Prediction by linear regression on a quantum computer

TL;DR

This paper presents a quantum algorithm for linear regression prediction that efficiently estimates outputs for new inputs, handling non-sparse data and improving runtime dependence on data properties.

Contribution

The authors develop a quantum prediction algorithm based on linear regression that overcomes previous readout limitations and adapts to low-rank, non-sparse data matrices.

Findings

Runtime is logarithmic in input dimension for quantum data inputs.

Algorithm effectively processes non-sparse, low-rank data matrices.

Prediction can be obtained via single qubit measurement.

Abstract

We give an algorithm for prediction on a quantum computer which is based on a linear regression model with least squares optimisation. Opposed to related previous contributions suffering from the problem of reading out the optimal parameters of the fit, our scheme focuses on the machine learning task of guessing the output corresponding to a new input given examples of data points. Furthermore, we adapt the algorithm to process non-sparse data matrices that can be represented by low-rank approximations, and significantly improve the dependency on its condition number. The prediction result can be accessed through a single qubit measurement or used for further quantum information processing routines. The algorithm's runtime is logarithmic in the dimension of the input space provided the data is given as quantum information as an input to the routine.