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We compare the failure probabilities of ensemble implementations of quantumalgorithms which use pseudo-pure initial states, quantified by theirpolarization, to those of competing classical probabilistic algorithms.Specifically we consider a class algorithms which require only one bit tooutput the solution to problems. For large ensemble sizes, we present a generalscheme to determine a critical polarization beneath which the quantum algorithmfails with greater probability than its classical competitor. We apply this tothe Deutsch-Jozsa algorithm and show that the critical polarization is 86.6%.Comment: 11 pages, 3 figure

Polarization requirements for ensemble implementations of quantum algorithms with a single-bit output