Non-unitary operations for ground-state calculations in near term quantum computers

TL;DR

This paper presents a hybrid quantum-classical method that uses non-unitary operators inspired by quantum Monte Carlo to improve ground-state energy calculations on near-term quantum computers, demonstrated on IBM hardware.

Contribution

It introduces a novel reweighting scheme combining short quantum circuits with classical filtering to enhance ground-state energy estimation.

Findings

Numerical validation on many-body lattice models shows improved accuracy.

Practical implementation achieved on IBM quantum hardware with up to 8 qubits.

The method effectively filters high-energy components from variational quantum states.

Abstract

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.