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We numerically study the implementation of a NOT gate by laser pulses in amodel molecular system presenting two electronic surfaces coupled by nonadiabatic interactions. The two states of the bit are the fundamental states ofthe cis-trans isomers of the molecule. The gate is classical in the sense thatit involves a one-qubit flip so that the encoding of the outputs is based onpopulation analysis which does not take the phases into account. This gate canalso be viewed as a double photo-switch process with the property that the sameelectric field controls the two isomerizations. As an example, we considerone-dimensional cuts in a model of the retinal in rhodopsin already proposed inthe literature. The laser pulses are computed by the Multi Target OptimalControl Theory with chirped pulses as trial fields. Very high fidelities areobtained. We also examine the stability of the control when the system iscoupled to a bath of oscillators modelled by an Ohmic spectral density. Thebath correlation time scale being smaller than the pulse duration the dynamicsis carried out in the Markovian approximation.

Not gate in a cis-trans photoisomerization model