Quantum search with multiple walk steps per oracle query

Thomas G. Wong, Andris Ambainis

Research output: Contribution to journalArticle

13 Scopus citations


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 a greater-than-quadratic speedup for quantum search over its corresponding classical random walk.

Original languageEnglish (US)
Article number022338
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number2
StatePublished - Aug 18 2015


All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

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