TY - JOUR

T1 - Quantum search with multiple walk steps per oracle query

AU - Wong, Thomas G.

AU - Ambainis, Andris

N1 - Publisher Copyright:
© 2015 American Physical Society. ©2015 American Physical Society.

PY - 2015/8/18

Y1 - 2015/8/18

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevA.92.022338

DO - 10.1103/PhysRevA.92.022338

M3 - Article

AN - SCOPUS:84940781125

VL - 92

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 2

M1 - 022338

ER -