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‎Project.toml‎

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@@ -17,7 +17,6 @@ Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
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SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
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Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
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StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
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Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
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TestItemRunner = "f8b46487-2199-4994-9208-9a1283c18c0a"
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[weakdeps]
@@ -54,3 +53,9 @@ NetworkLayout = "0.4.6"
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StatsBase = "0.34.2"
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WGLMakie = "0.8.15"
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julia = "≥ 1.9"
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[extras]
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Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
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[targets]
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test = ["Test"]

‎test/Quantum/misc_lit_codes_test.jl‎

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# misc codes from the literature
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@testitem "Quantum/misc_lit_codes.jl" begin
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using Oscar
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using CodingTheory
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@testset "Misc Codes From Literature" begin
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# TODO codes from "LRESC" paper, make tests (long range _ surface code?)
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# # the dual of any [3, 2, 2] code is a [3, 1, 3] repetition code
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# # but we'll build this the GAP way anyway
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# C_GAP = GAP.Globals.BestKnownLinearCode(3, 2, GAP.Globals.GF(2));
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# G = GAP.Globals.GeneratorMat(C_GAP);
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# y = [GAP.Globals.Int(G[i, j]) for i in 1:2, j in 1:3];
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# C32 = LinearCode(y, 2);
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# R4 = RepetitionCode(2, 4);
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# seed1 = concatenate(C32, R4)
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# LRESC1 = HypergraphProductCode(parity_check_matrix(seed1), parity_check_matrix(seed1))
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# # unclear as to which [6, 2, 4] code they used here
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# C_GAP = GAP.Globals.BestKnownLinearCode(6, 2, GAP.Globals.GF(2));
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# G = GAP.Globals.GeneratorMat(C_GAP);
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# y = [GAP.Globals.Int(G[i, j]) for i in 1:2, j in 1:6];
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# C62 = LinearCode(y, 2)
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# R2 = RepetitionCode(2, 2);
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# seed2 = concatenate(C62, R2)
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# LRESC2 = HypergraphProductCode(parity_check_matrix(seed2), parity_check_matrix(seed2))
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# # they either could have used this code or the extended Hamming code below
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# C_GAP = GAP.Globals.BestKnownLinearCode(8, 4, GAP.Globals.GF(2));
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# G = GAP.Globals.GeneratorMat(C_GAP);
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# y = [GAP.Globals.Int(G[i, j]) for i in 1:4, j in 1:8];
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# C84 = LinearCode(y, 2)
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# R3 = RepetitionCode(2, 3);
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# seed3 = concatenate(C84, R3)
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# LRESC3 = HypergraphProductCode(parity_check_matrix(seed3), parity_check_matrix(seed3))
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# ext_Ham = extend(HammingCode(2, 3))
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# seed3_alt = concatenate(ext_Ham, R3)
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# LRESC3_alt = HypergraphProductCode(parity_check_matrix(seed3_alt), parity_check_matrix(seed3_alt))
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# julia> are_permutation_equivalent(C84, ext_Ham)
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# (false, missing)
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# radial codes
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# using StatsBase, Graphs, Oscar, CodingTheory
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# F = Oscar.Nemo.Native.GF(2)
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# S, x = polynomial_ring(F, :x)
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# l = 5
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# R, _ = residue_ring(S, x^l - 1)
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# A1 = matrix(R, 3, 3,
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# [x^3, x^2, x,
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# x^4, x^1, x^4,
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# x, x^2, x^3])
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# A2 = matrix(R, 3, 3,
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# [x^3, x^3, 1,
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# x, 1, x,
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# x^4, x^2, 1])
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# code = LiftedProductCode(A1, A2)
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# # [[90, 8]]_2 CSS stabilizer code
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# # julia> check_weights(code)
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# # (w_X, q_X, w_Z, q_Z) = (6, 3, 6, 3)
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# L_X = LDPCCode(code.X_stabs);
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# G_X, _, _ = Tanner_graph(L_X);
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# D_X = DiGraph(G_X);
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# L_X_cycles = CodingTheory._modified_hawick_james(D_X, 12);
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# countmap(length.(L_X_cycles))
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# # Dict{Int64, Int64} with 3 entries:
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# # 6 => 48
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# # 10 => 4842
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# # 8 => 777
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# L_Z = LDPCCode(code.Z_stabs);
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# G_Z, _, _ = Tanner_graph(L_Z);
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# D_Z = DiGraph(G_Z);
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# L_Z_cycles = CodingTheory._modified_hawick_james(D_Z, 12);
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# countmap(length.(L_Z_cycles))
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# # Dict{Int64, Int64} with 3 entries:
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# # 6 => 20
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# # 10 => 4074
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# # 8 => 678
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# l = 11
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# R, _ = residue_ring(S, x^l - 1)
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# A1 = matrix(R, 4, 4,
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# [x^10, x^10, x, x^6,
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# x^4, x^7, x^5, x^2,
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# x^8, x^10, x^6, x^9,
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# x, x^6, 1, x^6])
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# A2 = matrix(R, 4, 4,
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# [x^9, x^5, x^8, x^3,
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# x^5, x^4, x, 1,
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# 1, x^4, x^6, x^10,
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# x^2, x^8, x^4, x^2])
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# code = LiftedProductCode(A1, A2)
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# # [[352, 18]]_2 CSS stabilizer code
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# # julia> check_weights(code)
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# # (w_X, q_X, w_Z, q_Z) = (8, 4, 8, 4)
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# L_X = LDPCCode(code.X_stabs);
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# G_X, _, _ = Tanner_graph(L_X);
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# D_X = DiGraph(G_X);
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# L_X_cycles = CodingTheory._modified_hawick_james(D_X, 12);
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# countmap(length.(L_X_cycles))
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# # Dict{Int64, Int64} with 3 entries:
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# # 6 => 96
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# # 10 => 61668
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# # 8 => 3970
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# L_Z = LDPCCode(code.Z_stabs);
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# G_Z, _, _ = Tanner_graph(L_Z);
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# D_Z = DiGraph(G_Z);
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# L_Z_cycles = CodingTheory._modified_hawick_james(D_Z, 12);
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# countmap(length.(L_Z_cycles))
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# # Dict{Int64, Int64} with 3 entries:
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# # 6 => 72
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# # 10 => 60787
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# # 8 => 3954
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end
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end

‎test/Quantum/product_codes_test.jl‎

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Original file line numberDiff line numberDiff line change
@@ -550,58 +550,61 @@
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Q = BivariateBicycleCode(a, b)
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@test length(Q) == 180
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@test dimension(Q) == 8
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@test_broken minimum_distance(S) == 16
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end
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@testset "HyperBicycleCode" begin
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# Quantum ``hyperbicycle'' low-density parity check codes with finite rate
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# Odd-distance rotated CSS toric codes
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# f1 = 1 + x^(2 * t^2 + 1)
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# f2 = x * (1 + x^(2 * t^2 - 1))
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# t - # errors
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# [[2t^2 + 2(t + 1)^2, 2, 2t + 1]]
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# [[10, 2, 3]]
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# [[26, 2, 5]]
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# [[50, 2, 7]]
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# [[82, 2, 9]]
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# ...
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# Figure 2
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F = Oscar.Nemo.Native.GF(2)
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S, x = polynomial_ring(F, :x)
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l = 21
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R = ResidueRing(S, x^l - 1)
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h = R(1 + x + x^3)
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A = residue_polynomial_to_circulant_matrix(h)
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a1 = A[1:7, 1:7]
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a2 = A[1:7, 8:14]
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a3 = A[1:7, 15:21]
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χ = 1
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Q = HyperBicycleCodeCSS([a1, a2, a3], [a1, a2, a3], χ)
582-
@test length(Q) == 294
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@test dimension(Q) == 18
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# Table 1 of https://arxiv.org/pdf/2404.17676
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# [[72, 8, 6]]
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l = 12
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m = 3
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R, _ = quo(S, ideal(S, [x^l - 1, y^m - 1]))
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a = R(x^9 + y^1 + y^2)
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b = R(1 + x^1 + x^11)
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Q = BivariateBicycleCode(a, b)
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@test length(Q) == 72
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@test dimension(Q) == 8
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@test_broken minimum_distance(S) == 6
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# Example 6
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l = 30
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R = ResidueRing(S, x^l - 1)
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h = R(1 + x + x^3 + x^5)
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A = residue_polynomial_to_circulant_matrix(h)
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a1 = A[1:15, 1:15]
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a2 = A[1:15, 16:30]
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χ = 1
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Q = HyperBicycleCodeCSS([a1, a2], [a1, a2], χ)
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@test length(Q) == 900
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@test dimension(Q) == 50
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# [[90, 8, 6]]
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l = 9
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m = 5
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R, _ = quo(S, ideal(S, [x^l - 1, y^m - 1]))
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a = R(x^8 + y^4 + y^1)
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b = R(y^5 + x^8 + x^7)
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Q = BivariateBicycleCode(a, b)
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@test length(Q) == 90
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@test dimension(Q) == 8
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@test_broken minimum_distance(S) == 6
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# Example 13
598-
l = 17
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R = ResidueRing(S, x^l - 1)
600-
h = R(x^(div(17 - 9, 2)) * (1 + x + x^3 + x^6 + x^8 + x^9))
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A = residue_polynomial_to_circulant_matrix(h)
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χ = 1
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Q = HyperBicycleCode([A], [A], χ)
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@test length(Q) == 289
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@test dimension(Q) == 81
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# [[120, 8, 8]]
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l = 12
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m = 5
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R, _ = quo(S, ideal(S, [x^l - 1, y^m - 1]))
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a = R(x^10 + y^4 + y^1)
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b = R(1 + x^1 + x^2)
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Q = BivariateBicycleCode(a, b)
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@test length(Q) == 120
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@test dimension(Q) == 8
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@test_broken minimum_distance(S) == 8
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# [[150, 8, 8]]
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l = 15
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m = 5
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R, _ = quo(S, ideal(S, [x^l - 1, y^m - 1]))
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a = R(x^5 + y^2 + y^3)
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b = R(y^2 + x^7 + x^6)
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Q = BivariateBicycleCode(a, b)
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@test length(Q) == 150
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@test dimension(Q) == 8
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@test_broken minimum_distance(S) == 8
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# [[196, 12, 8]]
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l = 14
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m = 7
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R, _ = quo(S, ideal(S, [x^l - 1, y^m - 1]))
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a = R(x^6 + y^5 + y^6)
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b = R(1 + x^4 + x^13)
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Q = BivariateBicycleCode(a, b)
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@test length(Q) == 196
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@test dimension(Q) == 12
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@test_broken minimum_distance(S) == 8
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end
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end

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