Machine Learning in the Quantum Era

Machine Learning aims at automatically identifying structures and patterns in large data sets. In order to identify these patterns, algorithms often resort to standard linear algebra routines such as matrix inversion or eigenvalue decompositions. For example, support vector machines, one of the most successful traditional machine learning approaches for classification, can be cast to a linear system of equation, and then be solved using matrix inversion. Similarly, identifying the important signals in a data set can be done by identifying the leading eigenvalues and vectors of the data matrix, a method called principal component analysis. The large dimensionality of the vector spaces involved in these operations make their implementation at large scale very resource intensive, thus motivating the development of innovative methods to lower their computational cost.