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 a greater-than-quadratic speedup for quantum search over its corresponding classical random walk.
| Original language | English (US) |
|---|---|
| Article number | 022338 |
| Journal | Physical Review A - Atomic, Molecular, and Optical Physics |
| Volume | 92 |
| Issue number | 2 |
| DOIs | |
| State | Published - Aug 18 2015 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Atomic and Molecular Physics, and Optics
Cite this
Quantum search with multiple walk steps per oracle query. / Wong, Thomas; Ambainis, Andris.
In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 92, No. 2, 022338, 18.08.2015.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Quantum search with multiple walk steps per oracle query
AU - Wong, Thomas
AU - Ambainis, Andris
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 -