Layer codes | Nature Communications
Nature Communications volume 15, Article number: 9528 (2024 ) Cite this article
Quantum computers require memories that are capable of storing quantum information reliably for long periods of time. The surface code is a two-dimensional quantum memory 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 present a family of three dimensional topological codes with optimal scaling code parameters and a polynomial energy barrier. Our codes are based on a construction that takes in a stabilizer code and outputs a three-dimensional topological code with related code parameters. The output codes are 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 quantum low-density parity-check codes the output codes have optimal scaling. Our results uncover strongly-correlated states of quantum matter that are capable of storing quantum information with the strongest possible protection from errors that is achievable in three dimensions.
Quantum computing promises to open a new window into highly-entangled quantum many-body physics1,2,3,4,5. Quantum error correction is a crucial ingredient in the design of scalable quantum computers that aim to access new regimes of physics beyond the reach of classical simulations6,7,8,9,10,11,12,13,14. Topological quantum codes form the basis of leading approaches to implement quantum error correction15,16,17,18,19,20,21,22. This can be attributed to their favorable properties, including relatively simple stabilizer checks and high thresholds. Topological codes form an important subclass of low-density parity check (LDPC) codes23,24,25,26, set apart by the geometric locality of their checks.
