论文标题
量子贝叶斯计算
Quantum Bayesian Computation
论文作者
论文摘要
量子贝叶斯计算（QBC）是一个新兴领域，它杠杆量的计算收益可从量子计算机中获得，以在贝叶斯计算中提供指数加速。我们的论文以两种方式增加了文献。首先，我们展示了如何使用von Neumann量子测量来模拟机器学习算法，例如马尔可夫链蒙特卡洛（MCMC）和深度学习（DL），这些算法是贝叶斯学习至关重要的。其次，我们描述了实现量子机学习所需的数据编码方法，包括传统特征提取和内核嵌入方法的对应方法。然后，我们的目标是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。在经验方面，我们将量子FFT模型应用于芝加哥住房数据。最后，我们以未来研究的指示得出结论。
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.
