Distilling magic T states without transversal T gates

Magic state distillation (MSD) is a crucial routine for providing non-Clifford resources in fault-tolerant quantum computation. Most previous work exploring new MSD protocols has focused on stabilizer codes with transversal non-Clifford gates (primarily T gates) due to the fault-tolerance properties of transversality. However, there exist MSD protocols that do not require codes with transversal non-Clifford gates, which we refer to as exotic MSD protocols. For example, the [[7,1,3]] Steane code enables T state distillation, as demonstrated by Reichardt [1].

In this work, we focus on these exotic MSD protocols and investigate their underlying code properties. We demonstrate that stabilizer codes with transversal Clifford gates can be used to distill their eigenstates, and we establish the necessary and sufficient conditions for these codes to function as exotic MSD protocols. Furthermore, we prove that all exotic MSD protocols are non-deterministic and possess a finite failure probability for noiseless input states. Finally, we explore a new class of stabilizer codes that could support exotic T state distillation and generalize this approach to distill other magic states.

[1] Reichardt, B.W. Quantum Inf Process 4, 251–264 (2005).