A triple homological product of good quantum LDPC codes achieves distance N^(2/3) with transversal CCZ gates and prepares N^(1/3) magic states in a single round.
[2, 10, 37, 38] applicable to more general stabilizer codes including non-Pauli stabilizer models
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Transversal non-Clifford gates on qLDPC codes breaking the $\sqrt{N}$ distance barrier and quantum-inspired geometry with $\mathbb{Z}_2$ systolic freedom
A triple homological product of good quantum LDPC codes achieves distance N^(2/3) with transversal CCZ gates and prepares N^(1/3) magic states in a single round.