initial commit: LP construction of bivariate bicycle using cyclic groups

Project.toml

@@ -27,14 +27,15 @@ CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
 Hecke = "3e1990a7-5d81-5526-99ce-9ba3ff248f21"
 LDPCDecoders = "3c486d74-64b9-4c60-8b1a-13a564e77efb"
 Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
+Oscar = "f1435218-dba5-11e9-1e4d-f1a5fab5fc13"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 PyQDecoders = "17f5de1a-9b79-4409-a58d-4d45812840f7"
 Quantikz = "b0d11df0-eea3-4d79-b4a5-421488cbf74b"
 QuantumOpticsBase = "4f57444f-1401-5e15-980d-4471b28d5678"
 
 [extensions]
 QuantumCliffordGPUExt = "CUDA"
-QuantumCliffordHeckeExt = "Hecke"
+QuantumCliffordHeckeExt = ["Hecke", "Oscar"]
 QuantumCliffordLDPCDecodersExt = "LDPCDecoders"
 QuantumCliffordMakieExt = "Makie"
 QuantumCliffordPlotsExt = "Plots"
@@ -48,15 +49,16 @@ Combinatorics = "1.0"
 DataStructures = "0.18"
 DocStringExtensions = "0.9"
 Graphs = "1.9"
-Hecke = "0.28, 0.29, 0.30, 0.31, 0.32, 0.33, 0.34"
+Hecke = "0.30, 0.31, 0.32, 0.33, 0.34, 0.34.3, 0.34.4"
 HostCPUFeatures = "0.1.6"
 ILog2 = "0.2.3"
 InteractiveUtils = "1.9"
 LDPCDecoders = "0.3.1"
 LinearAlgebra = "1.9"
 MacroTools = "0.5.9"
 Makie = "0.20, 0.21"
-Nemo = "0.42.1, 0.43, 0.44, 0.45, 0.46, 0.47"
+Nemo = "0.43.1, 0.44, 0.45, 0.46, 0.47"
+Oscar = "1.0.0, 1.0.4, 1.1.1"
 Plots = "1.38.0"
 PrecompileTools = "1.2"
 PyQDecoders = "0.2.1"

ext/QuantumCliffordHeckeExt/QuantumCliffordHeckeExt.jl

@@ -8,10 +8,12 @@ import Hecke: Group, GroupElem, AdditiveGroup, AdditiveGroupElem,
     multiplication_table, coefficients, abelian_group, group_algebra
 import Nemo
 import Nemo: characteristic, matrix_repr, GF, ZZ, lift
+import Oscar
+import Oscar: cyclic_group, direct_product
 
 import QuantumClifford.ECC: AbstractECC, CSS, ClassicalCode,
     hgp, code_k, code_n, code_s, iscss, parity_checks, parity_checks_x, parity_checks_z, parity_checks_xz,
-    two_block_group_algebra_codes, generalized_bicycle_codes, bicycle_codes
+    two_block_group_algebra_codes, generalized_bicycle_codes, bicycle_codes, bivariate_bicycle_codes
 
 include("types.jl")
 include("lifted.jl")

ext/QuantumCliffordHeckeExt/lifted_product.jl

@@ -120,6 +120,11 @@ function LPCode(shift_array1::Matrix{Int}, shift_array2::Matrix{Int}, l::Int; GA
     LPCode(LiftedCode(shift_array1, l; GA=GA), LiftedCode(shift_array2, l; GA=GA); GA=GA, repr=representation_matrix)
 end
 
+# TODO define LiftedProduct code constructor that takes `m` and `GA` as product of cyclic groups as input as well.
+function LPCode(shift_array1::Matrix{Int}, shift_array2::Matrix{Int}, l::Int, m::Int; GA::GroupAlgebra=group_algebra(GF(2), direct_product(cyclic_group(l), cyclic_group(m))))
+    LPCode(LiftedCode(shift_array1, l, m; GA=GA), LiftedCode(shift_array2, l, m; GA=GA); GA=GA, repr=representation_matrix)
+end
+
 iscss(::Type{LPCode}) = true
 
 function parity_checks_xz(c::LPCode)
@@ -185,3 +190,19 @@ function bicycle_codes(a_shifts::Array{Int}, l::Int)
     a = sum(GA[n÷l+1] for n in a_shifts)
     two_block_group_algebra_codes(a, a')
 end
+
+"""
+Bivariate Bicycle codes belong to a wider class of generalized bicycle (GB) codes,
+which are further generalized into of two block group algebra (2GBA) codes.
+
+BBQLDPC can be viewed as a special case of Lifted Product construction based on
+abelian group `ℤₗ x ℤₘ` where `ℤⱼ` cyclic group of order `j`.
+
+The ECC Zoo has an [entry for this family](https://errorcorrectionzoo.org/c/qcga).
+"""
+function bivariate_bicycle_codes(a_shifts::Array{Int}, b_shifts::Array{Int}, l::Int, m::Int)
+    GA = group_algebra(GF(2), direct_product(cyclic_group(l), cyclic_group(m)))
+    a = sum(GA[(n%l)+l*((n÷l)%m)+1] for n in a_shifts)
+    b = sum(GA[(n%l)+l*((n÷l)%m)+1] for n in b_shifts)
+    two_block_group_algebra_codes(a, b)
+end

src/ecc/ECC.jl

@@ -22,6 +22,7 @@ export parity_checks, parity_checks_x, parity_checks_z, iscss,
     Shor9, Steane7, Cleve8, Perfect5, Bitflip3,
     Toric, Gottesman, Surface, Concat, CircuitCode, QuantumReedMuller,
     LPCode, two_block_group_algebra_codes, generalized_bicycle_codes, bicycle_codes,
+    bivariate_bicycle_codes,
     random_brickwork_circuit_code, random_all_to_all_circuit_code,
     evaluate_decoder,
     CommutationCheckECCSetup, NaiveSyndromeECCSetup, ShorSyndromeECCSetup,

src/ecc/codes/lifted_product.jl

@@ -17,3 +17,6 @@ function generalized_bicycle_codes end
 
 """Implemented in a package extension with Hecke."""
 function bicycle_codes end
+
+"""Implemented in a package extension with Hecke."""
+function bivariate_bicycle_codes end

test/Project.toml

@@ -1,28 +1,39 @@
 [deps]
 AbstractAlgebra = "c3fe647b-3220-5bb0-a1ea-a7954cac585d"
+AlgebraicSolving = "66b61cbe-0446-4d5d-9090-1ff510639f9d"
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
 CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
 Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
+DeepDiffs = "ab62b9b5-e342-54a8-a765-a90f495de1a6"
+Distributed = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+GAP = "c863536a-3901-11e9-33e7-d5cd0df7b904"
 Graphs = "86223c79-3864-5bf0-83f7-82e725a168b6"
 Hecke = "3e1990a7-5d81-5526-99ce-9ba3ff248f21"
 HostCPUFeatures = "3e5b6fbb-0976-4d2c-9146-d79de83f2fb0"
 ILog2 = "2cd5bd5f-40a1-5050-9e10-fc8cdb6109f5"
 InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 JET = "c3a54625-cd67-489e-a8e7-0a5a0ff4e31b"
+JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
+JSON3 = "0f8b85d8-7281-11e9-16c2-39a750bddbf1"
 LDPCDecoders = "3c486d74-64b9-4c60-8b1a-13a564e77efb"
+LazyArtifacts = "4af54fe1-eca0-43a8-85a7-787d91b784e3"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 MacroTools = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
 Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a"
+Oscar = "f1435218-dba5-11e9-1e4d-f1a5fab5fc13"
+Polymake = "d720cf60-89b5-51f5-aff5-213f193123e7"
 PyQDecoders = "17f5de1a-9b79-4409-a58d-4d45812840f7"
 Quantikz = "b0d11df0-eea3-4d79-b4a5-421488cbf74b"
 QuantumInterface = "5717a53b-5d69-4fa3-b976-0bf2f97ca1e5"
 QuantumOpticsBase = "4f57444f-1401-5e15-980d-4471b28d5678"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
+Serialization = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 SIMD = "fdea26ae-647d-5447-a871-4b548cad5224"
+Singular = "bcd08a7b-43d2-5ff7-b6d4-c458787f915c"
 StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 Static = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
 StridedViews = "4db3bf67-4bd7-4b4e-b153-31dc3fb37143"

test/test_ecc_base.jl

@@ -6,6 +6,7 @@ using InteractiveUtils
 import Nemo: GF
 import LinearAlgebra
 import Hecke: group_algebra, abelian_group, gens
+import Oscar: cyclic_group, direct_product
 
 # generate instances of all implemented codes to make sure nothing skips being checked
 
@@ -64,7 +65,8 @@ const code_instance_args = Dict(
     :Concat => [(Perfect5(), Perfect5()), (Perfect5(), Steane7()), (Steane7(), Cleve8()), (Toric(2, 2), Shor9())],
     :CircuitCode => random_circuit_code_args,
     :LPCode => (c -> (c.A, c.B)).(vcat(LP04, LP118, test_gb_codes, other_lifted_product_codes)),
-    :QuantumReedMuller => [3, 4, 5]
+    :QuantumReedMuller => [3, 4, 5],
+    :bivariate_bicycle_codes =>[([3,1,2],[3,1,2],6,6),([3,1,2],[3,1,2],9,6)]
 )
 
 function all_testablable_code_instances(;maxn=nothing)

test/test_ecc_decoder_all_setups.jl

@@ -35,7 +35,8 @@
     ##
 
     @testset "belief prop decoders, good for sparse codes" begin
-        codes = vcat(LP04, LP118, test_gb_codes, other_lifted_product_codes)
+        codes = [vcat(LP04, LP118, test_gb_codes, other_lifted_product_codes),
+                 bivariate_bicycle_codes([3,1,2],[3,1,2],6,6), bivariate_bicycle_codes([3,1,2],[3,1,2],9,6)]
 
         noise = 0.001
 

test/test_jet.jl

@@ -9,6 +9,7 @@
     using Nemo
     using AbstractAlgebra
     using Hecke
+    using Oscar
 
     rep = report_package("QuantumClifford";
         ignored_modules=(
@@ -21,6 +22,7 @@
             AnyFrameModule(Nemo),
             AnyFrameModule(AbstractAlgebra),
             AnyFrameModule(Hecke),
+            AnyFrameModule(Oscar)
     ))
 
     @show rep