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Annual Symposium on Theoretical Aspects of Computer Science

STACS 2007: STACS 2007 pp 586–597Cite as

An Efficient Quantum Algorithm for the Hidden Subgroup Problem in Extraspecial Groups

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 4393)

Abstract

Extraspecial groups form a remarkable subclass of p-groups. They are also present in quantum information theory, in particular in quantum error correction. We give here a polynomial time quantum algorithm for finding hidden subgroups in extraspecial groups. Our approach is quite different from the recent algorithms presented in [17] and [2] for the Heisenberg group, the extraspecial p-group of size p 3 and exponent p. Exploiting certain nice automorphisms of the extraspecial groups we define specific group actions which are used to reduce the problem to hidden subgroup instances in abelian groups that can be dealt with directly.

Keywords

  • Abelian Group
  • Heisenberg Group
  • Quantum Algorithm
  • Quantum Procedure
  • Left Coset

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Research supported by the European Commission IST Integrated Project Qubit Applications (QAP) 015848, the OTKA grants T42559 and T46234, the NWO visitor’s grant Algebraic Aspects of Quantum Computing, and by the ANR Blanc AlgoQP grant of the French Research Ministry.

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Author information

Authors and Affiliations

  1. SZTAKI, Hungarian Academy of Sciences, H-1111 Budapest, Hungary

    Gábor Ivanyos

  2. Univ Paris-Sud, Orsay, F-91405,  

    Luc Sanselme & Miklos Santha

  3. CNRS, LRI, UMR 8623, Orsay, F-91405,  

    Miklos Santha

Authors
  1. Gábor Ivanyos
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  2. Luc Sanselme
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  3. Miklos Santha
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    Ivanyos, G., Sanselme, L., Santha, M. (2007). An Efficient Quantum Algorithm for the Hidden Subgroup Problem in Extraspecial Groups. In: Thomas, W., Weil, P. (eds) STACS 2007. STACS 2007. Lecture Notes in Computer Science, vol 4393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70918-3_50

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    • DOI: https://doi.org/10.1007/978-3-540-70918-3_50

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