提出高效学习开放量子系统结构的算法,支持非自适应测量与未知结构。
Learning the structure of open quantum systems
- 基于傅里叶系数迭代法,利用随机保罗测量电路学习量子系统动力学。
- 总演化时间仅需 $O(g d^2 /log(n) / \\ epsilon^2)$,误差可控。
- 适用于无先验结构信息的开放系统,也推广至高温吉布斯态学习。
我们设计了一种算法,可在总演化时间为 $O(g d^2 \log(n) / \varepsilon^2)$ 的条件下,以 $\varepsilon$ 误差学习 $n$-量子比特恒定局部林德布拉德算符的系数,其中 $g$ 为单位点能量,$d$ 为相互作用图的(近似)度。尽管林德布拉德算符相较于哈密顿量带来新挑战,该算法仍实现了当前最优哈密顿量学习算法的全部期望特性:(1)使用非自适应、无需辅助量子比特的随机保罗测量电路,时间分辨率达 $Θ(1/g)$;(2)无需已知未知林德布拉德算符的结构;(3)依赖平滑形式的度,支持学习准局域和幂律衰减的林德布拉德算符。该算法为简单迭代方法,目标函数由限制在少数位区域的林德布拉德算符的傅里叶系数构成。分析揭示了开放系统特有的难题,称为“混淆”项。当混淆受限时,算法性能提升。我们在从实时间演化学习哈密顿结构的场景中展示了这一优势,获得一个显著比之前工作更简单的算法。此外,利用相同迭代方法,我们首次设计出从高温吉布斯态高效学习哈密顿结构的算法。
原文摘要 · Abstract (English)
We design an algorithm for learning the coefficients of an $n$-qubit constant-local Lindbladian to $\varepsilon$ error with $O(g d^2 \log(n) / \varepsilon^2)$ total evolution time, where $g$ is the single-site energy and $d$ is the (approximate) degree of the interaction graph. Though Lindbladians present new challenges not present in the special case of Hamiltonians, our algorithm achieves the suite of desiderata attained by state-of-the-art Hamiltonian learning algorithms: (1) it uses non-adaptive, ancilla-free randomized Pauli measurement circuits with a time resolution of only $Θ(1/g)$; (2) it works without knowledge of the structure of the unknown Lindbladian; (3) it depends on a smooth form of degree, thereby supporting the learning of quasi-local and power-law Lindbladians. Our algorithm is a simple iterative method, where the objective function consists of Fourier coefficients of the Lindbladian restricted to few-site regions. Its analysis identifies the difficulty unique to open systems, which we call "confusing" terms. For settings where the "confusion" is limited, the performance of the algorithm improves. We demonstrate this for the case of structure learning of Hamiltonians from access to real-time evolution, where we obtain a new algorithm that is significantly simpler than previous work. In addition, using the same iterative method, we design the first efficient algorithm for structure learning Hamiltonians from high-temperature Gibbs states.
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