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A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
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Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
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Efficient routing algorithm for trusted relay quantum key distribution networks via quantum reinforcement learning.

Yuheng Xie, Yuanchen Hao, Yuefeng Lin

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    |December 19, 2025
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    Summary
    This summary is machine-generated.

    A new quantum reinforcement learning algorithm, hybrid quantum deep deterministic policy gradient (HQ-DDPG), optimizes routing in trusted relay quantum key distribution networks (TR-QKDNs). It significantly improves convergence speed and resource efficiency compared to classical methods.

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    Area of Science:

    • Quantum Information Science
    • Network Security
    • Artificial Intelligence

    Background:

    • Trusted relay quantum key distribution networks (TR-QKDNs) require efficient routing algorithms for scalability.
    • Current routing methods face limitations in adaptability, parameter configuration, and computational complexity.

    Purpose of the Study:

    • To develop an intelligent routing algorithm for TR-QKDNs that dynamically optimizes decisions.
    • To address the limitations of existing routing approaches in complex network environments.

    Main Methods:

    • Proposed a hybrid quantum deep deterministic policy gradient (HQ-DDPG) algorithm integrating a quantum neural network (QNN) with deep deterministic policy gradient (DDPG).
    • Utilized a quantum single-source shortest path (QSSP) algorithm to reduce computational complexity.
    • Leveraged distributed quantum computing for QNN implementation.

    Main Results:

    • HQ-DDPG demonstrated nearly double the training convergence speed and reduced resource requirements by approximately 45 times compared to DDPG.
    • Achieved a quantum key delivery ratio above 91.35% under high-load demand, outperforming DDPG and optimized link state routing (OLSR).
    • The QNN enabled efficient solutions for large-scale TR-QKDN problems with fewer quantum resources.

    Conclusions:

    • The HQ-DDPG algorithm offers a superior, efficient, and scalable solution for routing in TR-QKDNs.
    • Quantum reinforcement learning shows significant potential for optimizing complex network operations.
    • The proposed approach enhances network expressiveness and performance in demanding conditions.