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arXiv · 1502.04792

Quantum Search with Multiple Walk Steps per Oracle Query

Thomas G. Wong·Andris Ambainis
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Abstract

We identify a key difference between quantum search by discrete- and continuous-time quantum walks: a discrete-time walk typically performs one walk step per oracle query, whereas a continuous-time walk can effectively perform multiple walk steps per query while only counting query time. As a result, we show that continuous-time quantum walks can outperform their discrete-time counterparts, even though both achieve quadratic speedups over their corresponding classical random walks. To provide greater equity, we allow the discrete-time quantum walk to also take multiple walk steps per oracle query while only counting queries. Then it matches the continuous-time algorithm's runtime, but such that it is a cubic speedup over its corresponding classical random walk. This yields the first example of a greater-than-quadratic speedup for quantum search over its corresponding classical random walk.

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Thomas G. Wong, Andris Ambainis. 2015-07-22. Quantum Search with Multiple Walk Steps per Oracle Query. https://doi.org/10.1103/physreva.92.022338

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