Introduction To The Pontryagin Maximum Principle For Quantum Optimal Control ~upd~ Jun 2026

Before discussing the PMP, we must formalize the task. Consider a quantum system whose state ( |\psi(t)\rangle ) evolves under the time-dependent Schrödinger equation (setting ( \hbar = 1 )):

Where ( O ) is a target observable (e.g., projector onto a desired state) and ( \mathcalL ) penalizes large or oscillatory controls. Before discussing the PMP, we must formalize the task

While PMP is elegant, applying it to large quantum systems faces hurdles: Before discussing the PMP

In quantum optimal control, the PMP has been applied to optimize the control of quantum systems. The goal of quantum optimal control is to find a control input that steers a quantum system from an initial state to a target state while minimizing a cost functional. Before discussing the PMP, we must formalize the task