Pontryagin maximum principle for Rydberg-blockaded state-to-state transfers: A semianalytic approach

We study time-optimal state-to-state control for two- and multiqubit operations motivated by neutral-atom quantum processors within the Rydberg blockade regime. Block diagonalization of the Hamiltonian simplifies the dynamics and enables the application of a semianalytic approach to the Pontryagin maximum principle (PMP) to derive optimal laser controls. We provide a general formalism for N qubits. For N = 2 qubits, we classify normal and abnormal extremals, showcasing examples where abnormal solutions are either absent or suboptimal. For normal extremals, we establish a correspondence between the laser detuning from atomic transitions and the motion of a classical particle in a quartic potential, yielding a reduced, semianalytic formulation of the control problem. Combining PMP-based insights with numerical optimization, our approach bridges analytic and computational methods for high-fidelity, time-optimal control.