发表机构
Dulwich College Shanghai; Shanghai Jiao Tong University（上海德威国际学校; 上海交通大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对6量子比特Lindblad模型，确定从截断刘维尔谱恢复耗散率的可识别性阈值，发现最小二乘法在n=6时精度远优于表格学习方法，结论适用于无噪声模拟器谱。
AI 中文摘要
开放量子系统会通过不同的耗散过程损失能量和相位相干性，但这些过程可能产生重叠的动力学特征。刘维尔谱概括了这类系统的弛豫方式，但尚不清楚需要多少该谱的信息才能区分底层的耗散率。我们针对6量子比特Lindblad模型中的振幅阻尼和退相位研究该问题，其谱可解析推导。我们仅保留最慢的非稳态谱模式，探究需要多少个模式才能实现每个耗散率的可恢复性。我们证明布居数模式不含退相位信息，这在相关率区间内为均匀退相位可识别性设定了D=2^n个保留模式的下界。实测的恢复阈值在n=4、5、6时达到该下界，而n=3时仍高于该下界。在n=6时，最小二乘法实现的联合绝对误差均值为10^-9量级，而4种表格学习方法的对应值为4.355×10^-4。鲁棒性测试表明，当谱受到扰动或横向场破坏对易结构时，该优势会减弱。这些结果表明，保留的谱信息的数量和结构可决定耗散参数是否可恢复，且与所用估计器无关。本结论适用于无噪声模拟器谱，而非测量得到的谱。
英文摘要
Open quantum systems lose energy and phase coherence through different dissipative processes, but these processes can produce overlapping dynamical signatures. The Liouvillian spectrum summarizes how such a system relaxes, yet it is not obvious how much of that spectrum is needed to distinguish the underlying dissipation rates. We study this question for amplitude damping and dephasing in a six-qubit Lindblad model whose spectrum can be derived analytically. We retain only the slowest non-steady spectral modes and ask how many are required before each dissipative rate becomes recoverable. We show that population modes contain no dephasing information, which creates a lower bound of D = 2^n retained modes for uniform dephasing identifiability in the relevant rate regime. The measured recovery threshold reaches this bound at n = 4,5,6, while n = 3 remains above it. At n = 6, least squares achieves a mean joint absolute error of order 10^-9, compared with 4.355 x 10^-4 for four tabular learning methods. Robustness tests show that this advantage weakens when the spectra are perturbed and when a transverse field breaks the commuting structure. These results show that the amount and structure of retained spectral information can determine whether dissipative parameters are recoverable, independently of the estimator used. The present conclusions apply to noise-free simulator spectra rather than measurement-derived spectra.
Comments15 pages, 6 figures. Data and code are available at Zenodo, DOI: 10.5281/zenodo.22160077
