Quantum Riemannian Cubics with Obstacle Avoidance for Quantum Geometric Model Predictive Control

TL;DR

This paper introduces a geometric model predictive control method for quantum systems that ensures smooth, constraint-compliant trajectories on the projective Hilbert space, demonstrated on a two-level system.

Contribution

It develops a novel control framework using Riemannian cubics and structure-preserving discretization for quantum systems with constraints.

Findings

Successfully applied to a two-level quantum system on the Bloch sphere.

Provides stability guarantees for the closed-loop quantum control system.

Enables obstacle avoidance in quantum state trajectories.

Abstract

We propose a geometric model predictive control framework for quantum systems subject to smoothness and state constraints. By formulating quantum state evolution intrinsically on the projective Hilbert space, we penalize covariant accelerations to generate smooth trajectories in the form of Riemannian cubics, while incorporating state-dependent constraints through potential functions. A structure-preserving variational discretization enables receding-horizon implementation, and a Lyapunov-type stability result is established for the closed-loop system. The approach is illustrated on the Bloch sphere for a two-level quantum system, providing a viable pathway toward predictive feedback control of constrained quantum dynamics.