Low-depth circuit ansatz for preparing correlated fermionic states on a quantum computer

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 eigenvalue solver, 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. We show how this gaussian reference state can be prepared with a linear-depth quantum circuit. We also describe a low-depth circuit ansatz that can accurately prepare the ground state of correlated fermionic systems. This extends the range of applicability of the variational eigenvalue solver to systems with strong pairing correlations such as superconductors, atomic nuclei and topological materials.