Abstract
Kronecker graphs, obtained by repeatedly performing the Kronecker product of the adjacency matrix of an "initiator" graph with itself, have risen in popularity in network science due to their ability to generate complex networks with real-world properties. We explore spatial search by continuous-time quantum walk on Kronecker graphs. Specifically, we give analytical proofs for quantum search on first-, second-, and third-order Kronecker graphs with the complete graph as the initiator, showing that search takes Grover's O(N) time. Numerical simulations indicate that higher-order Kronecker graphs with the complete initiator also support optimal quantum search.
| Original language | English (US) |
|---|---|
| Article number | 012338 |
| Journal | Physical Review A |
| Volume | 98 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jul 31 2018 |
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All Science Journal Classification (ASJC) codes
- Atomic and Molecular Physics, and Optics
Cite this
Quantum walk search on Kronecker graphs. / Wong, Thomas; Wünscher, Konstantin; Lockhart, Joshua; Severini, Simone.
In: Physical Review A, Vol. 98, No. 1, 012338, 31.07.2018.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Quantum walk search on Kronecker graphs
AU - Wong, Thomas
AU - Wünscher, Konstantin
AU - Lockhart, Joshua
AU - Severini, Simone
PY - 2018/7/31
Y1 - 2018/7/31
N2 - Kronecker graphs, obtained by repeatedly performing the Kronecker product of the adjacency matrix of an "initiator" graph with itself, have risen in popularity in network science due to their ability to generate complex networks with real-world properties. We explore spatial search by continuous-time quantum walk on Kronecker graphs. Specifically, we give analytical proofs for quantum search on first-, second-, and third-order Kronecker graphs with the complete graph as the initiator, showing that search takes Grover's O(N) time. Numerical simulations indicate that higher-order Kronecker graphs with the complete initiator also support optimal quantum search.
AB - Kronecker graphs, obtained by repeatedly performing the Kronecker product of the adjacency matrix of an "initiator" graph with itself, have risen in popularity in network science due to their ability to generate complex networks with real-world properties. We explore spatial search by continuous-time quantum walk on Kronecker graphs. Specifically, we give analytical proofs for quantum search on first-, second-, and third-order Kronecker graphs with the complete graph as the initiator, showing that search takes Grover's O(N) time. Numerical simulations indicate that higher-order Kronecker graphs with the complete initiator also support optimal quantum search.
UR - http://www.scopus.com/inward/record.url?scp=85051234658&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85051234658&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.98.012338
DO - 10.1103/PhysRevA.98.012338
M3 - Article
AN - SCOPUS:85051234658
VL - 98
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
SN - 1050-2947
IS - 1
M1 - 012338
ER -