Anna Lopatnikova

Anna Lopatnikova, Minh-Ngoc Tran, Scott A. Sisson

Quantum computers promise to surpass the most powerful classical supercomputers when it comes to solving many critically important practical problems, such as pharmaceutical and fertilizer design, supply chain and traffic optimization, or optimization for machine learning tasks. Because quantum computers function fundamentally differently from classical computers, the emergence of quantum computing technology will lead to a new evolutionary branch of statistical and data analytics methodologies. This review provides an introduction to quantum computing designed to be accessible to statisticians and data scientists, aiming to equip them with an overarching framework of quantum computing, the basic language and building blocks of quantum algorithms, and an overview of existing quantum applications in statistics and data analysis. Our goal is to enable statisticians and data scientists to follow quantum computing literature relevant to their fields, to collaborate with quantum algorithm designers, and, ultimately, to bring forth the next generation of statistical and data analytics tools.

Anna Lopatnikova, Minh-Ngoc Tran

Variational Bayes (VB) is a critical method in machine learning and statistics, underpinning the recent success of Bayesian deep learning. The natural gradient is an essential component of efficient VB estimation, but it is prohibitively computationally expensive in high dimensions. We propose a computationally efficient regression-based method for natural gradient estimation, with convergence guarantees under standard assumptions. The method enables the use of quantum matrix inversion to further speed up VB. We demonstrate that the problem setup fulfills the conditions required for quantum matrix inversion to deliver computational efficiency. The method works with a broad range of statistical models and does not require special-purpose or simplified variational distributions.