Optimizing constants for asymptotically good codes with transversal non-Clifford gates and their practical advantage

Construct asymptotically good quantum codes that support transversally implementable non-Clifford gates with improved constant factors, and determine in the finite-length regime whether constant-overhead magic state distillation using such codes outperforms conventional polylogarithmic-overhead protocols.

Background

The paper proves the existence of asymptotically good codes enabling constant-overhead magic state distillation under a local stochastic error model, but does not optimize constant factors or finite-length performance.

Assessing practical benefits requires improved constructions with better constants and a comparative paper against existing polylog-overhead protocols at realistic blocklengths.