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Benchmarks for quantum computers from Shor's algorithm
E. Davis·November 27, 2021
Physics
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Abstract
Properties of Shor's algorithm and the related period-finding algorithm could serve as benchmarks for the operation of a quantum computer. Distinctive universal behaviour is expected for the probability for success of the period-finding algorithm as the input quantum register is increased through its critical size of $\mathfrak{m}_0=\lceil 2\log_2 r\rceil$ qubits (where $r$ is the period sought). Use of quadratic non-residues permits unequivocal predictions to be made about the outcome of the factoring algorithm.