High-threshold magic state distillation with quantum quadratic residue codes

Abstract:We present applications of quantum quadratic residue codes in magic state distillation. This includes showing that existing codes which are known to distill magic states, like the $5$-qubit perfect code, the $7$-qubit Steane code, and the $11$-qutrit and $23$-qubit Golay codes, are equivalent to certain quantum quadratic residue codes. We also present new examples of quantum quadratic residue codes that distill qubit $T$ states and qutrit Strange states with high thresholds, and we show that there are infinitely many quantum quadratic residue codes that distill $T$ states with a non-trivial threshold. All of these codes, including the codes with the highest currently known thresholds for $T$ state and Strange state distillation, are unified under the umbrella of quantum quadratic residue codes.

arXiv:2603.18560 [quant-ph]

(or arXiv:2603.18560v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2603.18560 Focus to learn more arXiv-issued DOI via DataCite

Quantum Sci. Technol. 11 045052 (2026)

https://doi.org/10.1088/2058-9565/aea362 Focus to learn more DOI(s) linking to related resources

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