  Quantum simulations are bound to be one of the main applications of near-term
quantum computers. Quantum chemistry and condensed matter physics are expected
to benefit from these technological developments. Several quantum simulation
methods are known to prepare a state on a quantum computer and measure the
desired observables. The most resource economic procedure is the variational
quantum eigensolver (VQE), which has traditionally employed unitary coupled
cluster as the ansatz to approximate ground states of many-body fermionic
Hamiltonians. A significant caveat of the method is that the initial state of
the procedure is a single reference product state with no entanglement
extracted from a classical Hartree-Fock calculation. In this work, we propose
to improve the method by initializing the algorithm with a more general
fermionic Gaussian state, an idea borrowed from the field of nuclear physics.
We show how this Gaussian reference state can be prepared with a linear-depth
circuit of quantum matchgates. By augmenting the set of available gates with
nearest-neighbor phase coupling, we generate a low-depth circuit ansatz that
can accurately prepare the ground state of correlated fermionic systems. This
extends the range of applicability of the VQE to systems with strong pairing
correlations such as superconductors, atomic nuclei, and topological materials.
