Pontryagin Maximum Principle for Rydberg-blockaded state-to-state transfers: A semi-analytic approach
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| Format: | Preprint |
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2025
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| _version_ | 1866916014884651008 |
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| author | Astolfi, Federico Alberto Jandura, Sven Pupillo, Guido |
| author_facet | Astolfi, Federico Alberto Jandura, Sven Pupillo, Guido |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_13549 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pontryagin Maximum Principle for Rydberg-blockaded state-to-state transfers: A semi-analytic approach Astolfi, Federico Alberto Jandura, Sven Pupillo, Guido Quantum Physics Optimization and Control 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. |
| title | Pontryagin Maximum Principle for Rydberg-blockaded state-to-state transfers: A semi-analytic approach |
| topic | Quantum Physics Optimization and Control |
| url | https://arxiv.org/abs/2512.13549 |