Local Equivalence of Surface Code States

  • Pradeep Sarvepalli
  • Robert Raussendorf
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6519)


Surface code states are an important class of stabilizer states that play a prominent role in quantum information processing. In this paper we show that these states do not contain any counterexamples to the recently disproved LU-LC conjecture. In the process we show that An important consequence of our result is that surface codes do not have any encoded non-Clifford transversal gates. We also prove some interesting structural properties of the CSS surface code states. We show that these states can be characterized as a class of minor closed binary matroids. This characterization could be of independent interest in that it makes a connection with the theory of binary matroids.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Pradeep Sarvepalli
    • 1
  • Robert Raussendorf
    • 1
  1. 1.Department of Physics and AstronomyUniversity of British ColumbiaVancouverCanada

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