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An Exact Quantum Polynomial-Time Algorithm for Simon's Problem

Gilles Brassard·Peter Hoyer
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Abstract

We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's problem can be solved in this way, whereas previous algorithms required quantum polynomial time in the expected sense only, without upper bounds on the worst-case running time. This is achieved by generalizing both Simon's and Grover's algorithms and combining them in a novel way. It follows that there is a decision problem that can be solved in exact quantum polynomial time, which would require expected exponential time on any classical bounded-error probabilistic computer if the data is supplied as a black box.

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Gilles Brassard, Peter Hoyer. 1997-04-14. An Exact Quantum Polynomial-Time Algorithm for Simon's Problem. https://doi.org/10.1109/istcs.1997.595153

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