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Implementing Graph-Theoretic Feature Selection by Quantum Approximate Optimization Algorithm.

Yaochong Li, Ri-Gui Zhou, Ruiqing Xu

    IEEE Transactions on Neural Networks and Learning Systems
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    Summary
    This summary is machine-generated.

    This study introduces three quantum-approximate optimization algorithm (QAOA)-based graph-theoretic feature selection (GTFS) methods. These novel quantum approaches outperform classical methods for feature selection tasks.

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    Area of Science:

    • Computer Science
    • Quantum Computing
    • Graph Theory

    Background:

    • Feature selection is crucial but computationally intractable due to exponential search space.
    • Near-term quantum computing offers potential advantages for complex computational tasks.

    Purpose of the Study:

    • To investigate three graph-theoretic feature selection (GTFS) methods using the quantum approximate optimization algorithm (QAOA).
    • To formulate GTFS problems as quadratic binary optimization problems solvable by QAOA.
    • To explore the integration of these quantum methods with classical algorithms for large-scale problems.

    Main Methods:

    • Formulation of minimum cut (MinCut), densest k-subgraph (DkS), and maximal independent set/minimal vertex cover (MIS/MVC) as quadratic binary problems.
    • Application of the quantum approximate optimization algorithm (QAOA) to solve these formulated problems.
    • Integration with Tabu search for enhanced performance on large-scale datasets.

    Main Results:

    • Quantum-based GTFS models demonstrate superior performance compared to their classical counterparts across 20 datasets.
    • The proposed methods achieve a complexity of O(p n^2), where p is QAOA layers and n is the number of features.
    • Successful application of QAOA for solving graph-theoretic problems in feature selection.

    Conclusions:

    • Quantum-enhanced GTFS methods provide a powerful alternative to classical approaches.
    • QAOA is effective for tackling intractable feature selection problems.
    • The proposed methods offer efficient solutions with manageable quantum resource requirements.