{"database":"biostudies-literature","file_versions":[],"scores":null,"additional":{"omics_type":["Unknown"],"volume":["15(1)"],"submitter":["Williamson DJ"],"pubmed_abstract":["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."],"journal":["Nature communications"],"pagination":["9528"],"full_dataset_link":["https://www.ebi.ac.uk/biostudies/studies/S-EPMC11535014"],"repository":["biostudies-literature"],"pubmed_title":["Layer codes."],"pmcid":["PMC11535014"],"pubmed_authors":["Williamson DJ","Baspin N"],"additional_accession":[]},"is_claimable":false,"name":"Layer codes.","description":"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.","dates":{"release":"2024-01-01T00:00:00Z","publication":"2024 Nov","modification":"2025-04-20T03:53:19Z","creation":"2025-04-20T03:53:19Z"},"accession":"S-EPMC11535014","cross_references":{"pubmed":["39496623"],"doi":["10.1038/s41467-024-53881-3"]}}