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Repeat-until-success strategy is a standard method to obtain success with aprobability which grows exponentially in the number of iterations. However,since quantum systems are disturbed after a quantum measurement, it is notstraightforward how to perform repeat-until-success strategies in certainquantum algorithms. In this paper, we propose a new structure for probabilistichigher-order transformation named success-or-draw, which allows arepeat-until-success implementation. For that we provide a universalconstruction of success-or-draw structure which works for any probabilistichigher-order transformation on unitary operations. We then present asemidefinite programming approach to obtain optimal success-or-draw protocolsand analyze in detail the problem of inverting a general unitary operation.

Success-or-Draw: A Strategy Allowing Repeat-Until-Success in Quantum Computation