Learning Quantum-Samplers for Stochastic Processes with Quantum Sequence Models

TL;DR

This paper introduces quantum sequence models with recurrent quantum circuits that efficiently generate coherent superpositions of stochastic processes, significantly improving accuracy over baseline models especially with limited data.

Contribution

The authors develop a novel recurrent quantum circuit architecture for modeling stochastic processes, enabling linear growth in complexity and improved training from observational data.

Findings

Models outperform baseline quantum Born machines in accuracy.

Recurrent quantum circuits grow linearly with time horizon.

Significant improvements in data-sparse regimes.

Abstract

Quantum circuits that generate coherent superpositions of stochastic processes are key to many downstream quantum-accelerated tasks, such as risk analysis, importance sampling, and DNA sequencing. However, traditional methods for designing such circuits from data face immense challenges, given the exponential growth in the size of the associated probability vectors as the desired simulation time horizon increases. Here, we introduce quantum sequence models that leverage a recurrent quantum circuit structure to generate coherent superpositions with circuit complexity that grows linearly with the desired time horizon; together with a recurrent variant of the parameter-shift rule, we train these models from observational data. When benchmarked against baseline quantum Born machines, our constructions exhibit orders-of-magnitude improvements in model accuracy in data-sparse regimes.