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Small codes for magic state distillation

Banff International Research Station for Mathematical Innovation and Discovery

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. As a consequence of recent results, this implies that there is a family of quantum states that enable universality if and only if they exhibit contextuality with respect to stabilizer measurements.

Mathematics; Quantum theory; Information and communication, circuits; Theoretical computer science

video/mp4

Author affiliation: University of Waterloo

2016-10-18

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59481

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/