@inproceedings{d1e80019d89f47bba67a200e25dfd9be,
title = "Local Equivalence of Surface Code States",
abstract = "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.",
author = "Pradeep Sarvepalli and Robert Raussendorf",
note = "Funding Information: We thank Jim Geelen, and Markus Grassl for useful discussions and the reviewers for their helpful comments. Some of the results of this paper have been presented at the Workshop on Applications of Matroid Theory and Combinatorial Optimization to Information and Coding Theory, Banff International Research Station, Banff, 2009 and an expanded version is available at [13]. This research is supported by CIFAR, IARPA, MITACS and NSERC.; 5th Conference on Theory of Quantum Computation, Communication, and Cryptography, TQC 2010 ; Conference date: 13-04-2010 Through 15-04-2010",
year = "2011",
month = jan,
day = "14",
doi = "10.1007/978-3-642-18073-6\_5",
language = "English",
isbn = "9783642180729",
series = "Lecture Notes in Computer Science",
publisher = "Springer Berlin",
pages = "47--62",
editor = "Wim Dam and Kendon, \{Vivien M.\} and Simone Severini",
booktitle = "Theory of Quantum Computation, Communication and Cryptography",
address = "Germany",
}