Universal quantum computation in the surface code using non-Abelian islands

2018/11/16 by Katharina Laubscher, Daniel Loss, James R. Wootton · 1 voice · 1 citation
Physics and Astronomy · #quant-ph #cond-mat.mes-hall

paper · pdf · doi:10.1103/physreva.100.012338

arxiv published 2018/11/16 · arxiv updated 2019/07/24

Abstract

The surface code is currently the primary proposed method for performing quantum error correction. However, despite its many advantages, it has no native method to fault-tolerantly apply non-Clifford gates. Additional techniques are therefore required to achieve universal quantum computation. Here we propose a hybrid scheme which uses small islands of a qudit variant of the surface code to enhance the computational power of the standard surface code. This allows the non-trivial action of the non-Abelian anyons in the former to process information stored in the latter. Specifically, we show that a non-stabilizer state can be prepared, which allows universality to be achieved.

Cited by

• Pauli Stabilizer Models for Gapped Boundaries of Twisted Quantum Doubles and Applications to Composite Dimensional Codes

Discussions

• We worked on something similar back in 2018, and it was unloved and incited for many years. Great to see that suddenly there is an uptick of interest in the topic again. arxiv.org/abs/1811.06738 [bsky, 4 points, 0 comments]

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