Abstract
The quantum factorization is probably the most famous algorithm in quantum computation. The algorithm succeeds only when some random number with an even order relative to factorized composite integer is fed as an input to the quantum period finding algorithm. Moreover, post processing of the quantum measurement recovers the correct order only for some subset of possible values. It is well known that numbers with even orders are found with probability not less than 1/2. However, numerical simulation proves that probability of such event exhibits grouping on some discrete levels above that limit. Thus, one may conclude that usage of the common bound leads to underestimation of the successful factorization probability. Empirical formulas on expected success probability introduced in the paper give rise to the more profound analysis of classic part behaviour of the Shor’s algorithm. The experimentally observed grouping still awaits for theoretical explanation.
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Zawadzki, P. (2010). Improved Estimation of Success Probability of the Shor’s Algorithm. In: Kwiecień, A., Gaj, P., Stera, P. (eds) Computer Networks. CN 2010. Communications in Computer and Information Science, vol 79. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13861-4_5
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DOI: https://doi.org/10.1007/978-3-642-13861-4_5
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