Quantum Bayesian Computation (QBC) is an emerging field that levers the computational gains available from quantum computers to provide an exponential speed-up in Bayesian computation. Our paper adds to the literature in two ways. First, we show how von Neumann quantum measurement can be used to simulate machine learning algorithms such as Markov chain Monte Carlo (MCMC) and Deep Learning (DL) that are fundamental to Bayesian learning. Second, we describe data encoding methods needed to implement quantum machine learning including the counterparts to traditional feature extraction and kernel embeddings methods. Our goal then is to show how to apply quantum algorithms directly to statistical machine learning problems. On the theoretical side, we provide quantum versions of high dimensional regression, Gaussian processes (Q-GP) and stochastic gradient descent (Q-SGD). On the empirical side, we apply a Quantum FFT model to Chicago housing data. Finally, we conclude with directions for future research.

翻译：量子贝叶斯计算（QBC）是一个新兴领域，它利用量子计算机的计算优势，为贝叶斯计算提供了指数级的加速。本文在两方面为现有文献做出贡献。首先，我们展示了如何利用冯·诺依曼量子测量来模拟对贝叶斯学习至关重要的机器学习算法，如马尔可夫链蒙特卡洛（MCMC）和深度学习（DL）。其次，我们描述了实现量子机器学习所需的数据编码方法，包括传统特征提取和核嵌入方法的对应技术。我们的目标旨在展示如何将量子算法直接应用于统计机器学习问题。在理论方面，我们提供了高维回归、高斯过程（Q-GP）和随机梯度下降（Q-SGD）的量子版本。在实证方面，我们将量子FFT模型应用于芝加哥房价数据。最后，我们总结了未来研究方向。