Time-optimal monotonic convergent algorithms for the control of spin systems

Marc Lapert (1) , Julien Salomon (2) , Dominique Sugny (1)

1 ICB - Laboratoire Interdisciplinaire Carnot de Bourgogne
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We present a new formulation of monotonically convergent algorithms which allows to optimize both the control duration and the laser fluence. A standard algorithm designs a control field of fixed duration which both brings the system close to the target state and minimizes the laser fluence, whereas here we include in addition the optimization of the duration in the cost functional. We apply this new algorithm to the control of spin systems in Nuclear Magnetic Resonance. We show how to implement CNOT gates in systems of two and four coupled spins.

Mots clés: Quantum Control; NMR; optimal control

Domaines: Optimisation et contrôle [math.OC]

Marc Lapert, Julien Salomon, Dominique Sugny. Time-optimal monotonic convergent algorithms for the control of spin systems. Physical Review A : Atomic, molecular, and optical physics [1990-2015], 2012, 85 (3), pp.033406. ⟨10.1103/PhysRevA.85.033406⟩. ⟨hal-00654133⟩