Abstract

Most of the problems of theoretical quantum physics are characterized by a high complexity. Practically, this means that solution of such a problem demands computational effort and resources that often scale exponentially with the size of the quantum model and the solution can be obtained—even for relatively small models—only by resorting to high performance computing (HPC) technologies. Here we discuss a particular problem of the theory of open quantum systems, the so-called ‘‘Markovianity problem’’. To get the answer to the question whether a given quantum map can be obtained as the result of a time-continuous open quantum evolution, one needs to implement an algorithm whose complexity grows exponentially with the dimension of the model’s Hilbert space. We discuss how machine learning (ML) methods can be used to get the answer and provide some evidence for potential efficiency of the ML-based approach. We demonstrate that neural networks that are used to classify images can be used to determine the boundary between answers ‘‘yes’’ and ‘‘no’’ in the parameter space of a particular open quantum model. For an open model consisting of two qubits, our ML algorithm is able to give correct answer with \(97\%\) accuracy. The computational experiments were performed on the Lomonosov-2 supercomputer.

中文翻译：

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开放量子系统理论特定问题的机器学习与半定规划方法

摘要

理论量子物理学的大多数问题都具有高度复杂性的特点。实际上，这意味着解决此类问题需要的计算工作和资源通常会随着量子模型的大小呈指数级增长，并且只有借助高性能计算 (HPC) 技术才能获得解决方案——即使对于相对较小的模型也是如此. 在这里，我们讨论开放量子系统理论的一个特殊问题，即所谓的“马尔可夫问题”。为了得到一个给定的量子映射是否可以作为时间连续开放量子演化的结果的问题的答案，需要实现一种算法，其复杂性随着模型的希尔伯特空间的维数呈指数增长。我们讨论了如何使用机器学习 (ML) 方法来获得答案，并为基于 ML 的方法的潜在效率提供一些证据。我们证明了用于分类图像的神经网络可用于确定特定开放量子模型的参数空间中答案“是”和“否”之间的边界。对于由两个量子位组成的开放模型，我们的 ML 算法能够给出正确的答案\(97\%\)精度。计算实验在 Lomonosov-2 超级计算机上进行。