Generalized filtering of laser fields in optimal control theory: application to symmetry filtering of quantum gate operations

We present a modified version of a previously published algorithm (Gollub et al 2008 Phys. Rev. Lett. 101 073002) for obtaining an optimized laser field with more general restrictions on the search space of the optimal field. The modification leads to enforcement of the constraints on the optimal field while maintaining good convergence behaviour in most cases. We demonstrate the general applicability of the algorithm by imposing constraints on the temporal symmetry of the optimal fields. The temporal symmetry is used to reduce the number of transitions that have to be optimized for quantum gate operations that involve inversion (NOT gate) or partial inversion (Hadamard gate) of the qubits in a three-dimensional model of ammonia.