Quantum Bayesian Computation
This work addresses the problem of accelerating Bayesian computation for machine learning researchers by leveraging quantum computing, though it appears incremental as it builds on existing quantum and Bayesian methods.
The paper tackles the challenge of applying quantum computing to Bayesian machine learning by demonstrating how quantum measurement can simulate MCMC and deep learning algorithms, and it introduces quantum versions of high-dimensional regression, Gaussian processes, and stochastic gradient descent, with an empirical application to Chicago housing data using a Quantum FFT model.
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.