Open Access from Applied Stochastic Models in Business and Industry: Quantum Bayesian computation

Each week, we select a recently published Open Access article to feature. This week’s article comes from Applied Stochastic Models in Business and Industry and  explores how quantum computers can make Bayesian computations speed-up by introducing new quantum algorithms.

The article’s abstract is given below, with the full article available to read here.

Polson, NSokolov, VXu, JQuantum Bayesian computationAppl Stochastic Models Bus Ind2023115. doi: 10.1002/asmb.2807

Quantum Bayesian computation is an emerging field that levers the computational gains available from quantum computers. They promise to provide an exponential speed-up in Bayesian computation. Our article adds to the literature in three ways. First, we describe how quantum von Neumann measurement provides quantum versions of popular machine learning algorithms such as Markov chain Monte Carlo and deep learning that are fundamental to Bayesian learning. Second, we describe quantum data encoding methods needed to implement quantum machine learning including the counterparts to traditional feature extraction and kernel embeddings methods. Third, we show how quantum algorithms naturally calculate Bayesian quantities of interest such as posterior distributions and marginal likelihoods. Our goal then is to show how quantum algorithms solve statistical machine learning problems. On the theoretical side, we provide quantum versions of high dimensional regression, Gaussian processes and stochastic gradient descent. On the empirical side, we apply a quantum FFT algorithm to Chicago house price data. Finally, we conclude with directions for future research.

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