论文标题
浮雕的机器学习方法 - 林德布拉德问题
Machine Learning approach to the Floquet--Lindbladian problem
论文作者
论文摘要
与其经典版本相似，量子马尔可夫进化可以是时间散文或时间连续的。离散的量子马尔可夫进化通常以完全阳性的痕量痕量图来建模，而时间连续的演化通常用称为“ lindbladians”的超级操作器指定。在这里，我们解决了以下问题：给出了量子图，我们可以找到一个lindbladian，该lindbladian在分散时间实例中生成相同的进化与映射的进化相同吗？已经证明，解决此问题的答案的问题可以降低到NP完整的问题（在Evolution在进化中发生的希尔伯特空间的尺寸$ n $）问题。我们从不同的角度考虑了各种机器学习（ML）方法，并试图估算其给出正确答案的潜在能力，从而解决了这个问题。免费，我们使用不同的ML方法的性能作为一种工具来检查问题的答案，即该问题的答案是在所谓的Choi矩阵的频谱属性中编码的，该矩阵可以从给定的量子映射构建。作为测试床，我们使用两个单量模型，可以通过使用还原程序获得答案。我们实验的结果是，对于给定的地图，由时间独立的Lindbladian生成的特性都在相应的Choi矩阵的特征值和特征态中编码。
Similar to its classical version, quantum Markovian evolution can be either time-discrete or time-continuous. Discrete quantum Markovian evolution is usually modeled with completely-positive trace-preserving maps while time-continuous evolution is often specified with superoperators referred to as "Lindbladians". Here we address the following question: Being given a quantum map, can we find a Lindbladian which generates an evolution identical -- when monitored at discrete instances of time -- to the one induced by the map? It was demonstrated that the problem of getting the answer to this question can be reduced to an NP-complete (in the dimension $N$ of the Hilbert space the evolution takes place in) problem. We approach this question from a different perspective by considering a variety of Machine Learning (ML) methods and trying to estimate their potential ability to give the correct answer. Complimentary, we use the performance of different ML methods as a tool to check the hypothesis that the answer to the question is encoded in spectral properties of the so-called Choi matrix, which can be constructed from the given quantum map. As a test bed, we use two single-qubit models for which the answer can be obtained by using the reduction procedure. The outcome of our experiment is that, for a given map, the property of being generated by a time-independent Lindbladian is encoded both in the eigenvalues and the eigenstates of the corresponding Choi matrix.
