Multilevel distillation of magic states for quantum computing

Cody Jones

doi:10.1103/PhysRevA.87.042305

paper

Multilevel distillation of magic states for quantum computing

arXiv:1210.3388 · doi:10.1103/PhysRevA.87.042305

Abstract

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 $ε \to 0$ for each input magic state, the number of input magic states consumed on average to yield an output state with infidelity $O (ε^{2^{r}})$ approaches $2^{r} + 1$ , 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 $ε_{in} = 0.01$ to $ε_{out}$ in the range $1 0^{- 5}$ to $1 0^{- 40}$ is about $14 lo g_{10} (1/ ε_{out}) - 40$ ; 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 $1 0^{- 7}$ . 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.

10 pages, 4 figures

Multilevel distillation of magic states for quantum computing

Abstract

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