The speed of quantum and classical learning for performing the kth root of NOT

Author(s)
Daniel Manzano, Marcin Pawlowski, Caslav Brukner
Abstract

We consider quantum learning machines—quantum computers that modify themselves in order to improve their performance in some way—that are trained to perform certain classical task, i.e. to execute a function that takes classical bits as input and returns classical bits as output. This allows a fair comparison between learning efficiency of quantum and classical learning machines in terms of the number of iterations required for completion of learning. We find an explicit example of the task for which numerical simulations show that quantum learning is faster than its classical counterpart. The task is extraction of the kth root of NOT (NOT = logical negation), with k=2m and . The reason for this speed-up is that the classical machine requires memory of size log k=m to accomplish the learning, while the memory of a single qubit is sufficient for the quantum machine for any k.

Organisation(s)
Quantum Optics, Quantum Nanophysics and Quantum Information
External organisation(s)
Universidad de Granada, University of Gdańsk
Journal
New Journal of Physics
Volume
11
No. of pages
9
ISSN
1367-2630
DOI
https://doi.org/10.1088/1367-2630/11/11/113018
Publication date
2009
Peer reviewed
Yes
Austrian Fields of Science 2012
103026 Quantum optics
Portal url
https://ucris.univie.ac.at/portal/en/publications/the-speed-of-quantum-and-classical-learning-for-performing-the-kth-root-of-not(5b9fdc3c-223e-475c-8d84-329dfc629cac).html