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arXiv · 1409.3305

Fixed-point quantum search with an optimal number of queries

Theodore J. Yoder·Guang Hao Low·Isaac L. Chuang
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Abstract

Grover's quantum search and its generalization, quantum amplitude amplification, provide quadratic advantage over classical algorithms for a diverse set of tasks, but are tricky to use without knowing beforehand what fraction $λ$ of the initial state is comprised of the target states. In contrast, fixed-point search algorithms need only a reliable lower bound on this fraction, but, as a consequence, lose the very quadratic advantage that makes Grover's algorithm so appealing. Here we provide the first version of amplitude amplification that achieves fixed-point behavior without sacrificing the quantum speedup. Our result incorporates an adjustable bound on the failure probability, and, for a given number of oracle queries, guarantees that this bound is satisfied over the broadest possible range of $λ$.

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Theodore J. Yoder, Guang Hao Low, Isaac L. Chuang. 2014-11-24. Fixed-point quantum search with an optimal number of queries. https://doi.org/10.1103/physrevlett.113.210501

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