Machine learning with classical data

Cambridge University Press eBooks, pp. 148–184

Abstract

This chapter covers a number of disparate applications of quantum computing in the area of machine learning. We only consider situations where the dataset is classical (rather than quantum). We cover quantum algorithms for big-data problems relying upon high-dimensional linear algebra, such as Gaussian process regression and support vector machines. We discuss the prospect of achieving a quantum speedup with these algorithms, which face certain input/output caveats and must compete against quantum-inspired classical algorithms. We also cover heuristic quantum algorithms for energy-based models, which are generative machine learning models that learn to produce outputs similar to those in a training dataset. Next, we cover a quantum algorithm for the tensor principal component analysis problem, where a quartic speedup may be available, as well as quantum algorithms for topological data analysis, which aim to compute topologically invariant properties of a dataset. We conclude by covering quantum neural networks and quantum kernel methods, where the machine learning model itself is quantum in nature.

Authors 4

1. Sam McArdle
   Affiliation as printed

   AWS Center for Quantum Computing

2. Connor T. Hann
   Affiliation as printed

   AWS Center for Quantum Computing

3. Aleksander Kubica

   Yale University

   Affiliation as printed

   Yale University

4. Fernando G. S. L. Brandão
   Affiliation as printed

   AWS Center for Quantum Computing