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Bioinspired Quantum Oracle Circuits for Biomolecular Solutions of the Maximum Cut Problem.

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    This study introduces novel biomolecular and quantum algorithms for the maximum cut problem, an NP-complete challenge. The quantum approach offers a quadratic speedup, significantly improving efficiency for complex graph partitioning tasks.

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    Area of Science:

    • Computer Science
    • Quantum Computing
    • Algorithm Analysis

    Background:

    • The maximum cut problem involves partitioning graph vertices to maximize edges between partitions.
    • It is an NP-complete problem with broad applications in various scientific and engineering fields.
    • Classical algorithms face significant computational challenges for large graphs.

    Purpose of the Study:

    • To propose novel biomolecular and quantum algorithms for solving the maximum cut problem.
    • To demonstrate a quadratic speedup in temporal and spatial complexity compared to classical methods.
    • To validate the quantum algorithm's feasibility through experimental simulation.

    Main Methods:

    • Development of a biomolecular algorithm for graph partitioning.
    • Inspiration from the biomolecular approach to design a quantum algorithm.
    • Analysis of temporal and spatial complexities for the quantum algorithm.
    • Experimental verification using IBM's quantum simulator.

    Main Results:

    • A biomolecular and a quantum algorithm are proposed for the maximum cut problem.
    • The quantum algorithm achieves a quadratic speedup, reducing complexity to O(n) and O(m).
    • The algorithm is identified as optimal among oracle-related quantum algorithms for NP-complete problems.
    • Successful experimental demonstration on a small graph instance.

    Conclusions:

    • The proposed quantum algorithm provides an efficient solution for the maximum cut problem.
    • The biomolecular inspiration offers a new avenue for quantum algorithm design.
    • Experimental results confirm the practical feasibility and potential of the quantum approach.