Quantum Spectral Clustering of Mixed Graphs

Spectral graph partitioning is a well known technique to estimate clusters in undirected graphs. Recent approaches explored efficient spectral algorithms for directed and mixed graphs utilizing various matrix representations. Despite its success in clustering tasks, classical spectral algorithms suf...

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Bibliographic Details
Published in:2021 58th ACM/IEEE Design Automation Conference (DAC) pp. 463 - 468
Main Authors: Volya, Daniel, Mishra, Prabhat
Format: Conference Proceeding
Language:English
Published: IEEE 05.12.2021
Subjects:
Clustering algorithms
Computers
eigenvalue computation
eigenvector projection
Machine learning
Machine learning algorithms
Partitioning algorithms
Quantum computing
Runtime
spectral graph clustering
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Summary:Spectral graph partitioning is a well known technique to estimate clusters in undirected graphs. Recent approaches explored efficient spectral algorithms for directed and mixed graphs utilizing various matrix representations. Despite its success in clustering tasks, classical spectral algorithms suffer from a cubic growth in runtime. In this paper, we propose a quantum spectral clustering algorithm for discovering clusters and properties of mixed graphs. Our experimental results based on numerical simulations demonstrate that our quantum spectral clustering outperforms classical spectral clustering techniques. Specifically, our approach leads to a linear growth in complexity, while state-of-the-art classical counterpart leads to cubic growth. In a case study, we apply our proposed algorithm to preform unsupervised machine learning using both real and simulated quantum computers. This work opens an avenue for efficient implementation of machine learning algorithms on directed as well as mixed graphs by making use of the inherent potential quantum speedup.
DOI:10.1109/DAC18074.2021.9586308