On Optimality of CSS Codes for Transversal T
In order to perform universal fault-tolerant quantum computation, one needs to implement a logical non-Clifford gate. Consequently, it is important to understand codes that implement such gates transversally. In this paper, we adopt an algebraic approach to characterize all stabilizer codes for which transversal T and T† gates preserve the codespace. Our Heisenberg perspective reduces this question to a finite geometry problem that translates to the design of certain classical codes.