Pontryagin Maximum Principle for Rydberg-blockaded state-to-state transfers: A semi-analytic approach

• URL: http://arxiv.org/abs/2512.13549v1
• Date: Mon, 15 Dec 2025 17:09:25 GMT
• Title: Pontryagin Maximum Principle for Rydberg-blockaded state-to-state transfers: A semi-analytic approach
• Authors: Federico Alberto Astolfi, Sven Jandura, Guido Pupillo,
• Abstract summary: We study time-optimal state-to-state control for two- and multi-qubit operations motivated by neutral-atom quantum processors.<n>For $N$ qubits, we classify normal and abnormal extremals, showcasing examples where abnormal solutions are either absent or suboptimal.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study time-optimal state-to-state control for two- and multi-qubit 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 semi-analytic approach to the Pontryagin Maximum Principle 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, semi-analytic 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.

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