  We introduce a quantum Monte Carlo inspired reweighting scheme to accurately
compute energies from optimally short quantum circuits. This effectively hybrid
quantum-classical approach features both entanglement provided by a short
quantum circuit, and the presence of an effective non-unitary operator at the
same time. The functional form of this projector is borrowed from classical
computation and is able to filter-out high-energy components generated by a
sub-optimal variational quantum heuristic ansatz. The accuracy of this approach
is demonstrated numerically in finding energies of entangled ground-states of
many-body lattice models. We demonstrate a practical implementation on IBM
quantum hardwares up to an 8 qubits circuit.
