Continuous-time evolution via probabilistic angle interpolation and its applications

TL;DR

This paper introduces a continuous-time stochastic evolution algorithm using probabilistic angle interpolation, eliminating Trotter errors and demonstrating applications in quantum chemistry and many-body physics.

Contribution

It presents a novel continuous-time limit approach for probabilistic angle interpolation algorithms, with noise mitigation and practical demonstrations on quantum hardware.

Findings

Eliminates Trotter errors in the evolution algorithm.

Successfully estimates molecular ground-state energy and out-of-time correlators.

Validates the approach through simulations and trapped-ion experiments.

Abstract

We explore the applicability of a stochastic time-evolution algorithm based on probabilistic angle interpolation. To simplify the pre-processing of the algorithm, we take the continuous-time limit, thereby explicitly eliminating Trotter errors and streamlining the resource analysis. We also introduce a noise-mitigation method tailored to it. As demonstrations, we apply the algorithm to two representative problems: estimating the ground-state energy of the $H_3^+$ molecular Hamiltonian and computing out-of-time-ordered correlators in the sparse Sachdev--Ye--Kitaev model. We evaluate the protocol's performance through numerical simulations and experiments on a trapped-ion quantum computer, Quantinuum Reimei.