Layer Codes

• URL: http://arxiv.org/abs/2309.16503v2
• Date: Fri, 10 May 2024 00:22:55 GMT
• Title: Layer Codes
• Authors: Dominic J. Williamson, Nouédyn Baspin,
• Abstract summary: In three dimensions an analogous simple yet optimal code was not previously known. The output codes have the special structure of being topological defect networks formed by layers of surface code joined along one-dimensional junctions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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