AI 中文总结
该研究提出一种高效非自适应两阶段算法，可在最小假设下从时间演化中近乎最优地学习任意林德布拉德算符，其实验与演化时间缩放匹配下界。
AI 中文摘要
我们研究从未知马尔可夫开放系统的时间演化中学习其生成元的问题，该生成元称为林德布拉德算符（Lindbladian），包含由指数级大量可能的泡利项索引的哈密顿量和耗散系数。我们提出一种高效算法，在最小假设下从时间演化中学习任意林德布拉德算符。对于动力学强度不超过Λ的林德布拉德算符，该算法用Õ(Λ²/ε²)次实验和Õ(Λ/ε²)总演化时间，结合多项式经典运行时间，将每个系数估计至误差ε。算法包含两个非自适应、无辅助量子比特、无控制的阶段：1. 支撑学习阶段，用Õ(Λ²/η²)次实验（制备乘积泡利本征态并进行单量子比特泡利测量），输出大小为poly(Λ/η)的候选支撑，包含所有幅度至少为η的哈密顿量和耗散坐标；2. 系数学习阶段，用Õ(Λ²logM/ε²)次实验（制备随机稳定子态并在随机克利福德基下测量），将任意大小为M的候选支撑中的所有系数估计至误差ε。两阶段结合可在多项式时间内识别并估计任意林德布拉德算符的所有系数，实验次数和总演化时间的缩放关系在对数因子内匹配下界，因此该算法对学习任意林德布拉德算符近乎最优。
英文摘要
We study the problem of learning an unknown Markovian open-system generator from access to its physical time evolution. This generator, called a Lindbladian, contains Hamiltonian and dissipative coefficients indexed by an exponentially large family of possible Pauli terms. We propose an efficient algorithm that learns arbitrary Lindbladians from time evolution under minimal assumptions. For a Lindbladian of dynamical strength at most $Λ$, the algorithm estimates every coefficient to error $ε$ using $\widetilde O(Λ^2/ε^2)$ experiments and $\widetilde O(Λ/ε^2)$ total evolution time, together with polynomial classical running time. The algorithm consists of two nonadaptive, ancilla-free, and control-free stages: 1. The support-learning stage outputs a candidate support of size $\mathrm{poly}(Λ/η)$ that contains every Hamiltonian and dissipative coordinate of magnitude at least $η$, using $\widetilde O(Λ^2/η^2)$ experiments with preparations of product Pauli eigenstates and single-qubit Pauli measurements. 2.The coefficient-learning stage estimates all coefficients in any candidate support of size $M$ to error $ε$, using $\widetilde O(Λ^2\log M/ε^{2})$ experiments with preparations of random stabilizer states and measurements in random Clifford bases. Composing the two stages identifies and estimates every coefficient of an arbitrary Lindbladian in polynomial time. The experiment-count and total-evolution-time scalings match the lower bounds up to logarithmic factors, so the algorithm is nearly optimal for learning arbitrary Lindbladians.
Comments45 pages
