Eur. Phys. J. D (2016) 70: 55
https://doi.org/10.1140/epjd/e2016-60682-y

Regular Article

Small codes for magic state distillation

¹ Department of Physics and Astronomy, University of Sheffield, Sheffield, UK
² Institute for Quantum Computing and Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
³ Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1

^a e-mail: m.howard@sheffield.ac.uk

Received: 30 November 2015
Received in final form: 1 February 2016
Published online: 15 March 2016

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.