利用分布式随机量子电路中的噪声
Taking Advantage of Noise in Distributed Random Quantum Circuits
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中文总结 AI 辅助
本文通过二阶矩传递矩阵理论，将噪声谱分解为径向和角向分支，发现振幅阻尼可在分布式随机电路中实现窄窗口的噪声辅助哈尔混合，但排除噪声的普遍加速作用。
中文摘要 AI 辅助
添加噪声可以使随机量子电路看起来更快，而不会使其幺正动力学更加随机。这一区别在模块化处理器中尤为重要，在模块化处理器中，局部门使每个核心随机化，而稀缺的核心间通信必须将该随机性传播到整个设备。在本文中，我们通过一种简化的二阶矩传递矩阵理论来研究这一问题，该理论针对受振幅阻尼、去极化和退相位噪声信道影响的分布式随机电路中的泡利二阶矩。关键步骤是将噪声谱分解为两个分支：径向分支，描述非恒等泡利权重的耗散损失；角向分支，描述在存活的非平凡扇区内的类哈尔混合。这种分离给出了一个简单的弱噪声判据：只有当噪声抑制纵向布洛赫分量强于横向平面时，噪声才对角向随机化有用。在所考虑的三种信道中，这选择振幅阻尼作为唯一局部有利的情况，而去极化噪声是中性的，退相位则受径向损失主导。对于多核架构，我们推导了径向泄漏的通用一阶定律，并在不同信道、拓扑和核心分区下数值跟踪角向分支。结果揭示了真正的噪声辅助哈尔混合的狭窄窗口，最明显的是振幅阻尼，但排除了噪声带来的普遍加速。因此，该框架区分了有用的噪声随机化与单纯的耗散。
英文摘要
Adding noise can make a random quantum circuit look faster without making its unitary dynamics more random. This distinction is especially relevant in modular processors, where local gates randomize each core and scarce inter-core communication must spread that randomness across the full device. In this paper, we study this problem with a reduced second-moment transfer-matrix theory for Pauli second moments in distributed random circuits affected by the amplitude-damping, depolarizing, and dephasing noise channels. The key step is to resolve the noisy spectrum into two branches: a radial branch, describing dissipative loss of non-identity Pauli weight, and an angular branch, describing Haar-like mixing within the surviving nontrivial sector. This separation gives a simple weak-noise criterion: noise is useful for angular randomization only when it suppresses the longitudinal Bloch component more strongly than the transverse plane. Among the three channels considered, this selects amplitude damping as the only locally favorable case, while depolarizing noise is neutral and dephasing is dominated by radial loss. For multicore architectures, we derive a universal first-order law for radial leakage and track the angular branch numerically across different channels, topologies, and core partitions. The results reveal narrow windows of genuine noise-assisted Haar mixing, most clearly for amplitude damping, but rule out a generic speed-up by noise. The framework therefore distinguishes useful noisy randomization from mere dissipation.
发表机构
- Universidad Politécnica de Madrid（马德里理工大学）
- Universidad Autónoma de Madrid（马德里自治大学）
- Comisión Nacional de Energía Atómica, CONICET（国家原子能委员会，CONICET）
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