Hamilton-Jacobi-Bellman equations for Rydberg-blockade processes

Abstract

We discuss time-optimal control problems for two setups involving globally driven Rydberg atoms in the blockade limit by deriving the associated Hamilton-Jacobi-Bellman equations. From these equations, we extract the globally optimal trajectories and the corresponding controls for several target processes of the atomic system, using a generalized method of characteristics. We apply this method to retrieve known results for CZ and C-phase gates, and to find new optimal pulses for all elementary processes involved in the universal quantum computation scheme introduced in [Physical Review Letters 131, 170601 (2023)].

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Cited by in corpus (2)

• Pontryagin Maximum Principle for Rydberg-blockaded state-to-state transfers: A semi-analytic approach
• Symmetric $C_Z$ gate for ultracold neutral atoms based on counterdiabatic driving at Rydberg excitation