From 95e8eba89094580fe1c0bcc5d9b51edfe2312e15 Mon Sep 17 00:00:00 2001 From: Fe-r-oz Date: Fri, 18 Oct 2024 20:10:44 +0500 Subject: [PATCH] Non-Abelian Dihedral Groups via Group Presentation --- test/Project.toml | 1 + test/test_ecc_dihedral2bga.jl | 294 ++++++++++++++++++++++++++++++++++ 2 files changed, 295 insertions(+) create mode 100644 test/test_ecc_dihedral2bga.jl diff --git a/test/Project.toml b/test/Project.toml index cd15ae310..c69088264 100644 --- a/test/Project.toml +++ b/test/Project.toml @@ -16,6 +16,7 @@ LDPCDecoders = "3c486d74-64b9-4c60-8b1a-13a564e77efb" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" MacroTools = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09" Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a" +Oscar = "f1435218-dba5-11e9-1e4d-f1a5fab5fc13" PyQDecoders = "17f5de1a-9b79-4409-a58d-4d45812840f7" Quantikz = "b0d11df0-eea3-4d79-b4a5-421488cbf74b" QuantumInterface = "5717a53b-5d69-4fa3-b976-0bf2f97ca1e5" diff --git a/test/test_ecc_dihedral2bga.jl b/test/test_ecc_dihedral2bga.jl new file mode 100644 index 000000000..dd6276f45 --- /dev/null +++ b/test/test_ecc_dihedral2bga.jl @@ -0,0 +1,294 @@ +@testitem "ECC 2BGA Reprroduce Table 3 lin2024quantum" begin + using Nemo: FqFieldElem + using Hecke: group_algebra, GF, abelian_group, gens, quo, one, GroupAlgebra + using QuantumClifford.ECC + using QuantumClifford.ECC: code_k, code_n, two_block_group_algebra_codes + using Oscar: free_group, small_group_identification, describe, order, FPGroupElem, FPGroup, FPGroupElem + + function get_code(a_elts::Vector{FPGroupElem}, b_elts::Vector{FPGroupElem}, F2G::GroupAlgebra{FqFieldElem, FPGroup, FPGroupElem}) + a = sum(F2G(x) for x in a_elts) + b = sum(F2G(x) for x in b_elts) + c = two_block_group_algebra_codes(a,b) + return c + end + + @testset "Reproduce Table 3 of lin2024quantum" begin + # [[24, 8, 3]] + m = 6 + F = free_group(["r", "s"]) + r, s = gens(F) + G, = quo(F, [r^m, s^2, (r*s)^2]) + F2G = group_algebra(GF(2), G) + r, s = gens(G) + a_elts = [one(G), r^4] + b_elts = [one(G), s*r^4, r^3, r^4, s*r^2, r] + c = get_code(a_elts, b_elts, F2G) + @test order(G) == 2*m + @test describe(G) == "D$(m*2)" + @test code_n(c) == 24 && code_k(c) == 8 + # Oscar.describe(Oscar.small_group(2*m, 4)) is D₁₂, cross-check it with G + @test small_group_identification(G) == (order(G), 4) + + # [[24, 12, 2]] + F = free_group(["r", "s"]) + r, s = gens(F) + G, = quo(F, [r^m, s^2, (r*s)^2]) + F2G = group_algebra(GF(2), G) + r, s = gens(G) + a_elts = [one(G), r^3] + b_elts = [one(G), s*r, r^3, r^4, s*r^4, r] + c = get_code(a_elts, b_elts, F2G) + @test order(G) == 2*m + @test describe(G) == "D$(m*2)" + @test code_n(c) == 24 && code_k(c) == 12 + # Oscar.describe(Oscar.small_group(2*m, 4)) is D₁₂, cross-check it with G + @test small_group_identification(G) == (order(G), 4) + + # [[32, 8, 4]] + m = 8 + F = free_group(["r", "s"]) + r, s = gens(F) + G, = quo(F, [r^m, s^2, (r*s)^2]) + F2G = group_algebra(GF(2), G) + r, s = gens(G) + a_elts = [one(G), r^2] + b_elts = [one(G), s*r^5, s*r^4, r^2, s*r^7, s*r^6] + c = get_code(a_elts, b_elts, F2G) + @test order(G) == 2*m + @test describe(G) == "D$(m*2)" + @test code_n(c) == 32 && code_k(c) == 8 + # Oscar.describe(Oscar.small_group(2*m, 7)) is D₁₆, cross-check it with G + @test small_group_identification(G) == (order(G), 7) + + # [[32, 16, 2]] + F = free_group(["r", "s"]) + r, s = gens(F) + G, = quo(F, [r^m, s^2, (r*s)^2]) + F2G = group_algebra(GF(2), G) + r, s = gens(G) + a_elts = [one(G), r^4] + b_elts = [one(G), s*r^3, s*r^6, r^4, s*r^7, s*r^2] + c = get_code(a_elts, b_elts, F2G) + @test order(G) == 2*m + @test describe(G) == "D$(m*2)" + @test code_n(c) == 32 && code_k(c) == 16 + # Oscar.describe(Oscar.small_group(2*m, 7)) is D₁₆, cross-check it with G + @test small_group_identification(G) == (order(G), 7) + + # [[36, 12, 3]] + m = 9 + F = free_group(["r", "s"]) + r, s = gens(F) + G, = quo(F, [r^m, s^2, (r*s)^2]) + F2G = group_algebra(GF(2), G) + r, s = gens(G) + a_elts = [one(G), r^3] + b_elts = [one(G), s, r, r^3, s*r^3, r^4] + c = get_code(a_elts, b_elts, F2G) + @test order(G) == 2*m + @test describe(G) == "D$(m*2)" + @test code_n(c) == 36 && code_k(c) == 12 + # Oscar.describe(Oscar.small_group(2*m, 1)) is D₁₈, cross-check it with G + @test small_group_identification(G) == (order(G), 1) + + # [[40, 8, 5]] + m = 10 + F = free_group(["r", "s"]) + r, s = gens(F) + G, = quo(F, [r^m, s^2, (r*s)^2]) + F2G = group_algebra(GF(2), G) + r, s = gens(G) + a_elts = [one(G), r^2] + b_elts = [one(G), s*r^4, r^5, r^2, s*r^6, r] + c = get_code(a_elts, b_elts, F2G) + @test order(G) == 2*m + @test describe(G) == "D$(m*2)" + @test code_n(c) == 40 && code_k(c) == 8 + # Oscar.describe(Oscar.small_group(2*m, 4)) is D₂₀, cross-check it with G + @test small_group_identification(G) == (order(G), 4) + + # [[40, 20, 2]] + F = free_group(["r", "s"]) + r, s = gens(F) + G, = quo(F, [r^m, s^2, (r*s)^2]) + F2G = group_algebra(GF(2), G) + r, s = gens(G) + a_elts = [one(G), r^5] + b_elts = [one(G), s*r^2, r^5, r^6, s*r^7, r] + c = get_code(a_elts, b_elts, F2G) + @test order(G) == 2*m + @test describe(G) == "D$(m*2)" + @test code_n(c) == 40 && code_k(c) == 20 + # Oscar.describe(Oscar.small_group(2*m, 4)) is D₂₀, cross-check it with G + @test small_group_identification(G) == (order(G), 4) + + # [[48, 8, 6]] + m = 12 + F = free_group(["r", "s"]) + r, s = gens(F) + G, = quo(F, [r^m, s^2, (r*s)^2]) + F2G = group_algebra(GF(2), G) + r, s = gens(G) + a_elts = [one(G), r^10] + b_elts = [one(G), s*r^8, r^9, r^4, s*r^2, r^5] + c = get_code(a_elts, b_elts, F2G) + @test order(G) == 2*m + @test describe(G) == "D$(m*2)" + @test code_n(c) == 48 && code_k(c) == 8 + # Oscar.describe(Oscar.small_group(2*m, 6)) is D₂₄, cross-check it with G + @test small_group_identification(G) == (order(G), 6) + + # [[48, 12, 4]] + F = free_group(["r", "s"]) + r, s = gens(F) + G, = quo(F, [r^m, s^2, (r*s)^2]) + F2G = group_algebra(GF(2), G) + r, s = gens(G) + a_elts = [one(G), r^3] + b_elts = [one(G), s*r^7, r^3, r^4, s*r^10, r^7] + c = get_code(a_elts, b_elts, F2G) + @test order(G) == 2*m + @test describe(G) == "D$(m*2)" + @test code_n(c) == 48 && code_k(c) == 12 + # Oscar.describe(Oscar.small_group(2*m, 6)) is D₂₄, cross-check it with G + @test small_group_identification(G) == (order(G), 6) + + # [[48, 16, 3]] + F = free_group(["r", "s"]) + r, s = gens(F) + G, = quo(F, [r^m, s^2, (r*s)^2]) + F2G = group_algebra(GF(2), G) + r, s = gens(G) + a_elts = [one(G), r^8] + b_elts = [one(G), s*r^8, r^9, r^8, s*r^4, r^5] + c = get_code(a_elts, b_elts, F2G) + @test order(G) == 2*m + @test describe(G) == "D$(m*2)" + @test code_n(c) == 48 && code_k(c) == 16 + # Oscar.describe(Oscar.small_group(2*m, 6)) is D₂₄, cross-check it with G + @test small_group_identification(G) == (order(G), 6) + + # [[48, 24, 2]] + F = free_group(["r", "s"]) + r, s = gens(F) + G, = quo(F, [r^m, s^2, (r*s)^2]) + F2G = group_algebra(GF(2), G) + r, s = gens(G) + a_elts = [one(G), r^6] + b_elts = [one(G), s*r^11, r^6, s*r^5, r, r^7] + c = get_code(a_elts, b_elts, F2G) + @test order(G) == 2*m + @test describe(G) == "D$(m*2)" + @test code_n(c) == 48 && code_k(c) == 24 + # Oscar.describe(Oscar.small_group(2*m, 6)) is D₂₄, cross-check it with G + @test small_group_identification(G) == (order(G), 6) + + # [[56, 8, 7]] + m = 14 + F = free_group(["r", "s"]) + r, s = gens(F) + G, = quo(F, [r^m, s^2, (r*s)^2]) + F2G = group_algebra(GF(2), G) + r, s = gens(G) + a_elts = [one(G), r^4] + b_elts = [one(G), s*r^11, r^7, s*r^5, r^12, r^9] + c = get_code(a_elts, b_elts, F2G) + @test order(G) == 2*m + @test describe(G) == "D$(m*2)" + @test code_n(c) == 56 && code_k(c) == 8 + # Oscar.describe(Oscar.small_group(2*m, 3)) is D₂₈, cross-check it with G + @test small_group_identification(G) == (order(G), 3) + + # [[56, 28, 2]] + F = free_group(["r", "s"]) + r, s = gens(F) + G, = quo(F, [r^m, s^2, (r*s)^2]) + F2G = group_algebra(GF(2), G) + r, s = gens(G) + a_elts = [one(G), r^7] + b_elts = [one(G), s*r^2, r^7, r^8, s*r^9, r] + c = get_code(a_elts, b_elts, F2G) + @test order(G) == 2*m + @test describe(G) == "D$(m*2)" + @test code_n(c) == 56 && code_k(c) == 28 + # Oscar.describe(Oscar.small_group(2*m, 3)) is D₂₈, cross-check it with G + @test small_group_identification(G) == (order(G), 3) + + # [[60, 12, 5]] + m = 15 + F = free_group(["r", "s"]) + r, s = gens(F) + G, = quo(F, [r^m, s^2, (r*s)^2]) + F2G = group_algebra(GF(2), G) + r, s = gens(G) + a_elts = [one(G), r^12] + b_elts = [one(G), s*r^14, r^5, r^12, s*r^11, r^14] + c = get_code(a_elts, b_elts, F2G) + @test order(G) == 2*m + @test describe(G) == "D$(m*2)" + @test code_n(c) == 60 && code_k(c) == 12 + # Oscar.describe(Oscar.small_group(2*m, 3)) is D₃₀, cross-check it with G + @test small_group_identification(G) == (order(G), 3) + + # [[60, 20, 3]] + F = free_group(["r", "s"]) + r, s = gens(F) + G, = quo(F, [r^m, s^2, (r*s)^2]) + F2G = group_algebra(GF(2), G) + r, s = gens(G) + a_elts = [one(G), r^5] + b_elts = [one(G), s*r^13, r^5, r^12, s*r^3, r^2] + c = get_code(a_elts, b_elts, F2G) + @test order(G) == 2*m + @test describe(G) == "D$(m*2)" + @test code_n(c) == 60 && code_k(c) == 20 + # Oscar.describe(Oscar.small_group(2*m, 3)) is D₃₀, cross-check it with G + @test small_group_identification(G) == (order(G), 3) + + # [[64, 8, 8]] + m = 16 + F = free_group(["r", "s"]) + r, s = gens(F) + G, = quo(F, [r^m, s^2, (r*s)^2]) + F2G = group_algebra(GF(2), G) + r, s = gens(G) + a_elts = [one(G), r^6] + b_elts = [one(G), s*r^12, s*r^9, r^6, s, s*r] + c = get_code(a_elts, b_elts, F2G) + @test order(G) == 2*m + @test describe(G) == "D$(m*2)" + @test code_n(c) == 64 && code_k(c) == 8 + # Oscar.describe(Oscar.small_group(2*m, 18)) is D₃₂, cross-check it with G + @test small_group_identification(G) == (order(G), 18) + + # [[64, 16, 8]] + F = free_group(["r", "s"]) + r, s = gens(F) + G, = quo(F, [r^m, s^2, (r*s)^2]) + F2G = group_algebra(GF(2), G) + r, s = gens(G) + a_elts = [one(G), r^4] + b_elts = [one(G), s*r^10, s*r^3, r^4, s*r^14, s*r^7] + c = get_code(a_elts, b_elts, F2G) + @test order(G) == 2*m + @test describe(G) == "D$(m*2)" + @test code_n(c) == 64 && code_k(c) == 16 + # Oscar.describe(Oscar.small_group(2*m, 18)) is D₃₂, cross-check it with G + @test small_group_identification(G) == (order(G), 18) + + # [[64, 32, 2]] + F = free_group(["r", "s"]) + r, s = gens(F) + G, = quo(F, [r^m, s^2, (r*s)^2]) + F2G = group_algebra(GF(2), G) + r, s = gens(G) + a_elts = [one(G), r^8] + b_elts = [one(G), s*r^11, s*r^12, r^8, s*r^3, s*r^4] + c = get_code(a_elts, b_elts, F2G) + @test order(G) == 2*m + @test describe(G) == "D$(m*2)" + @test code_n(c) == 64 && code_k(c) == 32 + # Oscar.describe(Oscar.small_group(2*m, 18)) is D₃₂, cross-check it with G + @test small_group_identification(G) == (order(G), 18) + end +end