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Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
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Qudit-based high-dimensional controlled-not gate.

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    We developed a deterministic high-dimensional quantum logic gate using photons and nitrogen-vacancy centers. This hybrid approach enhances quantum computing speed and can be extended to larger quantum systems.

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    Area of Science:

    • Quantum Information Science
    • Quantum Computing
    • Quantum Optics

    Background:

    • High-dimensional quantum systems offer greater capacity for quantum information processing.
    • Quantum logic gates are essential for building quantum computers.
    • Previous implementations often require ancillary systems, complicating operations.

    Purpose of the Study:

    • To propose a deterministic high-dimensional controlled-not (CNOT) gate.
    • To utilize a hybrid system of photons and nitrogen-vacancy (NV) centers.
    • To avoid the need for ancillary qudits in the quantum gate implementation.

    Main Methods:

    • A single photon's spatial and polarization states act as a 4-dimensional control qudit.
    • Two electron-spin states in NV centers function as a 4-dimensional target qudit.
    • The gate operates deterministically using optical elements and NV center storage.

    Main Results:

    • A deterministic 4x4-dimensional CNOT gate was successfully proposed.
    • The hybrid system leverages easily operated photonic control and stable NV center targets.
    • The proposed gate is scalable to n x n dimensions (n > 4).

    Conclusions:

    • The implemented CNOT gate demonstrates satisfactory efficiency and fidelity.
    • This work provides a pathway for enhanced quantum computing speeds.
    • The flexible design is applicable to various hybrid quantum systems and photonic degrees of freedom.