Multiple Network Alignment on Quantum Computers

TL;DR

This paper proposes a quantum computing approach to solve multiple network alignment problems efficiently, leveraging phase estimation to achieve exponential speedups over classical algorithms.

Contribution

It introduces a quantum algorithm for multiple network alignment that utilizes phase estimation, providing a potentially exponential speedup over traditional methods.

Findings

Quantum algorithm achieves exponential speedup.

Method accurately aligns multiple networks.

Potential for practical quantum network analysis.

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.