Sampling, rates, and reaction currents through reverse stochastic quantization on quantum computers

TL;DR

This paper introduces a quantum computing approach using stochastic quantization to efficiently sample from Boltzmann distributions and compute reaction currents, addressing challenges in statistical mechanics and rare-event processes.

Contribution

It presents a novel quantum algorithm leveraging stochastic quantization for sampling and reaction rate calculations, without relying on oracles or quantum walk operators.

Findings

Quantum states can be variationally prepared for unbiased sampling.

Reaction rate constants are obtained as ground state energies.

Hybrid quantum-classical schemes help explore complex configuration spaces.

Abstract

The quest for improved sampling methods to solve statistical mechanics problems of physical and chemical interest proceeds with renewed efforts since the invention of the Metropolis algorithm, in 1953. In particular, the understanding of thermally activated rare-event processes between long-lived metastable states, such as protein folding, is still elusive. In this case, one needs both the finite-temperature canonical distribution function and the reaction current between the reactant and product states, to completely characterize the dynamic. Here we show how to tackle this problem using a quantum computer. We use the connection between a classical stochastic dynamics and the Schroedinger equation, also known as stochastic quantization, to variationally prepare quantum states allowing us to unbiasedly sample from a Boltzmann distribution. Similarly, reaction rate constants can be computed as ground state energies of suitably transformed operators, following the supersymmetric extension of the formalism. Finally, we propose a hybrid quantum-classical sampling scheme to escape local minima, and explore the configuration space in both real-space and spin hamiltonians. We indicate how to realize the quantum algorithms constructively, without assuming the existence of oracles, or quantum walk operators. The quantum advantage concerning the above applications is discussed.