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How Many Query Superpositions Are Needed to Learn?

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Algorithmic Learning Theory (ALT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4264))

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Abstract

This paper introduces a framework for quantum exact learning via queries, the so-called quantum protocol. It is shown that usual protocols in the classical learning setting have quantum counterparts. A combinatorial notion, the general halving dimension, is also introduced. Given a quantum protocol and a target concept class, the general halving dimension provides lower and upper bounds on the number of queries that a quantum algorithm needs to learn. For usual protocols, the lower bound is also valid even if only involution oracle teachers are considered. Under some protocols, the quantum upper bound improves the classical one. The general halving dimension also approximates the query complexity of ordinary randomized learners. From these bounds we conclude that quantum devices can allow moderate improvements on the query complexity. However, any quantum polynomially query learnable concept class must be also polynomially learnable in the classical setting.

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Author information

Authors and Affiliations

  1. Software Department., Universitat Politècnica de Catalunya, Campus Nord, 08034, Barcelona, Spain

    Jorge Castro

Authors
  1. Jorge Castro
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Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informàtics Laboratori d’Algorísmica Relacional, Complexitat i Aprenentatge, Universitat Politècnica de Catalunya, Barcelona,  

    José L. Balcázar

  2. Google, 1600 Amphitheatre Parkway, 94043, Mountain View, CA, USA

    Philip M. Long

  3. Department of Computer Science and Department of Mathematics, National University of Singapore, 117543, Singapore, Republic of Singapore

    Frank Stephan

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© 2006 Springer-Verlag Berlin Heidelberg

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Castro, J. (2006). How Many Query Superpositions Are Needed to Learn?. In: Balcázar, J.L., Long, P.M., Stephan, F. (eds) Algorithmic Learning Theory. ALT 2006. Lecture Notes in Computer Science(), vol 4264. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11894841_10

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  • DOI: https://doi.org/10.1007/11894841_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46649-9

  • Online ISBN: 978-3-540-46650-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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