Introduction To The Pontryagin Maximum Principle For Quantum Optimal Control Direct

The Pontryagin Maximum Principle is much more than an arcane mathematical theorem. For quantum optimal control, it:

Result: optimal control is — pulse switches sign at specific times. Matches known “π-pulse” but allows shorter if bounded amplitude. The Pontryagin Maximum Principle is much more than

$x(0) = x_0$

where $L(\psi(t),u(t))$ is the cost functional, $\gamma$ is a penalty parameter, and $|\psi_f \rangle$ is the target state. u(t))$ is the cost functional

One defines the costate as an operator ( \Lambda(t) ) (the "influence matrix"). The PMP then yields control laws involving commutators of ( \Lambda ) with control Hamiltonians. This is now used to design optimal pulses for and noise-resistant gate synthesis . $\gamma$ is a penalty parameter

$u^ (t) = \arg\max_u \in U H(x^ (t),\lambda^*(t),u)$