Quantum walk search on Kronecker graphs

Thomas Wong, Konstantin Wünscher, Joshua Lockhart, Simone Severini

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish (US)
Article number012338
JournalPhysical Review A
Volume98
Issue number1
DOIs
StatePublished - Jul 31 2018

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initiators
orthogonality
matrices
simulation

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

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 journalArticle

Wong, T, Wünscher, K, Lockhart, J & Severini, S 2018, 'Quantum walk search on Kronecker graphs', Physical Review A, vol. 98, no. 1, 012338. https://doi.org/10.1103/PhysRevA.98.012338
Wong T, Wünscher K, Lockhart J, Severini S. Quantum walk search on Kronecker graphs. Physical Review A. 2018 Jul 31;98(1). 012338. https://doi.org/10.1103/PhysRevA.98.012338
Wong, Thomas ; Wünscher, Konstantin ; Lockhart, Joshua ; Severini, Simone. / Quantum walk search on Kronecker graphs. In: Physical Review A. 2018 ; Vol. 98, No. 1.
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