum variational errorsuppression, e.g., unitary quasi-static errors are mitigated within thealgorithm. We test the performance of the VHA when applied to the Hubbard modelin the presence of unitary control errors on quantum computers with realisticgate fidelities.

Finding the ground state of the Hubbard model by variational methods on a quantum computer with gate errors