The Variational Quantum Eigensolver (VQE) was the first near-term algorithm for quantum computers. One of the constraints on scaling VQE to be relevant for molecules of industrial interest is the number of operations that a quantum computer must perform to get a sufficiently accurate answer. In this paper, we devise a new framework that aims to cut down the number of operations to make solving these problems much more feasible.
Quantum simulations are bound to be one of the main applications of near-term quantum com- puters. Quantum chemistry and condensed matter physics are expected to benefit from these tech- nological 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 sig- nificant 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 Gaus- sian 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,
