Time-optimal control of two-level quantum systems by piecewise constant pulses
E Dionis, Dominique Sugny
Abstract
We apply an extension of the Pontryagin maximum principle to derive time-optimal controls of two-level quantum systems by means of piecewise constant pulses. Global optimal solutions are obtained for state-to-state transfer in the cases with one and two controls. Exact quantum speed limits are established as a function of the sampling period. We observe numerically an exponential convergence towards the minimum time in the continuous limit when this period goes to zero. We show that this convergence is only polynomial for a linearized quantum system. We discuss the experimental impact of this result.
Topics & Concepts
PiecewiseConstant (computer programming)MathematicsOptimal controlQuantumConvergence (economics)PolynomialApplied mathematicsMaximum principleLimit (mathematics)Exponential functionMathematical analysisControl theory (sociology)Mathematical optimizationPhysicsQuantum mechanicsControl (management)Computer scienceArtificial intelligenceEconomicsProgramming languageEconomic growthQuantum Information and CryptographyLaser-Matter Interactions and ApplicationsQuantum Mechanics and Applications