Layer Codes

TL;DR

This paper introduces a method to construct three-dimensional topological quantum codes from stabilizer codes, creating layered defect networks with optimal parameters and manageable stabilizer weights, advancing quantum error correction.

Contribution

It presents a novel construction of 3D topological codes from stabilizer codes, featuring layered defect networks with optimal scaling and low stabilizer weights.

Findings

Constructed 3D topological codes with optimal parameters.

Codes have maximum stabilizer check weight of six.

Achieved polynomial energy barrier with good low-density parity-check codes.

Abstract

The surface code is a two-dimensional topological code with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet optimal code was not previously known. Here, we introduce a construction that takes as input a stabilizer code and produces as output a three-dimensional topological code with related code parameters. The output codes have the special structure of being topological defect networks formed by layers of surface code joined along one-dimensional junctions, with a maximum stabilizer check weight of six. When the input is a family of good low-density parity-check codes, the output is a three-dimensional topological code with optimal scaling code parameters and a polynomial energy barrier.