2012/10/31 by Cody Jones · 5 citations
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physreva.87.042305
10 pages, 4 figures
arxiv created 2013/03/27 · arxiv updated 2013/04/10
We develop a procedure for distilling magic states used in universal quantum computing that requires substantially fewer initial resources than prior schemes. Our distillation circuit is based on a family of concatenated quantum codes that possess a transversal Hadamard operation, enabling each of these codes to distill the eigenstate of the Hadamard operator. A crucial result of this design is that low-fidelity magic states can be consumed to purify other high-fidelity magic states to even higher fidelity, which we call "multilevel distillation." When distilling in the asymptotic regime of infidelity ε→ 0 for each input magic state, the number of input magic states consumed on average to yield an output state with infidelity O(ε2r) approaches 2r+1, which comes close to saturating the conjectured bound in [Phys. Rev. A 86, 052329]. We show numerically that there exist multilevel protocols such that the average number of magic states consumed to distill from error rate εin = 0.01 to εout in the range 10-5 to 10-40 is about 14log10(1/εout) - 40; the efficiency of multilevel distillation dominates all other reported protocols when distilling Hadamard magic states from initial infidelity 0.01 to any final infidelity below 10-7. These methods are an important advance for magic-state distillation circuits in high-performance quantum computing, and they provide insight into the limitations of nearly resource-optimal quantum error correction.