Revisiting Shor's quantum algorithm for computing general discrete logarithms
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We heuristically demonstrate that Shor's algorithm for computing general discrete logarithms, modified to allow the semi-classical Fourier transform to be used with control qubit recycling, achieves a success probability of approximately 60 group operations that are evaluated quantumly, and by performing a limited search in the classical post-processing, we furthermore show how the algorithm can be modified to achieve a success probability over 99 provide concrete heuristic estimates of the success probability of the modified algorithm, as a function of the group order, the size of the search space in the classical post-processing, and the additional number of group operations evaluated quantumly. In analogy with our earlier works, we show how the modified quantum algorithm may be simulated classically when the logarithm and group order are both known.
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