Nezami, Sepehr and Haah, Jeongwan (2022) Classification of small triorthogonal codes. Physical Review A, 106 (1). Art. No. 012437. ISSN 2469-9926. doi:10.1103/physreva.106.012437. https://resolver.caltech.edu/CaltechAUTHORS:20220729-722022000
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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≤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 we 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 we classify the Reed-Muller polynomials of low weight using the results of Kasami, Tokura, and Azumi [IEEE Trans. Inf. Theory 16, 752 (1970); Inf. Contr. 30, 380 (1976)] 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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| Additional Information: | © 2022 American Physical Society. (Received 22 June 2022; accepted 11 July 2022; published 28 July 2022) S.N. is supported by the Walter Burke Institute for Theoretical Physics and IQIM at Caltech. Part of this work was done while S.N. was an intern in the Quantum Architectures and Computation group (QuArC), Microsoft Research. | |||||||||
| Group: | Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics | |||||||||
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| Issue or Number: | 1 | |||||||||
| DOI: | 10.1103/physreva.106.012437 | |||||||||
| Record Number: | CaltechAUTHORS:20220729-722022000 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20220729-722022000 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 115960 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | George Porter | |||||||||
| Deposited On: | 01 Aug 2022 19:29 | |||||||||
| Last Modified: | 01 Aug 2022 19:29 |
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