Genons, Double Covers and Fault-tolerant Clifford Gates

TL;DR

This paper introduces a construction that transforms quantum codes into double codes supporting fault-tolerant Clifford gates, leveraging genons and topological operations, with experimental validation on a trapped-ion quantum computer.

Contribution

The authors present a novel method to generate symplectic double codes from existing quantum codes, enabling fault-tolerant Clifford gates and topological operations like Dehn twists.

Findings

Double codes support fault-tolerant Clifford gates.

Genon-free symplectic doubles can have higher genus.

Experimental demonstration on Quantinuum's H1-1 quantum computer.

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.