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Polarization Requirements for Ensemble Implementations of Quantum Algorithms with a Single Bit Output

Brandon M. Anderson·David Collins
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Abstract

We compare the failure probabilities of ensemble implementations of quantum algorithms which use pseudo-pure initial states, quantified by their polarization, to those of competing classical probabilistic algorithms. Specifically we consider a class algorithms which require only one bit to output the solution to problems. For large ensemble sizes, we present a general scheme to determine a critical polarization beneath which the quantum algorithm fails with greater probability than its classical competitor. We apply this to the Deutsch-Jozsa algorithm and show that the critical polarization is 86.6%.

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Brandon M. Anderson, David Collins. 2005-08-07. Polarization Requirements for Ensemble Implementations of Quantum Algorithms with a Single Bit Output. https://doi.org/10.1103/physreva.72.042337

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