Graph comparison via nonlinear quantum search

M. Chiew, K. de Lacy, C. H. Yu, S. Marsh, J. B. Wang

Research output: Contribution to journalArticle

Abstract

Graph comparison is an established NP-hard problem. In this paper, we present an efficiently scaling quantum algorithm which finds the size of the maximum common edge subgraph for any pair of unlabelled graphs and thus provides a meaningful measure of graph similarity. The algorithm makes use of a two-part quantum dynamic process: in the first part, we obtain information crucial for the comparison of two graphs through linear quantum computation. However, this information is hidden in the quantum system with such a vanishingly small amplitude that even quantum algorithms such as Grover’s search are not fast enough to distil it efficiently. In order to extract the information, we call upon techniques in nonlinear quantum computing to provide the speed-up necessary for an efficient algorithm. The linear quantum circuit requires O(n3log 3(n) log log (n)) elementary quantum gates, and the nonlinear evolution under the Gross–Pitaevskii equation has a time scaling of O(1gn2log3(n)loglog(n)), where n is the number of vertices in each graph and g is the strength of the Gross–Pitaevskii nonlinearity. Through this example, we demonstrate the power of nonlinear quantum search techniques to solve a subset of NP-hard problems.

Original languageEnglish
Article number302
JournalQuantum Information Processing
Volume18
Issue number10
DOIs
Publication statusPublished - 1 Oct 2019

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quantum computation
Graph in graph theory
Quantum Algorithms
Computational complexity
NP-hard Problems
scaling
Quantum computers
Scaling
Quantum Circuits
Gross-Pitaevskii Equation
Quantum Computing
Quantum Computation
Quantum Dynamics
set theory
Dynamic Process
apexes
Quantum Systems
nonlinearity
Subgraph
Speedup

Cite this

Chiew, M. ; de Lacy, K. ; Yu, C. H. ; Marsh, S. ; Wang, J. B. / Graph comparison via nonlinear quantum search. In: Quantum Information Processing. 2019 ; Vol. 18, No. 10.
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Graph comparison via nonlinear quantum search. / Chiew, M.; de Lacy, K.; Yu, C. H.; Marsh, S.; Wang, J. B.

In: Quantum Information Processing, Vol. 18, No. 10, 302, 01.10.2019.

Research output: Contribution to journalArticle

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