Small Codes for Magic State Distillation

Understand

Magic state distillation is a critical component in leading proposals for fault-tolerant quantum computation.

• Relatively little is known, however, about how to construct a magic state distillation routine or, more specifically, which stabilizer codes are suitable for the task.
• While transversality of a non-Clifford gate within a code often leads to efficient distillation routines, it appears to not be a necessary condition.
• Here we have examined a number of small stabilizer codes and highlight a handful of which displaying interesting, albeit inefficient, distillation behaviour.