D-dimensional surface and toric codes via Oscar's chain complexes and GF2 homology (#534)

Author: Fe-r-oz

.typos.toml

@@ -2,6 +2,7 @@
 ket = "ket"
 anc = "anc"
 ba = "ba"
+hom = "hom"
 IY = "IY"
 mor = "mor"
 

CHANGELOG.md

@@ -7,6 +7,7 @@
 
 ## v0.10.1-dev
 
+- The D-dimensional Surface and Toric codes are now implemented using `Oscar`'s chain complexes and `GF2` homology in the ECC submodule.
 - Implementing `apply_inv!` for direct application of the inverse of a given gate.
 - The lifted product code constructor `LPCode` now supports non-commutative group algebras by appropriate switching left/right representations — particularly useful now that there is also an `Oscar` extension, which provides many non-abelian group constructors.
 - Introduce `metacheck_matrix_x`, `metacheck_matrix_z`, and `metacheck_matrix` for CSS codes built using chain complexes and homology.

docs/src/references.bib

@@ -774,3 +774,45 @@ @inproceedings{leverrier2015quantum
   year={2015},
   organization={IEEE}
 }
+
+@article{Berthusen_2024,
+  title={Experiments with the four-dimensional surface code on a quantum charge-coupled device quantum computer},
+  volume={110},
+  ISSN={2469-9934},
+  url={http://dx.doi.org/10.1103/PhysRevA.110.062413},
+  DOI={10.1103/physreva.110.062413},
+  number={6},
+  journal={Physical Review A},
+  publisher={American Physical Society (APS)},
+  author={Berthusen, Noah and Dreiling, Joan and Foltz, Cameron and Gaebler, John P. and Gatterman, Thomas M. and Gresh, Dan and Hewitt, Nathan and Mills, Michael and Moses, Steven A. and Neyenhuis, Brian and Siegfried, Peter and Hayes, David},
+  year={2024},
+  month=dec
+}
+
+@article{Zeng_2019,
+  title={Higher-Dimensional Quantum Hypergraph-Product Codes with Finite Rates},
+  volume={122},
+  ISSN={1079-7114},
+  url={http://dx.doi.org/10.1103/PhysRevLett.122.230501},
+  DOI={10.1103/physrevlett.122.230501},
+  number={23},
+  journal={Physical Review Letters},
+  publisher={American Physical Society (APS)},
+  author={Zeng, Weilei and Pryadko, Leonid P.},
+  year={2019},
+  month=jun
+}
+
+@article{Higgott_2023,
+  title={Improved Single-Shot Decoding of Higher-Dimensional Hypergraph-Product Codes},
+  volume={4},
+  ISSN={2691-3399},
+  url={http://dx.doi.org/10.1103/PRXQuantum.4.020332},
+  DOI={10.1103/prxquantum.4.020332},
+  number={2},
+  journal={PRX Quantum},
+  publisher={American Physical Society (APS)},
+  author={Higgott, Oscar and Breuckmann, Nikolas P.},
+  year={2023},
+  month=may
+}

docs/src/references.md

@@ -50,6 +50,8 @@ For quantum code construction routines:
 - [naghipour2015quantum](@cite)
 - [eberhardt2024logical](@cite)
 - [delfosse2020short](@cite)
+- [Berthusen_2024](@cite)
+- [Zeng_2019](@cite)
 
 For classical code construction routines:
 - [muller1954application](@cite)

ext/QuantumCliffordOscarExt/QuantumCliffordOscarExt.jl

@@ -2,21 +2,34 @@ module QuantumCliffordOscarExt
 
 using DocStringExtensions
 
+import LinearAlgebra
+import LinearAlgebra: rank
+import QuantumClifford
+import QuantumClifford: Stabilizer
 import Nemo
 import Nemo: FqFieldElem
 import Hecke: group_algebra, GF, abelian_group, gens, quo, one, GroupAlgebra,
-   GroupAlgebraElem, direct_product, sub
+   GroupAlgebraElem, direct_product, sub, ZZ, lift
 import Oscar
 import Oscar: free_group, small_group_identification, describe, order, FPGroupElem, FPGroup,
-    BasicGAPGroupElem, DirectProductGroup, cyclic_group
+    BasicGAPGroupElem, DirectProductGroup, cyclic_group, free_module, hom, transpose, tensor_product,
+    chain_complex, total_complex, map, summands, MatElem, matrix, nrows, ncols, kernel, dim, range, image,
+    base_ring, ComplexOfMorphisms
+import Oscar.Generic.DirectSumModule
 
-import QuantumClifford.ECC: two_block_group_algebra_codes, twobga_from_direct_product, twobga_from_fp_group
+import QuantumClifford.ECC: two_block_group_algebra_codes, twobga_from_direct_product, twobga_from_fp_group,
+    boundary_maps
+
+import QECCore: AbstractECC, CSS, RepCode, AbstractCSSCode,
+    hgp, code_k, code_n, code_s, distance, parity_matrix_x, parity_matrix_z, parity_matrix_xz, parity_matrix,
+    metacheck_matrix_x, metacheck_matrix_z, metacheck_matrix
 
 # exported from extension so that Documenter.jl sees them when autogenerating API lists
-export twobga_from_direct_product, twobga_from_fp_group
+export twobga_from_direct_product, twobga_from_fp_group, DDimensionalSurfaceCode, DDimensionalToricCode, boundary_maps
 
 include("types.jl")
 include("direct_product.jl")
 include("group_presentation.jl")
+include("d_dimensional_codes.jl")
 
 end # module