量子统计推断

摘要：

在这篇论文中，我从以下两个方向给出了量子统计推断的一些结果。首先，我证明了量子算法可以应用于增强高斯过程（GP）的计算和训练，这是一种广泛用于经典统计推断和监督机器学习的强大模型。量子GP算法的一个关键组成部分是用量子计算机求解线性系统，为此我提出了一种新的算法，该算法比以前已知的方法具有可证明的优势。我还将明确地解决将经典数据编码为机器学习应用程序的量子态的任务。然后，我将量子增强的GP应用于贝叶斯深度学习，并在当代硬件和模拟器上进行实验演示。其次，我研究了量子因果关系的概念，并将其应用于推断空间和时间的量子相关性，并提出了一个分析工具包，用于量子数据中的因果推断。我也将因果关系和量子通信之间的联系，并提出了一个一般的限制量子容量的噪声通信信道。

英文摘要：

In this thesis, I present several results on quantum statistical inference in the following two directions. Firstly, I demonstrate that quantum algorithms can be applied to enhance the computing and training of Gaussian processes (GPs), a powerful model widely used in classical statistical inference and supervised machine learning. A crucial component of the quantum GP algorithm is solving linear systems with quantum computers, for which I present a novel algorithm that achieves a provable advantage over previously known methods. I will also explicitly address the task of encoding the classical data into a quantum state for machine learning applications. I then apply the quantum enhanced GPs to Bayesian deep learning and present an experimental demonstration on contemporary hardware and simulators. Secondly, I look into the notion of quantum causality and apply it to inferring spatial and temporal quantum correlations, and present an analytical toolkit for causal inference in quantum data. I will also make the connection between causality and quantum communications, and present a general bound for the quantum capacity of noisy communication channels.

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。