基于随机张量网络模拟的可扩展林德布拉德噪声学习

中文摘要 AI 辅助

学习大规模开放量子系统中的耗散率是近期量子技术面临的主要障碍，因为现有的林德布拉德估计方法通常受限于小系统规模，原因是优化过程中反复求解林德布拉德方程会带来计算复杂度。在此，我们提出一种用于林德布拉德耗散率的可扩展噪声学习框架，将随机模拟方法张量跳跃法（Tensor Jump Method, TJM）与基于局域可观测量期望值时间序列定义的最小二乘代价函数的无梯度优化相结合。我们在伊辛模型的两种噪声模型上验证了该方法：一是位点分辨（局域）模型，对每个位点学习独立的耗散率，位点规模N_site达16；二是空间均匀（全局）模型，仅含7个参数，可扩展至N_site=160。我们补充了一系列严格的可证明保证以完善这些数值结果：TJM密度矩阵估计量的弗罗贝尼乌斯方差被证明等于(1-Tr[ρ²])/N_traj，这是基于纯度的随机估计误差的精确表征；对于厄米跳跃算子，相应的纯度演化被证明是单调非递增的；在有限协方差距离假设下，代价函数的标准差随系统规模减小，因此当系统增大时，需要更少的轨迹即可达到固定的目标精度。这种可扩展数值方法与严格理论保证的结合，使基于TJM的噪声学习成为表征大型量子设备中耗散、指导未来误差缓解和量子纠错工作的实用基础。

英文摘要

Learning dissipation rates in large-scale open quantum systems is a major obstacle for near-term quantum technologies, as existing Lindblad estimation methods are typically limited to small system sizes due to the computational complexity of repeatedly solving the Lindblad equation during optimization. Here, we propose a scalable noise-learning framework for Lindblad dissipation rates that combines a stochastic simulation method, the Tensor Jump Method (TJM), with gradient-free optimization of a least-squares cost-function defined on time series of local-observable expectation values. We demonstrate the approach on two noise models in the Ising model: a site-resolved (local) model, in which independent dissipation rates are learned for each site up to $N_{\mathrm{site}}=16$, and a spatially homogeneous (global) model with only seven parameters, scaled to $N_{\mathrm{site}}=160$ sites.We complement these numerical results with a series of exact, provable guarantees: the Frobenius variance of the TJM density-matrix estimator is shown to equal $(1-\mathrm{Tr}[ρ^2])/N_{\mathrm{traj}}$, an exact purity-based characterization of the stochastic estimation error; the corresponding purity evolution is proven to be monotonically non-increasing for Hermitian jump operators; and, under a finite covariance distance assumption, the standard deviation of the cost-function is shown to decrease with system size, so that fewer trajectories are needed to reach a fixed target accuracy as the system grows. Together, this combination of scalable numerics and rigorous theoretical guarantees positions TJM-based noise learning as a practical foundation for characterizing dissipation in large quantum devices and for guiding future work on error mitigation and quantum error correction.

发表机构

• Zuse Institute Berlin（柏林齐泽研究所）
• Weierstrass Institute（魏尔斯特拉斯研究所）
• Technical University of Munich（慕尼黑工业大学）
• MQSC
• Software Competence Center Hagenberg (SCCH)（哈根贝格软件能力中心）

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