Metropolis-style random sampling of quantum gates for the estimation of low-energy observables

TL;DR

This paper introduces a quantum algorithm that uses a Metropolis-style sampling method on quantum gates to estimate low-energy observables of a Hamiltonian, enabling ground state property approximation.

Contribution

It presents a novel quantum sampling approach that applies Metropolis algorithms directly to quantum circuits for low-energy state estimation.

Findings

Efficient sampling of quantum gates for low-energy observables

Ability to extrapolate from higher-energy states to ground state

Potential for improved quantum simulation accuracy

Abstract

We propose a quantum algorithm to compute low-energy expectation values of a quantum Hamiltonian by sampling a partition function associated with the average energy of that Hamiltonian. For any given quantum circuit-Hamiltonian pair, there is an associated average energy. The sampling is done through an accept/reject Metropolis-style algorithm on the quantum gates of the circuit itself. Observables calculated under the canonical ensemble from these samples of circuits are extrapolated from higher-energies to the ground state.