Quantum Bayesian Computation

TL;DR

This paper explores how quantum computing can accelerate Bayesian machine learning by introducing quantum algorithms, data encoding methods, and empirical applications like quantum FFT on housing data.

Contribution

It introduces quantum versions of key machine learning algorithms and demonstrates their application to real-world data, advancing quantum Bayesian computation.

Findings

Quantum measurement can simulate MCMC and Deep Learning algorithms.

Quantum algorithms for high-dimensional regression and Gaussian processes are developed.

Quantum FFT applied to Chicago housing data shows practical potential.

Abstract

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.