Abstract
A randomly walking quantum particle evolving by Schrödinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time Θ(N3/4). We give a weighted version of this graph that preserves vertex transitivity, and we show that the time to search on it can be reduced to nearly Θ(N). To prove this, we introduce two extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges and a method to determine how precisely the jumping rate of the quantum walk must be chosen.
| Original language | English (US) |
|---|---|
| Article number | 032320 |
| Journal | Physical Review A - Atomic, Molecular, and Optical Physics |
| Volume | 92 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 21 2015 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Atomic and Molecular Physics, and Optics
Cite this
Faster quantum walk search on a weighted graph. / Wong, Thomas.
In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 92, No. 3, 032320, 21.09.2015.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Faster quantum walk search on a weighted graph
AU - Wong, Thomas
PY - 2015/9/21
Y1 - 2015/9/21
N2 - A randomly walking quantum particle evolving by Schrödinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time Θ(N3/4). We give a weighted version of this graph that preserves vertex transitivity, and we show that the time to search on it can be reduced to nearly Θ(N). To prove this, we introduce two extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges and a method to determine how precisely the jumping rate of the quantum walk must be chosen.
AB - A randomly walking quantum particle evolving by Schrödinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time Θ(N3/4). We give a weighted version of this graph that preserves vertex transitivity, and we show that the time to search on it can be reduced to nearly Θ(N). To prove this, we introduce two extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges and a method to determine how precisely the jumping rate of the quantum walk must be chosen.
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U2 - 10.1103/PhysRevA.92.032320
DO - 10.1103/PhysRevA.92.032320
M3 - Article
VL - 92
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
SN - 1050-2947
IS - 3
M1 - 032320
ER -