Fighting noise with noise: a stochastic projective quantum eigensolver

Abstract

Quantum Monte Carlo (QMC) algorithms have proven extremely effective at lowering the computational overhead of electronic structure calculations in a classical setting. In the current noisy intermediate scale quantum (NISQ) era of quantum computation, there are several limitations on the available hardware resources, such as low qubit count, decoherence times and gate noise, which preclude the application of many current hybrid quantum-classical algorithms to non-trivial quantum chemistry problems. Here, we propose combining some of the fundamental elements of conventional QMC algorithms -- stochastic sampling of both the wavefunction and the Hamiltonian of interest -- with an imaginary-time propagation based projective quantum eigensolver. At the cost of increased noise, which can be easily averaged over in a classical Monte Carlo estimation, we obtain a method with quantum computational requirements that are both generally low and highly tunable.