# Quantum learning chosen for IOP Select

18. Nov 2009 — The paper "The speed of quantum and classical learning for performing the kth root of NOT" by D. Manzano, M. Pawlowski and C. Brukner, published in New J. Phys. 11 113018 (2009), has been selected for inclusion in IOP Select. IoP Select is a collection of journal articles, chosen by IOP Editors for their novelty, significance and potential impact on future research.

#### 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 = 2m and m 2 N. 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.