Improving performance of probabilistic programmable quantum processors

We present a systematic analysis how one can improve performance of probabilistic programmable quantum processors. We generalize a simple Vidal-Masanes-Cirac processor that realizes U(1) rotations on a qubit with the phase of the rotation encoded in a state of the program register. We show how the probability of success of the probabilistic processor can be enhanced by using the processor in loops. In addition we show that the same strategy can be utilized for a probabilistic implementation of non-unitary transformations on qubits. In addtion, we show that an arbitrary SU(2) transformations of qubits can be encoded in program state of a universal programmable probabilistic quantum processor. The probability of success of this processor can be enhanced by a systematic correction of errors via conditional loops. Finally, we show that all our results can be generalized also for qudits. In particular, we show how to implement SU (N) rotations of qudits via programmable quantum processor and how the performance of the processor can be enhanced when it is used in loops.