Time-Optimal Control of Finite Dimensional Open Quantum Systems via a Model Predictive Strategy

TL;DR

This paper introduces a model predictive control framework for finite-dimensional open quantum systems that incorporates POVMs, providing a robust method to stabilize quantum states efficiently amidst environmental noise.

Contribution

It extends existing control strategies by integrating POVMs and stability analysis, enabling adaptive, measurement-guided control in open quantum systems.

Findings

Effective preservation of quantum coherence demonstrated in simulations.

High fidelity achieved across various noise channels.

Stability conditions ensure monotonic cost function decrease.

Abstract

To mitigate dissipative effects from environmental interactions and efficiently stabilize quantum states, time-optimal control has emerged as an effective strategy for open quantum systems. This paper extends the framework by incorporating Positive Operator-Valued Measures (POVMs) into the control process, enabling quantum measurements to guide control updates at each step. To address uncertainties in measurement outcomes, we derive a lower bound on the probability of obtaining a desired outcome from POVM-based measurements and establish stability conditions that ensure a monotonic decrease in the cost function. The proposed method is applied to finite-level open quantum systems, and we also present a detailed analysis of two-level systems under depolarizing, phase-damping, and amplitude-damping channels. Numerical simulations validate the effectiveness of the strategy in preserving coherence and achieving high fidelity across diverse noise environments.