  We propose a modification of the Variational Quantum Eigensolver algorithm
for electronic structure optimization using quantum computers, named
non-unitary Variational Quantum Eigensolver (nu-VQE), in which a non-unitary
operator is combined with the original system Hamiltonian leading to a new
variational problem with a simplified wavefunction Ansatz. In the present work,
we use, as non-unitary operator, the Jastrow factor, inspired from classical
Quantum Monte Carlo techniques for simulation of strongly correlated electrons.
The method is applied to prototypical molecular Hamiltonians for which we
obtain accurate ground state energies with shallower circuits, at the cost of
an increased number of measurements. Finally, we also show that this method
achieves an important error mitigation effect that drastically improves the
quality of the results for VQE optimizations on today's noisy quantum
computers. The absolute error in the calculated energy within our scheme is one
order of magnitude smaller than the corresponding result using traditional VQE
methods, with the same circuit depth.
