The speed of quantum and classical learning for performing the kth root of NOT
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=2^{m} and m \in {\mathbb{N}} . The reason for this speedup 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.
 Publication:

New Journal of Physics
 Pub Date:
 November 2009
 DOI:
 10.1088/13672630/11/11/113018
 arXiv:
 arXiv:0904.4571
 Bibcode:
 2009NJPh...11k3018M
 Keywords:

 Quantum Physics
 EPrint:
 4 pages, 4 figures