Small Codes for Magic State Distillation

Abstract

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. Many of these distill noisy states right up to the boundary of the known undististillable region, while some distill toward non-stabilizer states that have not previously been considered.

Some additional comments and clarifications. Close to published version. Contribution to the Topical Issue "Quantum Information Processing and Communication". 6 pages, 6 figures

References in corpus (6)

• Restrictions on Transversal Encoded Quantum Gate Sets
• Magic state distillation with low overhead
• Improved magic states distillation for quantum universality
• Multilevel distillation of magic states for quantum computing
• Codeword Stabilized Quantum Codes
• Qutrit Magic State Distillation Tight in Some Directions

Cited by in corpus (3)

• Towers of generalized divisible quantum codes
• From Magic State Distillation to Dynamical Systems
• Low Overhead Qutrit Magic State Distillation