Abstract
A randomly walking quantum particle evolving by Schrödinger's equation searches on d-dimensional cubic lattices in O(N) time when d≥5, and with progressively slower runtime as d decreases. This suggests that graph connectivity (including vertex, edge, algebraic, and normalized algebraic connectivities) is an indicator of fast quantum search, a belief supported by fast quantum search on complete graphs, strongly regular graphs, and hypercubes, all of which are highly connected. In this Letter, we show this intuition to be false by giving two examples of graphs for which the opposite holds true: one with low connectivity but fast search, and one with high connectivity but slow search. The second example is a novel two-stage quantum walk algorithm in which the walking rate must be adjusted to yield high search probability.
| Original language | English (US) |
|---|---|
| Article number | 110503 |
| Journal | Physical Review Letters |
| Volume | 114 |
| Issue number | 11 |
| DOIs | |
| State | Published - Mar 18 2015 |
| Externally published | Yes |
Fingerprint
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)
Cite this
Connectivity is a poor indicator of fast quantum search. / Meyer, David A.; Wong, Thomas.
In: Physical Review Letters, Vol. 114, No. 11, 110503, 18.03.2015.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Connectivity is a poor indicator of fast quantum search
AU - Meyer, David A.
AU - Wong, Thomas
PY - 2015/3/18
Y1 - 2015/3/18
N2 - A randomly walking quantum particle evolving by Schrödinger's equation searches on d-dimensional cubic lattices in O(N) time when d≥5, and with progressively slower runtime as d decreases. This suggests that graph connectivity (including vertex, edge, algebraic, and normalized algebraic connectivities) is an indicator of fast quantum search, a belief supported by fast quantum search on complete graphs, strongly regular graphs, and hypercubes, all of which are highly connected. In this Letter, we show this intuition to be false by giving two examples of graphs for which the opposite holds true: one with low connectivity but fast search, and one with high connectivity but slow search. The second example is a novel two-stage quantum walk algorithm in which the walking rate must be adjusted to yield high search probability.
AB - A randomly walking quantum particle evolving by Schrödinger's equation searches on d-dimensional cubic lattices in O(N) time when d≥5, and with progressively slower runtime as d decreases. This suggests that graph connectivity (including vertex, edge, algebraic, and normalized algebraic connectivities) is an indicator of fast quantum search, a belief supported by fast quantum search on complete graphs, strongly regular graphs, and hypercubes, all of which are highly connected. In this Letter, we show this intuition to be false by giving two examples of graphs for which the opposite holds true: one with low connectivity but fast search, and one with high connectivity but slow search. The second example is a novel two-stage quantum walk algorithm in which the walking rate must be adjusted to yield high search probability.
UR - http://www.scopus.com/inward/record.url?scp=84925967768&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84925967768&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.114.110503
DO - 10.1103/PhysRevLett.114.110503
M3 - Article
AN - SCOPUS:84925967768
VL - 114
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 11
M1 - 110503
ER -