TY - JOUR
T1 - Quantum walk search on Kronecker graphs
AU - Wong, Thomas G.
AU - Wünscher, Konstantin
AU - Lockhart, Joshua
AU - Severini, Simone
N1 - Funding Information:
Thanks to Chris Godsil for useful discussions. This project is a part of K.W.'s Master's thesis. J.L. acknowledges financial support by the Engineering and Physical Sciences Research Council (Grant No. EP/L015242/1). S.S. is supported by the Royal Society, EPSRC, the National Natural Science Foundation of China, and the ARO-MURI Grant No. W911NF-17-1-0304 (US DOD, UK MOD, and UK EPSRC under the Multidisciplinary University Research Initiative).
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.
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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 -