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

Physical Review A
 Pub Date:
 August 2015
 DOI:
 10.1103/PhysRevA.92.022338
 arXiv:
 arXiv:1502.04792
 Bibcode:
 2015PhRvA..92b2338W
 Keywords:

 03.67.Ac;
 Quantum algorithms protocols and simulations;
 Quantum Physics
 EPrint:
 10 pages, 5 figures