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    Area of Science:

    • Quantum Information Science
    • Quantum Computing
    • Quantum Technologies

    Background:

    • High-dimensional quantum gates are crucial for advancing quantum computing.
    • Existing quantum gate designs can be complex and require numerous components.

    Purpose of the Study:

    • To present a simplified 4x4-dimensional controlled-NOT (CNOT) quantum gate.
    • To utilize a weak cross-Kerr medium with two photons and two degrees of freedom (DoFs).

    Main Methods:

    • Encoding control qudits in photonic polarization and target qudits in the path DoF.
    • Implementing the CNOT gate using only two instances of the Kerr medium.
    • Utilizing two photons, each with distinct degrees of freedom.

    Main Results:

    • Achieved a simplified circuit design requiring only two Kerr medium interactions, down from six.
    • Demonstrated high fidelity and success probability, approaching 1 under optimal conditions.
    • Successfully implemented a 4x4-dimensional CNOT gate.

    Conclusions:

    • The proposed protocol offers a more efficient and simplified approach to high-dimensional quantum gates.
    • This advancement has significant implications for the development of quantum computing and related technologies.
    • The use of fewer components leads to more practical and scalable quantum circuits.