Classification on a quantum computer: Linear regression and ensemble methods

Abstract

Quantum machine learning algorithms usually translate a machine learning methods into an algorithm that can exploit the advantages of quantum information processing. One approach is to tackle methods that rely on matrix inversion with the quantum linear system of equations routine. We give such a quantum algorithm based on unregularised linear regression. Opposed to closely related work from Wiebe, Braun and Lloyd [PRL 109 (2012)] our scheme focuses on a classification task and uses a different combination of core routines that allows us to process non-sparse inputs, and significantly improves the dependence on the condition number. The second part of the talk presents an idea that transcends the reproduction of classical results. Instead of considering a single trained classifier, practicioners often use ensembles of models to make predictions more robust and accurate. Under certain conditions, having infinite ensembles can lead to good results. We introduce a quantum sampling scheme that uses the parallelism inherent to a quantum computer in order to sample from 'exponentially large' ensembles that are not explicitely trained.