用神经微分方程学习开放量子系统的退相干行为,突破噪声干扰限制。
Lindbladian Learning with Neural Differential Equations
- 结合最大似然与瞬时测量数据,构建非凸损失函数优化框架。
- 在噪声比达10⁴、6个量子比特下仍能准确还原退相干过程。
- 适用于中性原子、超导等多类量子硬件,对相位和热噪声鲁棒。
从测量数据中推断多体量子系统的动力学生成元,对量子处理器的验证、校准与控制至关重要。当系统为开放系统时,该任务远比纯幺正情况复杂,因为相干与耗散机制可能产生相似的测量统计,且长时间数据对相干耦合不敏感。本文针对此所谓林德布拉德学习问题,采用在多个实验友好瞬时时间点进行泡利测量的最大似然方法,利用瞬态动力学更丰富的信息内容。为克服由此带来的非凸似然损失曲面,引入神经微分方程项增强物理模型,并在训练过程中逐步移除,以提取可解释的林德布拉德算符解。该方法在具有二维连接性的中性原子、超导哈密顿量以及自旋-1/2链上的海森堡XYZ和PXP模型上均能可靠学习开放系统动力学。对于耗散部分,展示出对相位噪声、热噪声及其组合的鲁棒性。算法可在噪声信号比跨度达四个数量级、系统规模至N=6量子比特、采样次数少于5×10⁵的情况下稳健推断耗散系统。
原文摘要 · Abstract (English)
Inferring the dynamical generator of a many-body quantum system from measurement data is essential for the verification, calibration, and control of quantum processors. When the system is open, this task becomes considerably harder than in the purely unitary case, because coherent and dissipative mechanisms can produce similar measurement statistics and long-time data can be insensitive to coherent couplings. Here we tackle this so-called Lindbladian learning problem of open-system characterisation with maximum-likelihood on Pauli measurements at multiple experimentally friendly \emph{transient} times, exploiting the richer information content of transient dynamics. To navigate the resulting non-convex likelihood loss-landscape, we augment the physical model neural differential-equation term, which is progressively removed during training to distil an interpretable Lindbladian solution. Our method reliably learns open-system dynamics across neutral-atom (with 2D connectivity) and superconducting Hamiltonians, as well as the Heisenberg XYZ, and PXP models on a spin-1/2 chain. For the dissipative part, we show robustness over phase noise, thermal noise, and their combination. Our algorithm can robustly infer these dissipative systems over noise-to-signal ratios spanning four orders of magnitude, and system sizes up to $N=6$ qubits with fewer than $5 \times 10^5$ shots.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。