Layer Codes
arXiv:2309.16503 · doi:10.1038/s41467-024-53881-3
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.
80 pages, 33 figures; v2 substantial changes to improve clarity
References in corpus (5)
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- Fault-tolerant quantum computation with high threshold in two dimensions
- Topological fault-tolerance in cluster state quantum computation
- A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
- On combinatorial structures in linear codes