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GA-based approach to find the stabilizers of a given sub-space

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Abstract

Stabilizer formalism is a powerful framework for understanding a wide class of operations in quantum information. This formalism is a framework where multiple qubit states and sub-spaces are described in a compact way in terms of operators under which they are invariant. In stabilizer formalism, one focuses the members of Pauli groups which have the stabilizing property of a given sub-space. Therefore, finding the Pauli stabilizers of a given sub-space in an efficient way is of great interest. In this paper, this problem is addressed in the field of quantum information theory. We present a two-phase algorithm to solve the problem whose order of complexity is considerably smaller than the common solution. In the first phase, a genetic algorithm is run. The results obtained by this algorithm are the matrices that can potentially be the Pauli stabilizers of the given sub-space. Then an analytical approach is applied to find the correct answers among the results of the first phase. Experimental results show that speed-ups are remarkable as compared to the common solution.

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Authors and Affiliations

  1. Quantum Design Automation Lab, Department of Computer Engineering and Information Technology, Amirkabir University of Technology, Tehran, Iran

    Mahboobeh Houshmand, Morteza Saheb Zamani & Mehdi Sedighi

  2. Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    Monireh Houshmand

Authors
  1. Mahboobeh Houshmand
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  2. Morteza Saheb Zamani
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  3. Mehdi Sedighi
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  4. Monireh Houshmand
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Correspondence to Morteza Saheb Zamani.

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Houshmand, M., Saheb Zamani, M., Sedighi, M. et al. GA-based approach to find the stabilizers of a given sub-space. Genet Program Evolvable Mach 16, 57–71 (2015). https://doi.org/10.1007/s10710-014-9219-z

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  • DOI: https://doi.org/10.1007/s10710-014-9219-z

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