Prediction by linear regression on a quantum computer
Abstract
We give an algorithm for prediction on a quantum computer which is based on a linear regression model with leastsquares optimization. In contrast to related previous contributions suffering from the problem of reading out the optimal parameters of the fit, our scheme focuses on the machinelearning task of guessing the output corresponding to a new input given examples of data points. Furthermore, we adapt the algorithm to process nonsparse data matrices that can be represented by lowrank approximations, and significantly improve the dependency on its condition number. The prediction result can be accessed through a singlequbit 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.
 Publication:

Physical Review A
 Pub Date:
 August 2016
 DOI:
 10.1103/PhysRevA.94.022342
 arXiv:
 arXiv:1601.07823
 Bibcode:
 2016PhRvA..94b2342S
 Keywords:

 Quantum Physics
 EPrint:
 6 pages, 1 figure