Enhancements: fix QuantumSavory#405, new API, decoder testing for non…

…-abelian 2BGA, and misc polish

docs/src/references.bib

@@ -498,3 +498,30 @@ @article{lin2024quantum
   year={2024},
   publisher={APS}
 }
+
+@inproceedings{wang2023abelian,
+  title={Abelian and non-Abelian quantum two-block codes},
+  author={Wang, Renyu and Lin, Hsiang-Ku and Pryadko, Leonid P},
+  booktitle={2023 12th International Symposium on Topics in Coding (ISTC)},
+  pages={1--5},
+  year={2023},
+  organization={IEEE}
+}
+
+@article{naghipour2015quantum,
+  title={Quantum stabilizer codes from Abelian and non-Abelian groups association schemes},
+  author={Naghipour, Avaz and Jafarizadeh, Mohammad Ali and Shahmorad, Sedaghat},
+  journal={International Journal of Quantum Information},
+  volume={13},
+  number={03},
+  pages={1550021},
+  year={2015},
+  publisher={World Scientific}
+}
+
+@article{willenborg2023dihedral,
+  title={Dihedral Quantum Codes},
+  author={Willenborg, Nadja and Borello, Martino and Horlemann, Anna-Lena and Islam, Habibul},
+  journal={arXiv preprint arXiv:2310.15092},
+  year={2023}
+}

docs/src/references.md

@@ -41,6 +41,9 @@ For quantum code construction routines:
 - [campbell2012magic](@cite)
 - [anderson2014fault](@cite)
 - [lin2024quantum](@cite)
+- [wang2023abelian](@cite)
+- [naghipour2015quantum](@cite)
+- [willenborg2023dihedral](@cite)
 
 For classical code construction routines:
 - [muller1954application](@cite)

ext/QuantumCliffordOscarExt/QuantumCliffordOscarExt.jl

@@ -4,12 +4,15 @@ using DocStringExtensions
 
 import Nemo
 import Nemo: FqFieldElem
-import Hecke: group_algebra, GF, abelian_group, gens, quo, one, GroupAlgebra
+import Hecke: group_algebra, GF, abelian_group, gens, quo, one, GroupAlgebra, GroupAlgebraElem
 import Oscar
-import Oscar: free_group, small_group_identification, describe, order, FPGroupElem, FPGroup, FPGroupElem
+import Oscar: free_group, small_group_identification, describe, order, FPGroupElem, FPGroup, FPGroupElem,
+    semidirect_product, automorphism_group, hom, gen, cyclic_group, SemidirectProductGroup, PcGroup,
+    BasicGAPGroupElem, normal_subgroup
 
 import QuantumClifford.ECC: two_block_group_algebra_codes
 
 include("group_presentation.jl")
+include("semidirect_product.jl")
 
 end # module

ext/QuantumCliffordOscarExt/group_presentation.jl

@@ -3,7 +3,7 @@
 
 For quantum error-correcting codes, such as the two-block algebra (2BGA) code, functionalities
 like designing specific group presentations for both abelian and non-abelian groups are crucial.
-These specific presentations are the key ingredient for construction of group algebra of 2BGA
+These specific presentations are the key ingredient for the construction of group algebra of 2BGA
 with abelian and non-abelian groups.
 
 # Example
@@ -80,13 +80,13 @@ julia> code_n(c), code_k(c)
 Dihedral groups with specific group presentations `Dₘ = ⟨r, s|rᵐ = s² = (rs)² = 1⟩` where order
 is `2m` are supported.
 
-To construct a group algebra for non-abelian Dihedral groups, specify the group's presentation
+To construct a group algebra for non-abelian dihedral groups, specify the group's presentation
 `⟨S|R⟩` using its generators `S` and defining relations `R`.
 
 # Example
 
 [[24, 8, 3]] 2BGA code from Appendix C, Table III of [lin2024quantum](@cite) for non-abelian
-Dihedral group `D₆`.
+dihedral group `D₆`.
 
 ```jldoctest finitegrp
 julia> m = 6;

ext/QuantumCliffordOscarExt/semidirect_product.jl

@@ -0,0 +1,58 @@
+"""
+# Semidirect Product of Groups
+
+The semidirect product of groups `Gₘ ⋉ Gₙ` is supported, where `m` and `n` represent
+the orders of the groups `Gₘ` and `Gₙ`, respectively. This functionality enhances the
+capabilities of 2BGA codes, as the resulting group is used to construct the group
+algebra for these codes.
+
+# Example:`Cₘ ⋉ C₂`
+
+The non-abelian [[24, 8, 3]] 2BGA code is constructed from the dihedral group
+`Dₘ = Cₘ ⋉ C₂`, with an order of `l = 12` and a standard group presentation, as
+defined in Appendix C, Table III of [lin2024quantum](@cite).
+
+```jldoctest semidirectproduct
+julia> using Nemo: FqFieldElem # hide
+
+julia> using Hecke: group_algebra, GF, abelian_group, gens, quo, one, GroupAlgebra, GroupAlgebraElem # hide
+
+julia> using Oscar: small_group_identification, describe, order, FPGroupElem, FPGroup, FPGroupElem, semidirect_product, automorphism_group, hom, gen, cyclic_group, SemidirectProductGroup, PcGroup, BasicGAPGroupElem, normal_subgroup # hide
+
+julia> m = 6;
+
+julia> Cₘ = cyclic_group(m);
+
+julia> C₂ = cyclic_group(2);
+
+julia> A = automorphism_group(Cₘ); # Given dihedral group presentation, choose r -> r⁻¹
+
+julia> au = A(hom(Cₘ,Cₘ,[Cₘ[1]],[Cₘ[1]^-1]));
+
+julia> f = hom(C₂,A,[C₂[1]],[au]);
+
+julia> G = semidirect_product(Cₘ,f,C₂);
+
+julia> GA = group_algebra(GF(2), G);
+
+julia> r, s = gens(GA)[2], gens(GA)[3];
+
+julia> a = [one(r), r^4];
+
+julia> b = [one(r), s*r^4, r^3, r^4, s*r^2, r];
+
+julia> c = twobga_via_semidirect_product(a, b, GA);
+
+julia> order(G), describe(G)
+(12, "D12")
+
+julia> describe(normal_subgroup(G)), small_group_identification(G)
+("C6", (12, 4))
+```
+"""
+function twobga_via_semidirect_product(a_elts::Vector{GroupAlgebraElem{FqFieldElem, GroupAlgebra{FqFieldElem, SemidirectProductGroup{PcGroup, PcGroup}, BasicGAPGroupElem{SemidirectProductGroup{PcGroup, PcGroup}}}}}, b_elts::Vector{GroupAlgebraElem{FqFieldElem, GroupAlgebra{FqFieldElem, SemidirectProductGroup{PcGroup, PcGroup}, BasicGAPGroupElem{SemidirectProductGroup{PcGroup, PcGroup}}}}}, GA::GroupAlgebra{FqFieldElem, SemidirectProductGroup{PcGroup, PcGroup}, BasicGAPGroupElem{SemidirectProductGroup{PcGroup, PcGroup}}})
+    a = sum(GA(x) for x in a_elts)
+    b = sum(GA(x) for x in b_elts)
+    c = two_block_group_algebra_codes(a,b)
+    return c
+end

src/ecc/ECC.jl

@@ -23,7 +23,7 @@ export parity_checks, parity_checks_x, parity_checks_z, iscss,
     Toric, Gottesman, Surface, Concat, CircuitCode, QuantumReedMuller,
     LPCode, two_block_group_algebra_codes, generalized_bicycle_codes, bicycle_codes,
     random_brickwork_circuit_code, random_all_to_all_circuit_code,
-    twobga_from_fp_group,
+    twobga_from_fp_group, twobga_via_semidirect_product,
     evaluate_decoder,
     CommutationCheckECCSetup, NaiveSyndromeECCSetup, ShorSyndromeECCSetup,
     TableDecoder,
@@ -387,6 +387,9 @@ include("codes/classical/lifted.jl")
 include("codes/lifted_product.jl")
 
 # group presentation
-include("codes/group_presentation.jl")
+include("codes/twobga_extension/group_presentation.jl")
+
+# semidirect product
+include("codes/twobga_extension/semidirect_product.jl")
 
 end #module

src/ecc/codes/twobga_extension/semidirect_product.jl

@@ -0,0 +1,12 @@
+"""
+The `twobga_via_semidirect_product` method constructs the semidirect product `Gₘ ⋉ Gₙ` of groups, where `m` and `n` represent the order of each group, respectively.
+
+Implemented as a package extension with Oscar. Check the [QuantumClifford documentation](http://qc.quantumsavory.org/stable/ECC_API/) for more details on that extension.
+"""
+function twobga_via_semidirect_product(args...)
+    ext = Base.get_extension(QuantumClifford, :QuantumCliffordOscarExt)
+    if isnothing(ext)
+        throw("The `twobga_via_semidirect_product` depends on the package `Oscar` but you have not installed or imported it yet. Immediately after you import `Oscar`, the `twobga_via_semidirect_product` will be available.")
+    end
+    return ext.twobga_via_semidirect_product(args...)
+end

test/test_ecc_base.jl

@@ -6,7 +6,7 @@ using InteractiveUtils
 import Nemo: GF
 import LinearAlgebra
 import Hecke: group_algebra, abelian_group, gens, quo, one
-import Oscar: free_group
+import Oscar: free_group, semidirect_product, automorphism_group, hom, cyclic_group
 
 # generate instances of all implemented codes to make sure nothing skips being checked
 
@@ -97,7 +97,35 @@ a = [one(G), x^6]
 b = [one(G), s * x^7, s * x^4, x^6, s * x^5, s * x^2]
 tb22 = twobga_from_fp_group(a, b, GA)
 
-test_twobga_codes = [t1b1, t1b3, tb21, tb22]
+# [[24, 8, 3]] dihedral 2BGA taken from Appendix C, Table III of [lin2024quantum](@cite)
+m = 6
+Cₘ = cyclic_group(m)
+C₂ = cyclic_group(2)
+A = automorphism_group(Cₘ); # Given dihedral group presentation, choose r -> r⁻¹
+au = A(hom(Cₘ,Cₘ,[Cₘ[1]],[Cₘ[1]^-1]))
+f = hom(C₂,A,[C₂[1]],[au])
+G = semidirect_product(Cₘ,f,C₂)
+GA = group_algebra(GF(2), G)
+r, s = gens(GA)[2], gens(GA)[3]
+a = [one(r), r^4]
+b = [one(r), s*r^4, r^3, r^4, s*r^2, r]
+tb31 = twobga_via_semidirect_product(a, b, GA)
+
+# [[64, 32, 2]] dihedral 2BGA taken from Appendix C, Table III of [lin2024quantum](@cite)
+m = 16
+Cₘ = cyclic_group(m)
+C₂ = cyclic_group(2)
+A = automorphism_group(Cₘ); # Given dihedral group presentation, choose r -> r⁻¹
+au = A(hom(Cₘ,Cₘ,[Cₘ[1]],[Cₘ[1]^-1]))
+f = hom(C₂,A,[C₂[1]],[au])
+G = semidirect_product(Cₘ,f,C₂)
+GA = group_algebra(GF(2), G)
+r, s = gens(GA)[2], gens(GA)[3]
+a = [one(r), r^8]
+b = [one(r), s*r^11, s*r^12, r^8, s*r^3, s*r^4]
+tb32 = twobga_via_semidirect_product(a, b, GA)
+
+test_twobga_codes = [t1b1, t1b3, tb21, tb22, tb31, tb32]
 
 const code_instance_args = Dict(
     :Toric => [(3,3), (4,4), (3,6), (4,3), (5,5)],