Merge pull request #24 from esabo/fix/hyperbicycle

fixed hyperbicycle constructors, added tests

Author: esabo

src/Quantum/product_codes.jl

@@ -162,38 +162,20 @@ function HyperBicycleCodeCSS(a::Vector{T}, b::Vector{T}, χ::Int; char_vec::Unio
         (k2, n2) == size(b[i]) || throw(ArgumentError("Second set of matrices must all have the same dimensions."))
     end
 
-    # Julia creates a new scope for every iteration of the for loop,
-    # so the else doesn't work without declaring these variables outside here
-    H1::T
-    H2::T
-    HT1::T
-    HT2::T
+    H1 = zero_matrix(F, c * k1, c * n1)
+    H2 = zero_matrix(F, c * k2, c * n2)
+    HT1 = zero_matrix(F, c * n1, c * k1)
+    HT2 = zero_matrix(F, c * n2, c * k2)
+    Ic = identity_matrix(F, c)
+    Sχ = Ic[mod1.(1:χ:c * χ, c), :]
     for i in 1:c
-        Sχi = zero_matrix(F, c, c)
-        Ii = zero_matrix(F, c, c)
-        for c1 in 1:c
-            for r in 1:c
-                if (c1 - r) % c == 1
-                    Ii[r, c1] = F(1)
-                end
-                if (c1 - r) % c == (r - 1) * (χ - 1) % c
-                    Sχi[r, c1] = F(1)
-                end
-            end
-        end
-        Iχi = Sχi * Ii
-        ITχi = transpose(Sχi) * transpose(Ii)
-        if i == 1
-            H1 = Iχi ⊗ a[i]
-            H2 = b[i] ⊗ Iχi
-            HT1 = ITχi ⊗ transpose(a[i])
-            HT2 = transpose(b[i]) ⊗ ITχi
-        else
-            H1 += Iχi ⊗ a[i]
-            H2 += b[i] ⊗ Iχi
-            HT1 += ITχi ⊗ transpose(a[i])
-            HT2 += transpose(b[i]) ⊗ ITχi
-        end
+        Ii = vcat(Ic[i:end, :], Ic[1:i - 1, :])
+        Iχi = Sχ * Ii
+        ITχi = transpose(Sχ) * transpose(Ii)
+        H1 += Iχi ⊗ a[i]
+        H2 += b[i] ⊗ Iχi
+        HT1 += ITχi ⊗ transpose(a[i])
+        HT2 += transpose(b[i]) ⊗ ITχi
     end
 
     Ek1 = identity_matrix(F, k1)
@@ -204,22 +186,20 @@ function HyperBicycleCodeCSS(a::Vector{T}, b::Vector{T}, χ::Int; char_vec::Unio
     GX = hcat(Ek2 ⊗ H1, H2 ⊗ Ek1)
     GZ = hcat(HT2 ⊗ En1, En2 ⊗ HT1)
     return CSSCode(GX, GZ, char_vec = char_vec, logs_alg = logs_alg)
-    # equations 41 and 42 of the paper give matrices from which the logicals may be chosen
-    # not really worth it, just use standard technique from StabilizerCode.jl
 end
 
 """
     HyperBicycleCode(a::Vector{CTMatrixTypes}, b::Vector{CTMatrixTypes}, χ::Int; char_vec::Union{Vector{nmod}, Missing} = missing, logs_alg::Symbol = :stnd_frm)
 
-Return the hyperbicycle CSS code of `a` and `b` given `χ`.
+Return the hyperbicycle non-CSS code of `a` and `b` given `χ`.
 
 # Arguments
 - a: A vector of length `c` of binary matrices of the same dimensions.
 - b: A vector of length `c` of binary matrices of the same dimensions,
   potentially different from those of `a`.
 - χ: A strictly positive integer coprime with `c`.
 """
-function HyperBicycleCode(a::Vector{T}, b::Vector{T}, χ::Int, char_vec::Union{Vector{nmod},
+function HyperBicycleCode(a::Vector{T}, b::Vector{T}, χ::Int; char_vec::Union{Vector{nmod},
     Missing} = missing, logs_alg::Symbol = :stnd_frm) where T <: CTMatrixTypes
 
     logs_alg ∈ (:stnd_frm, :VS, :sys_eqs) || throw(ArgumentError("Unrecognized logicals algorithm"))
@@ -238,35 +218,29 @@ function HyperBicycleCode(a::Vector{T}, b::Vector{T}, χ::Int, char_vec::Union{V
         (k2, n2) == size(b[i]) || throw(ArgumentError("Second set of matrices must all have the same dimensions."))
     end
 
+    H1 = zero_matrix(F, c * k1, c * n1)
+    H2 = zero_matrix(F, c * k2, c * n2)
+    HT1 = zero_matrix(F, c * n1, c * k1)
+    HT2 = zero_matrix(F, c * n2, c * k2)
+    Ic = identity_matrix(F, c)
+    Sχ = Ic[mod1.(1:χ:c * χ, c), :]
     for i in 1:c
-        Sχi = zero_matrix(F, c, c)
-        Ii = zero_matrix(F, c, c)
-        for c1 in 1:c
-            for r in 1:c
-                if (c1 - r) % c == 1
-                    Ii[r, c1] = F(1)
-                end
-                if (c1 - r) % c == (r - 1) * (χ - 1) % c
-                    Sχi[r, c1] = F(1)
-                end
-            end
-        end
-        Iχi = Sχi * Ii
-        if i == 1
-            H1 = Iχi ⊗ a[i]
-            H2 = b[i] ⊗ Iχi
-        else
-            H1 += Iχi ⊗ a[i]
-            H2 += b[i] ⊗ Iχi
-        end
+        Ii = vcat(Ic[i:end, :], Ic[1:i - 1, :])
+        Iχi = Sχ * Ii
+        ITχi = transpose(Sχ) * transpose(Ii)
+        H1 += Iχi ⊗ a[i]
+        H2 += b[i] ⊗ Iχi
+        HT1 += ITχi ⊗ transpose(a[i])
+        HT2 += transpose(b[i]) ⊗ ITχi
     end
 
+    (H1 == HT1 && H2 == HT2) || throw(ArgumentError("H_i must equal H̃_i for i = 1, 2."))
+
     Ek1 = identity_matrix(F, k1)
     Ek2 = identity_matrix(F, k2)
+
     stabs = hcat(Ek2 ⊗ H1, H2 ⊗ Ek1)
     return StabilizerCode(stabs, char_vec = char_vec, logs_alg = logs_alg)
-    # equations 41 and 42 of the paper give matrices from which the logicals may be chosen
-    # not really worth it, just use standard technique from StabilizerCode.jl
 end
 
 """

test/Quantum/product_codes_test.jl

@@ -47,6 +47,48 @@
     @test LogicalTrait(typeof(Q)) == HasLogicals()
     @test GaugeTrait(typeof(Q)) == HasNoGauges()
 
+    # Quantum kronecker sum-product low-density parity-check codes with finite rate
+    # Fig 2
+    l = 21
+    R = residue_ring(S, x^l - 1)
+    h = R(1 + x + x^3)
+    A = residue_polynomial_to_circulant_matrix(h)
+    a1 = A[1:7, 1:7]
+    a2 = A[1:7, 8:14]
+    a3 = A[1:7, 15:21]
+    χ = 1
+    Q = HyperBicycleCodeCSS([a1, a2, a3], [a1, a2, a3], χ)
+    @test length(Q) == 294
+    @test CodingTheory.dimension(Q) == 18
+    @test LogicalTrait(typeof(Q)) == HasLogicals()
+    @test GaugeTrait(typeof(Q)) == HasNoGauges()
+
+    # Example 6
+    l = 30
+    R = residue_ring(S, x^l - 1)
+    h = R(1 + x + x^3 + x^5)
+    A = residue_polynomial_to_circulant_matrix(h)
+    a1 = A[1:15, 1:15]
+    a2 = A[1:15, 16:30]
+    χ = 1
+    Q = HyperBicycleCodeCSS([a1, a2], [a1, a2], χ)
+    @test length(Q) == 900
+    @test CodingTheory.dimension(Q) == 50
+    @test LogicalTrait(typeof(Q)) == HasLogicals()
+    @test GaugeTrait(typeof(Q)) == HasNoGauges()
+
+    # Example 13 (non-CSS example)
+    l = 17
+    R = residue_ring(S, x^l - 1)
+    h = R(x^4 * (1 + x + x^3 + x^6 + x^8 + x^9))
+    A = residue_polynomial_to_circulant_matrix(h)
+    χ = 1
+    Q = HyperBicycleCode([A], [A], χ)
+    @test length(Q) == 289
+    @test CodingTheory.dimension(Q) == 81
+    @test LogicalTrait(typeof(Q)) == HasLogicals()
+    @test GaugeTrait(typeof(Q)) == HasNoGauges()
+
     # HGP codes are (l, q)-QLDPC code
     # l, q = columnrowweights(Sq2)