利用随机低秩近似增强量子典型性的收敛性
Enhanced Convergence of Quantum Typicality using a Randomized Low-Rank Approximation
摘要：
我们提出了一种方法，以减少量子典型性（QT）的方法通过随机低秩近似的有限温度密度矩阵$e^{-βH}$的随机跟踪估计的方差。在低秩子空间中，用QT估计器逼近余子空间中的迹，可以获得更高的估计精度。我们提出了两种变体的跟踪估计，并证明了它们的有效性，使用数值实验。实验表明，低秩近似优于标准的QT轨迹估计的中低温。我们认为，这是由于低秩近似准确地表示在低温下的密度矩阵，允许跟踪的准确结果。
英文摘要：
We present a method to reduce the variance of stochastic trace estimators used in quantum typicality (QT) methods via a randomized low-rank approximation of the finite-temperature density matrix $e^{-βH}$. The trace can be evaluated with higher accuracy in the low-rank subspace while using the QT estimator to approximate the trace in the complementary subspace. We present two variants of the trace estimator and demonstrate their efficacy using numerical experiments. The experiments show that the low-rank approximation outperforms the standard QT trace estimator for moderate- to low-temperature. We argue this is due to the low-rank approximation accurately represent the density matrix at low temperatures, allowing for accurate results for the trace.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
