  A key goal of digital quantum computing is the simulation of fermionic
systems such as molecules or the Hubbard model. Unfortunately, for present and
near-future quantum computers the use of quantum error correction schemes is
still out of reach. Hence, the finite error rate limits the use of quantum
computers to algorithms with a low number of gates. The variational Hamiltonian
ansatz (VHA) has been shown to produce the ground state in good approximation
in a manageable number of steps. Here we study explicitly the effect of gate
errors on its performance. The VHA is inspired by the adiabatic quantum
evolution under the influence of a time-dependent Hamiltonian, where the -
ideally short - fixed Trotter time steps are replaced by variational
parameters. The method profits substantially from quantum variational error
suppression, e.g., unitary quasi-static errors are mitigated within the
algorithm. We test the performance of the VHA when applied to the Hubbard model
in the presence of unitary control errors on quantum computers with realistic
gate fidelities.
