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Transduction and Active Learning in the Quantum Learning of Unitary Transformations
University of Borås, Swedish School of Library and Information Science.
2014 (English)Conference paper, Poster (Other academic)
Abstract [en]

Quantum learning of a unitary transformation estimates a quantum channel in a process similar to quantum process tomography. The classical counterpart of this goal, finding an unknown function, is regression, although the methodology hardly resembles the outline of classical algorithms. To gain a better understanding what such a methodology means to learning theory, we anchor it to the familiar concepts of active learning and transduction. Learning the unitary transformation translates to optimally storing it in quantum memory, but the quantum learning procedure also requires an optimal, maximally entangled input state. We argue that this is akin to active learning. Two different retrieval strategies apply when we would like to use the learned unitary transformation: a coherent strategy, which stores the unitary in quantum memory, and an incoherent one, which measures the unitary and stores it in classical memory; the latter strategy is considered optimal. We further argue that the incoherent strategy is a blend of inductive and transductive learning, as the optimal input state depends on the number of target states on which the transformation should be applied, yet once it is learned, the transformation can be used an arbitrary number of times. On the other hand, the sub-optimal coherent strategy of storing and applying the unitary is a form of transduction with no inductive element.

Place, publisher, year, edition, pages
Keyword [en]
quantum process tomography, quantum learning of unitary, transductive learning, active learning, regression, Quantum Information Theory
National Category
Computer and Information Science
Research subject
Library and Information Science
URN: urn:nbn:se:hb:diva-7208Local ID: 2320/14001OAI: diva2:887916
14th Asian Quantum Information Science Conference, 20-24 August, 2014, Kyoto, Japan
Available from: 2015-12-22 Created: 2015-12-22

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Wittek, Peter
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Swedish School of Library and Information Science
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