3-d topological quantum memory with a power-law energy barrier

TL;DR

This paper introduces a 3D quantum memory code with a significantly improved energy barrier, achieved by combining solid codes through welding, which enhances self-correcting capabilities in quantum computing.

Contribution

The authors develop a novel 3D stabilizer code with an exponential increase in energy barrier by welding solid codes, breaking microscopic translation invariance to avoid no-go results.

Findings

Energy barrier of the new code is O(L^{2/3})

Code parameters are [[O(L^3),1,O(L^{4/3})]]

Significant improvement over previous 3D quantum memory codes

Abstract

We discuss energy barriers and their relationship to self-correcting quantum memories. We introduce the solid code, a 3-d version of Kitaev's surface code, and then combine several solid codes using a technique called welding. The resulting code is a $[[O(L^3),1,O(L^{\frac{4}{3}})]]$ stabilizer code with an energy barrier of $O(L^{\frac{2}{3}})$, which is an exponential improvement over the previous highest energy barrier in 3-d. No-go results are avoided by breaking microscopic translation invariance.