Abstract
Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes the structure of the graph causes the walker to get trapped, such that the probability of finding the marked vertex is limited. We give an example with two linked cliques, proving that the captive probability can be liberated by increasing the weights of the links. This allows the search to succeed with probability 1 without increasing the energy scaling of the algorithm. Further increasing the weights, however, slows the runtime, so the optimal search requires weights that are neither too weak nor too strong.
| Original language | English (US) |
|---|---|
| Article number | 022304 |
| Journal | Physical Review A |
| Volume | 94 |
| Issue number | 2 |
| DOIs | |
| State | Published - Aug 4 2016 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Atomic and Molecular Physics, and Optics
Cite this
Engineering the success of quantum walk search using weighted graphs. / Wong, Thomas; Philipp, Pascal.
In: Physical Review A, Vol. 94, No. 2, 022304, 04.08.2016.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Engineering the success of quantum walk search using weighted graphs
AU - Wong, Thomas
AU - Philipp, Pascal
PY - 2016/8/4
Y1 - 2016/8/4
N2 - Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes the structure of the graph causes the walker to get trapped, such that the probability of finding the marked vertex is limited. We give an example with two linked cliques, proving that the captive probability can be liberated by increasing the weights of the links. This allows the search to succeed with probability 1 without increasing the energy scaling of the algorithm. Further increasing the weights, however, slows the runtime, so the optimal search requires weights that are neither too weak nor too strong.
AB - Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes the structure of the graph causes the walker to get trapped, such that the probability of finding the marked vertex is limited. We give an example with two linked cliques, proving that the captive probability can be liberated by increasing the weights of the links. This allows the search to succeed with probability 1 without increasing the energy scaling of the algorithm. Further increasing the weights, however, slows the runtime, so the optimal search requires weights that are neither too weak nor too strong.
UR - http://www.scopus.com/inward/record.url?scp=84983469990&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84983469990&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.94.022304
DO - 10.1103/PhysRevA.94.022304
M3 - Article
AN - SCOPUS:84983469990
VL - 94
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
SN - 1050-2947
IS - 2
M1 - 022304
ER -