Southwest Quantum Information and Technology

Classification of Small Triorthogonal Codes

Presenting Author: Sepehr Nezami, California Institute of Technology
Contributing Author(s): Jeongwan Haah

Triorthogonal codes are a class of quantum error correcting codes used in magic state distillation protocols. We classify all triorthogonal codes with n + k ≤ 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 ≤ 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.

Read this article online: http://arxiv.org/pdf/2107.09684.pdf

(Session 5 : Thursday from 12:00pm-2:00 pm)