Daniel Manzano et al 2009 New J. Phys. 11 113018 doi:10.1088/1367-2630/11/11/113018
The speed of quantum and classical learning for performing the kth root of NOT
Daniel Manzano1,2,4, Marcin Pawłowski3 and Časlav Brukner4,5
Show affiliationsWe 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.
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GENERAL SCIENTIFIC SUMMARY
Introduction and background. Learning can be defined as the changes in a system that result in an improved performance over time on tasks that are similar to those performed in the system's previous history. Recent progress in quantum communication and quantum computation – development of novel and efficient ways to process information on the basis of laws of quantum theory – provides motivations to generalize the theory of machine learning into the quantum domain. Can one have quantum improvements in the speed of learning in a sense that a quantum machine requires fewer steps than the best classical machine to learn some classical task?Main results. We present evidence for the first explicit classical computational task that quantum machines can learn faster than their classical counterparts. The task is extraction of the kth root of NOT (NOT = logical negation), for certain k. The reason for this speed-up is that the classical machine requires memory of size log k to accomplish the learning, while the memory of a single qubit is sufficient for the quantum machine for any k. Since the classical machine requires a significantly larger number of independent parameters to be optimized, it also requires a larger number of learning steps to accomplish learning.
Wider implications. In a broader context, our results are expected to contribute to understanding the learning process in a world in which information is fundamentally quantum mechanical and where our classical intuition is often challenged.
- PACS
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03.67.Lx Quantum computation architectures and implementations
07.05.Mh Neural networks, fuzzy logic, artificial intelligence
- Subjects
- Dates
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Issue 11 (November 2009)
Received 6 July 2009
Published 10 November 2009
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The speed of quantum and classical learning for performing the kth root of NOT
Daniel Manzano et al 2009 New J. Phys. 11 113018
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