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We present a new formulation of monotonically convergent algorithms whichallows to optimize both the control duration and the field fluence. A standardalgorithm designs a control field of fixed duration which both brings thesystem close to the target state and minimizes its fluence, whereas here weinclude in addition the optimization of the duration in the cost functional. Weapply this new algorithm to the control of spin systems in Nuclear MagneticResonance. We show how to implement CNOT gates in systems of two and fourcoupled spins.

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