Quantum walk search on Kronecker graphs

Thomas Wong, Konstantin Wünscher, Joshua Lockhart, Simone Severini

Research output: Contribution to journalArticle

2 Scopus citations


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 languageEnglish (US)
Article number012338
JournalPhysical Review A
Issue number1
Publication statusPublished - Jul 31 2018


All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics

Cite this

Wong, T., Wünscher, K., Lockhart, J., & Severini, S. (2018). Quantum walk search on Kronecker graphs. Physical Review A, 98(1), [012338]. https://doi.org/10.1103/PhysRevA.98.012338