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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>N</a:mi> </a:math> qubits. For <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mi>N</b:mi> <b:mo>=</b:mo> <b:mn>2</b:mn> </b:mrow> </b:math> 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.