Magic State Distillation using Asymptotically Good Codes on Qudits

Journal Article · Fri Dec 26 00:00:00 EST 2025 · No journal information

OSTI ID:3011984

Cervia, Michael J. ^[1]; Lamm, Henry ^[2]; Liu, Diyi ^[3]; Murairi, Edison M. ^[2]; Zhu, Shuchen ^[4]

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1. Washington U., Seattle
2. Fermilab
3. LBNL, Berkeley
4. Duke U.

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.

• Research Organization: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Duke U.; Washington U., Seattle; LBNL, Berkeley
• Sponsoring Organization: US Department of Energy
• DOE Contract Number: 89243024CSC000002
• OSTI ID: 3011984
• Report Number(s): FERMILAB-PUB-25-0709-SQMS-T; NT@UW-25-19; oai:inspirehep.net:3095920; arXiv:2512.21874
• Journal Information: No journal information, Journal Name: No journal information
• Country of Publication: United States
• Language: English