Magic State Distillation using Asymptotically Good Codes on Qudits

• URL: http://arxiv.org/abs/2512.21874v1
• Date: Fri, 26 Dec 2025 05:28:54 GMT
• Title: Magic State Distillation using Asymptotically Good Codes on Qudits
• Authors: Michael J. Cervia, Henry Lamm, Diyi Liu, Edison M. Murairi, Shuchen Zhu,
• Abstract summary: Previous results forally good codes have required qudit dimension $qgg 100$ or code length $mathcalNgg 100$.<n>We construct the first family of good triorthogonal codes on the $mathbbF_22m$ alphabet with $m geq 3$ that lies above the Tsfasman-Vladut-Zink bound.<n>We identify a promising code with parameters $[[42,14,6]]_64$.
• Score: 1.4854797901022863
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Qudits offer the potential for low-overhead magic state distillation, although previous results for asymptotically good codes have required qudit dimension $q\gg 100$ or code length $\mathcal{N}\gg 100$. These parameters far exceed experimental demonstrations of qudit platforms, and thus motivate the search for better codes. Using a novel lifting procedure, we construct the first family of good triorthogonal codes on the $\mathbb{F}_{2^{2m}}$ alphabet with $m \geq 3$ that lies above the Tsfasman-Vladut-Zink bound. These codes yield a family of asymptotically good quantum codes with transversal CCZ gates, enabling constant space overhead magic state distillation with qudit dimension as small as $q=64$. Further, we identify a promising code with parameters $[[42,14,6]]_{64}$. Finally, we show that a distilled $|{CCZ}\rangle_{2^{2m}}$ can be reduced to a $|{CCZ}\rangle_{2^n}$ state for arbitrary $n$ with a constant-depth Clifford circuit of at most 9 computational basis measurements, 12 single-qudit and 9 two-qudit Clifford gates.

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