Tractable Infinite-Horizon Stochastic Model Predictive Control for Quantum Filtering via Eigenstate Reduction

TL;DR

This paper introduces a computationally efficient stochastic model predictive control framework for quantum systems, leveraging eigenstate reduction to simplify the infinite-horizon problem and improve scalability.

Contribution

It develops a tractable SMPC method for quantum filtering that avoids Monte Carlo sampling by using eigenstate reduction, enabling scalable quantum control.

Findings

Reduces computational complexity of quantum SMPC

Maintains stability and performance guarantees

Demonstrates scalability on multi-level and Ising systems

Abstract

Model predictive control has shown potential to enhance the robustness of quantum control systems. In this work, we propose a tractable Stochastic Model Predictive Control (SMPC) framework for finite-dimensional quantum systems under continuous-time measurement and quantum filtering. Using the almost-sure eigenstate reduction of quantum trajectories, we prove that the infinite-horizon stochastic objective collapses to a fidelity term that is computable in closed form from the one-step averaged state. Consequently, the online SMPC step requires only deterministic propagation of the filter and a terminal fidelity evaluation. An advantage of this method is that it eliminates per-horizon Monte Carlo scenario sampling and significantly reduces computational load while retaining the essential stochastic dynamics. We establish equivalence and mean-square stability guarantees, and validate the approach on multi-level and Ising-type systems, demonstrating favorable scalability compared to sampling-based SMPC.