Related papers: Classification of Small Triorthogonal Codes

Classification of Small Triorthogonal Codes

URL: http://arxiv.org/abs/2107.09684v2
Date: Tue, 26 Jul 2022 13:21:48 GMT
Title: Classification of Small Triorthogonal Codes
Authors: Sepehr Nezami, Jeongwan Haah
Abstract summary: Triorthogonal codes are a class of quantum error correcting codes used in magic state distillation protocols. We classify all triorthogonal codes with $n+kle 38$, where $n$ is the number of physical qubits and $k is the number of qubits of the code. In an appendix independent of the main text, we improve a magic state distillation protocol by reducing the time variance due to Clifford corrections.
Score: 0.30458514384586394
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Triorthogonal codes are a class of quantum error correcting codes used in magic state distillation protocols. We classify all triorthogonal codes with $n+k \le 38$, where $n$ is the number of physical qubits and $k$ is the number of logical qubits of the code. We find $38$ distinguished triorthogonal subspaces and show that every triorthogonal code with $n+k\le 38$ descends from one of these subspaces through elementary operations such as puncturing and deleting qubits. Specifically, we associate each triorthogonal code with a Reed-Muller polynomial of weight $n+k$, and classify the Reed-Muller polynomials of low weight using the results of Kasami, Tokura, and Azumi and an extensive computerized search. In an appendix independent of the main text, we improve a magic state distillation protocol by reducing the time variance due to stochastic Clifford corrections.

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