将量子电路分解为局部子电路，解决训练量子模型时的内存与梯度消失问题。
Quantum Algorithm for Distributed Reduction of Entanglements (QADR): A Trainable and Simulation-Efficient QML Framework
- 把大尺寸量子电路拆成围绕每个目标比特的局部子电路，减少计算依赖。
- 在2000个特征上成功运行，而传统方法因内存不足崩溃。
- 适合高维量子机器学习任务，尤其在资源受限的量子设备上使用。
在噪声中等规模量子（NISQ）环境下训练变分量子电路（VQC）面临严重计算瓶颈：经典态矢量模拟的内存随量子比特数呈指数增长（$\mathcal{O}(2^n)$），且全局代价函数易出现梯度消失（$\mathcal{O}(1/2^n)$）。本文提出量子分布式纠缠削减算法（QADR），一种混合量子-经典机器学习框架，将全局 $n$-量子比特 VQC 分解为作用于各目标量子比特因果光锥内的局部子电路。该方法使经典模拟内存复杂度从 $\mathcal{O}(2^n)$ 降低至 $\mathcal{O}(n \cdot 2^{2d+1})$（$d$ 为光锥半径），同时自然缓解全局梯度消失问题。我们在 MNIST 数据集和高维 NASA IMS 风力涡轮机诊断任务上对比了 QADR 与标准全局 VQC、支持向量机（SVM）、两种定制化类比神经网络（CANN 与 PMNN）。结果表明，QADR 具有优异可扩展性，在 $n_{\text{features}}=2000$ 时仍能运行，而标准 VQC 因内存耗尽失败，且性能达到或超过优化后的经典架构。
原文摘要 · Abstract (English)
Training Variational Quantum Circuits (VQCs) under Noisy Intermediate-Scale Quantum (NISQ) constraints introduces severe computational limitations: classical statevector simulation memory scales exponentially ($\mathcal{O}(2^n)$), and global cost functions suffer from barren plateaus where gradient variance decays exponentially ($\mathcal{O}(1/2^n)$). This paper introduces and evaluates the Quantum Algorithm for Distributed Reduction of Entanglements (QADR), a hybrid quantum-classical machine learning framework that decomposes a global $n$-qubit VQC into localized sub-circuits operating approximately within the causal light cones of individual target qubits. QADR reduces classical simulation memory scaling from $\mathcal{O}(2^n)$ to $\mathcal{O}(n \cdot 2^{2d+1})$ for a light cone radius $d$, while naturally mitigating global barren plateaus. We benchmark QADR against standard global VQCs, Support Vector Machines (SVM), and two customized classical parameter-matched neural networks (CANN and PMNN) on the MNIST dataset and the high-dimensional NASA IMS wind turbine drivetrain diagnostic task. QADR demonstrates excellent scalability, operating successfully at $n_{\text{features}}=2000$ where standard global VQCs crash due to memory exhaustion, while matching or exceeding the performance of optimized classical architectures.
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