This paper is available at https://arxiv.org/abs/2603.18560
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.
