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Paper 1

High-threshold magic state distillation with quantum quadratic residue codes

Michael Zurel, Santanil Jana, Nadish de Silva

Year

2026

Journal

arXiv preprint

DOI

arXiv:2603.18560

arXiv

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.

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Paper 2

Fault tolerance with noisy and slow measurements and preparation.

Paz-Silva GA, Brennen GK, Twamley J.

Year

2010

Journal

Phys Rev Lett

DOI

10.1103/physrevlett.105.100501

arXiv

-

No abstract.

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