Related papers: Genons, Double Covers and Fault-tolerant Clifford Gates

Genons, Double Covers and Fault-tolerant Clifford Gates

URL: http://arxiv.org/abs/2406.09951v1
Date: Fri, 14 Jun 2024 11:57:51 GMT
Title: Genons, Double Covers and Fault-tolerant Clifford Gates
Authors: Simon Burton, Elijah Durso-Sabina, Natalie C. Brown,
Abstract summary: We show a construction that produces symplectic double code with naturally occurring fault-tolerant logical Clifford gates. We demonstrate this experimentally on Quantinuum's H1-1 trapped-ion quantum computer.
Score: 2.5866180357107242
License: http://creativecommons.org/licenses/by/4.0/
Abstract: A great deal of work has been done developing quantum codes with varying overhead and connectivity constraints. However, given the such an abundance of codes, there is a surprising shortage of fault-tolerant logical gates supported therein. We define a construction, such that given an input $[[n,k,d]]$ code, yields a $[[2n,2k,\ge d]]$ symplectic double code with naturally occurring fault-tolerant logical Clifford gates. As applied to 2-dimensional $D(\mathbb{Z}_2)$-topological codes with genons (twists) and domain walls, we find the symplectic double is genon free, and of possibly higher genus. Braiding of genons on the original code becomes Dehn twists on the symplectic double. Such topological operations are particularly suited for architectures with all-to-all connectivity, and we demonstrate this experimentally on Quantinuum's H1-1 trapped-ion quantum computer.

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