Multiple network alignment on quantum computers

Anmer Daskin, Ananth Grama, Sabre Kais

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Comparative analyses of graph-structured datasets underly diverse problems. Examples of these problems include identification of conserved functional components (biochemical interactions) across species, structural similarity of large biomolecules, and recurring patterns of interactions in social networks. A large class of such analyses methods quantify the topological similarity of nodes across networks. The resulting correspondence of nodes across networks, also called node alignment, can be used to identify invariant subgraphs across the input graphs. Given k graphs as input, alignment algorithms use topological information to assign a similarity score to each k-tuple of nodes, with elements (nodes) drawn from each of the input graphs. Nodes are considered similar if their neighbors are also similar. An alternate, equivalent view of these network alignment algorithms is to consider the Kronecker product of the input graphs and to identify high-ranked nodes in the Kronecker product graph. Conventional methods such as PageRank and HITS (Hypertext-Induced Topic Selection) can be used for this purpose. These methods typically require computation of the principal eigenvector of a suitably modified Kronecker product matrix of the input graphs. We adopt this alternate view of the problem to address the problem of multiple network alignment. Using the phase estimation algorithm, we show that the multiple network alignment problem can be efficiently solved on quantum computers. We characterize the accuracy and performance of our method and show that it can deliver exponential speedups over conventional (non-quantum) methods.

Original languageEnglish
Pages (from-to)2653-2666
Number of pages14
JournalQuantum Information Processing
Volume13
Issue number12
DOIs
Publication statusPublished - 1 Jan 2014

Fingerprint

Quantum computers
Quantum Computer
quantum computers
Alignment
alignment
orthogonality
Vertex of a graph
Kronecker Product
Graph in graph theory
hypertext
Alternate
Information use
Biomolecules
Eigenvalues and eigenfunctions
Product Graph
Hypertext
PageRank
Structural Similarity
Identification Problem
Estimation Algorithms

Keywords

  • Network alignment
  • NP Problems
  • Phase estimation algorithms
  • Quantum algorithms
  • Quantum bioinformatics

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Electronic, Optical and Magnetic Materials
  • Statistical and Nonlinear Physics
  • Signal Processing
  • Modelling and Simulation
  • Theoretical Computer Science

Cite this

Multiple network alignment on quantum computers. / Daskin, Anmer; Grama, Ananth; Kais, Sabre.

In: Quantum Information Processing, Vol. 13, No. 12, 01.01.2014, p. 2653-2666.

Research output: Contribution to journalArticle

Daskin, Anmer ; Grama, Ananth ; Kais, Sabre. / Multiple network alignment on quantum computers. In: Quantum Information Processing. 2014 ; Vol. 13, No. 12. pp. 2653-2666.
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