For Quantum Optimal Control !link! | Introduction To The Pontryagin Maximum Principle

to be optimal, it must maximize the Hamiltonian at every point in time. This often leads to "bang-bang" control solutions where the field switches between its maximum and minimum allowed values. Why it Matters for Quantum Tech PMP is essential for reaching the physical limits of quantum dynamics, such as the Quantum Speed Limit . Key applications include: Quantum State Transfer

where $x(t) \in \mathbbR^n$ is the state of the system, $u(t) \in \mathbbR^m$ is the control input, $L(x(t),u(t))$ is the cost functional, and $f(x(t),u(t))$ is the system dynamics. to be optimal, it must maximize the Hamiltonian

System: [ \dot\psi = -i\left( \frac\omega_02\sigma_z + u_x(t) \sigma_x \right) \psi,\quad |u_x(t)|\le 1 ] Goal: transfer (|0\rangle \to |1\rangle) in minimal time (T). to be optimal