  One of the most promising applications for near term quantum computers is the
simulation of physical quantum systems, particularly many-electron systems in
chemistry and condensed matter physics. In solid state physics, finding the
correct symmetry broken ground state of an interacting electron system is one
of the central challenges. The Variational Hamiltonian Ansatz (VHA), a
variational hybrid quantum-classical algorithm especially suited for finding
the ground state of a solid state system, will in general not prepare a broken
symmetry state unless the initial state is chosen to exhibit the correct
symmetry. In this work, we discuss three variations of the VHA designed to find
the correct broken symmetry states close to a transition point between
different orders. As a test case we use the two-dimensional Hubbard model where
we break the symmetry explicitly by means of external fields coupling to the
Hamiltonian and calculate the response to these fields. For the calculation we
simulate a gate-based quantum computer and also consider the effects of
dephasing noise on the algorithms. We find that two of the three algorithms are
in good agreement with the exact solution for the considered parameter range.
The third algorithm agrees with the exact solution only for a part of the
parameter regime, but is more robust with respect to dephasing compared to the
other two algorithms.
