Abstract
We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has l integer self-loops, can be generalized to a quantum walk where each vertex has a single self-loop of real-valued weight l. We apply this real-valued lackadaisical quantum walk to two problems. First, we analyze it on the line or one-dimensional lattice, showing that it is exactly equivalent to a continuous deformation of the three-state Grover walk with faster ballistic dispersion. Second, we generalize Grover's algorithm, or search on the complete graph, to have a weighted self-loop at each vertex, yielding an improved success probability when 1 < 3+2 √2 ≈ 5.828.
| Original language | English (US) |
|---|---|
| Article number | 475301 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 50 |
| Issue number | 47 |
| DOIs | |
| State | Published - Oct 25 2017 |
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All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)
Cite this
Coined quantum walks on weighted graphs. / Wong, Thomas.
In: Journal of Physics A: Mathematical and Theoretical, Vol. 50, No. 47, 475301, 25.10.2017.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Coined quantum walks on weighted graphs
AU - Wong, Thomas
PY - 2017/10/25
Y1 - 2017/10/25
N2 - We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has l integer self-loops, can be generalized to a quantum walk where each vertex has a single self-loop of real-valued weight l. We apply this real-valued lackadaisical quantum walk to two problems. First, we analyze it on the line or one-dimensional lattice, showing that it is exactly equivalent to a continuous deformation of the three-state Grover walk with faster ballistic dispersion. Second, we generalize Grover's algorithm, or search on the complete graph, to have a weighted self-loop at each vertex, yielding an improved success probability when 1 < 3+2 √2 ≈ 5.828.
AB - We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has l integer self-loops, can be generalized to a quantum walk where each vertex has a single self-loop of real-valued weight l. We apply this real-valued lackadaisical quantum walk to two problems. First, we analyze it on the line or one-dimensional lattice, showing that it is exactly equivalent to a continuous deformation of the three-state Grover walk with faster ballistic dispersion. Second, we generalize Grover's algorithm, or search on the complete graph, to have a weighted self-loop at each vertex, yielding an improved success probability when 1 < 3+2 √2 ≈ 5.828.
UR - http://www.scopus.com/inward/record.url?scp=85034219808&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85034219808&partnerID=8YFLogxK
U2 - 10.1088/1751-8121/aa8c17
DO - 10.1088/1751-8121/aa8c17
M3 - Article
AN - SCOPUS:85034219808
VL - 50
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 47
M1 - 475301
ER -