Quantum Tensor-product code

docs/src/references.bib

@@ -402,3 +402,30 @@ @inproceedings{brown2013short
   pages = {346--350},
   doi = {10.1109/ISIT.2013.6620245}
 }
+
+@article{wolf1965codes,
+  title={On codes derivable from the tensor product of check matrices},
+  author={Wolf, Jack},
+  journal={IEEE Transactions on Information Theory},
+  volume={11},
+  number={2},
+  pages={281--284},
+  year={1965},
+  publisher={IEEE}
+}
+
+@inproceedings{wolf2006introduction,
+  title={An introduction to tensor product codes and applications to digital storage systems},
+  author={Wolf, Jack Keil},
+  booktitle={2006 IEEE Information Theory Workshop-ITW'06 Chengdu},
+  pages={6--10},
+  year={2006},
+  organization={IEEE}
+}
+
+@article{fan2016quantum,
+  title={On quantum tensor product codes},
+  author={Fan, Jihao and Li, Yonghui and Hsieh, Min-Hsiu and Chen, Hanwu},
+  journal={arXiv preprint arXiv:1605.09598},
+  year={2016}
+}

docs/src/references.md

@@ -37,6 +37,7 @@ For quantum code construction routines:
 - [kitaev2003fault](@cite)
 - [fowler2012surface](@cite)
 - [knill1996concatenated](@cite)
+- [fan2016quantum](@cite)
 
 For classical code construction routines:
 - [muller1954application](@cite)
@@ -48,6 +49,8 @@ For classical code construction routines:
 - [bose1960class](@cite)
 - [bose1960further](@cite)
 - [error2024lin](@cite)
+- [wolf1965codes](@cite)
+- [wolf2006introduction](@cite)
 
 # References
 

src/ecc/ECC.jl

@@ -9,19 +9,20 @@ using DocStringExtensions
 using Combinatorics: combinations
 using SparseArrays: sparse
 using Statistics: std
-using Nemo: ZZ, residue_ring, matrix, finite_field, GF, minpoly, coeff, lcm, FqPolyRingElem, FqFieldElem, is_zero, degree, defining_polynomial, is_irreducible, echelon_form
+using Nemo: ZZ, residue_ring, matrix, finite_field, GF, minpoly, coeff, lcm, FqPolyRingElem, FqFieldElem, is_zero, degree, defining_polynomial, is_irreducible, echelon_form, kronecker_product
 
 abstract type AbstractECC end
 
 export parity_checks, parity_checks_x, parity_checks_z, iscss,
     code_n, code_s, code_k, rate, distance,
     isdegenerate, faults_matrix,
     naive_syndrome_circuit, shor_syndrome_circuit, naive_encoding_circuit,
-    RepCode,
+    RepCode, BCH, TensorProduct,
     CSS,
     Shor9, Steane7, Cleve8, Perfect5, Bitflip3,
     Toric, Gottesman, Surface, Concat, CircuitCode,
     random_brickwork_circuit_code, random_all_to_all_circuit_code,
+    QuantumTensorProduct,
     evaluate_decoder,
     CommutationCheckECCSetup, NaiveSyndromeECCSetup, ShorSyndromeECCSetup,
     TableDecoder,
@@ -365,8 +366,10 @@ include("codes/toric.jl")
 include("codes/gottesman.jl")
 include("codes/surface.jl")
 include("codes/concat.jl")
+include("codes/quantumtensorproduct.jl")
 include("codes/random_circuit.jl")
 include("codes/classical/reedmuller.jl")
 include("codes/classical/bch.jl")
 include("codes/classical/recursivereedmuller.jl")
+include("codes/classical/tensorproduct.jl")
 end #module

src/ecc/codes/classical/bch.jl

@@ -32,7 +32,7 @@ struct BCH <: AbstractPolynomialCode
     m::Int 
     t::Int 
     function BCH(m, t)
-        if m < 3 || t < 0 || t >= 2 ^ (m - 1)
+        if m < 3 || t < 0 || (3 <= t <= 4 && t >= 2^(m - 1) - 1) || (t > 4 && t >= 2^(m - 1))
             throw(ArgumentError("Invalid parameters: `m` and `t` must be positive. Additionally, ensure `m ≥ 3` and `t < 2ᵐ ⁻ ¹` to obtain a valid code."))
         end
         new(m, t)

src/ecc/codes/classical/tensorproduct.jl

@@ -0,0 +1,20 @@
+"""
+The classical Tensor-product code was discovered by Wolf in his 1963 paper [wolf1965codes](@cite). It combines two component linear error correcting codes by taking the tensor product of their parity check matrices.
+
+The ECC Zoo has an [entry for this family](https://errorcorrectionzoo.org/c/tensor).
+"""
+struct TensorProduct
+    A::AbstractMatrix
+    B::AbstractMatrix
+    function TensorProduct(A, B)
+        all(x -> x isa Bool, A) && all(x -> x isa Bool, B) || throw(ArgumentError("All matrices should be defined over the Boolean field, GF(2)"))
+        new(A, B)
+    end
+end
+
+function parity_checks(tp::TensorProduct)
+    A, B = tp.A, tp.B
+    C = kronecker_product(matrix(ZZ, B), matrix(ZZ, A))
+    C = Matrix{Bool}(Matrix{Int}(C))
+    return C
+end

src/ecc/codes/classical_codes.jl

@@ -9,5 +9,5 @@ function parity_checks(c::RepCode)
     I = [i for i in 1:n for δ in (0,1)]
     J = [(i+δ-1)%n+1 for i in 1:n for δ in (0,1)]
     V = true
-    sparse(I,J,V,n,n)
+    Matrix{Bool}(sparse(I,J,V,n,n))
 end

src/ecc/codes/quantumtensorproduct.jl

@@ -0,0 +1,19 @@
+"""
+The binary quantum Tensor Product Code(TQC) is derived from classical TPCs using the CSS construction. A classical TPC is dual-containing if at least one of its component codes is.
+
+The ECC Zoo has an [entry for this family](https://errorcorrectionzoo.org/c/quantum_tensor_product).
+"""
+struct QuantumTensorProduct
+    A::AbstractMatrix
+    B::AbstractMatrix
+    function QuantumTensorProduct(A, B)
+        all(x -> x isa Bool, A) && all(x -> x isa Bool, B) || throw(ArgumentError("All matrices should be defined over the Boolean field, GF(2)."))
+        new(A, B)
+    end
+end
+
+function parity_checks(Tₚ::QuantumTensorProduct)
+    T = parity_checks(TensorProduct(Tₚ.A, Tₚ.B))
+    H = Stabilizer(CSS(T, T))
+    return H
+end

test/test_ecc_base.jl

@@ -20,7 +20,8 @@ const code_instance_args = Dict(
     Gottesman => [3, 4, 5],
     CSS => (c -> (parity_checks_x(c), parity_checks_z(c))).([Shor9(), Steane7(), Toric(4, 4)]),
     Concat => [(Perfect5(), Perfect5()), (Perfect5(), Steane7()), (Steane7(), Cleve8()), (Toric(2, 2), Shor9())],
-    CircuitCode => random_circuit_code_args
+    CircuitCode => random_circuit_code_args,
+    QuantumTensorProduct => [(RepCode(3),RepCode(4)), (RepCode(5),RepCode(6)), (BCH(3,1),BCH(3,2)), (BCH(3,2),BCH(4,1))]
 )
 
 function all_testablable_code_instances(;maxn=nothing)

test/test_ecc_bch.jl

@@ -2,7 +2,7 @@
     using LinearAlgebra
     using QuantumClifford.ECC
     using QuantumClifford.ECC: AbstractECC, BCH, generator_polynomial
-    using Nemo: ZZ, residue_ring, matrix, finite_field, GF, minpoly, coeff, lcm, FqPolyRingElem, FqFieldElem, is_zero, degree, defining_polynomial, is_irreducible 
+    using Nemo: ZZ, residue_ring, matrix, finite_field, GF, minpoly, coeff, lcm, FqPolyRingElem, FqFieldElem, is_zero, degree, defining_polynomial, is_irreducible
 
     """
     - To prove that `t`-bit error correcting BCH code indeed has minimum distance of at least `2 * t + 1`, it is shown that no `2 * t` or fewer columns of its binary parity check matrix `H` sum to zero. A formal mathematical proof can be found on pages 168 and 169 of Ch6 of Error Control Coding by Lin, Shu and Costello, Daniel. 
@@ -26,7 +26,7 @@
         m_cases = [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
         for m in m_cases
             n = 2 ^ m - 1
-            for t in rand(1:m, 2)
+            for t in rand(1:m-1, 2)
                 H = parity_checks(BCH(m, t))
                 @test check_designed_distance(H, t) == true
                 # n - k == degree of generator polynomial, `g(x)` == rank of binary parity check matrix, `H`.

test/test_ecc_tensorproduct.jl

@@ -0,0 +1,10 @@
+@testitem "Tensor Producr codes" begin
+    using QuantumClifford.ECC
+    using QuantumClifford.ECC: TensorProduct, parity_checks
+    A = [1 1 1 1 1] .== 1 
+    B = [1 1 1 0 1 0 0; 1 1 0 1 0 1 0; 1 0 1 1 0 0 1] .== 1
+    # Example 1 of [wolf2006introduction](@cite)
+    @test parity_checks(TensorProduct(A, B)) == Matrix{Bool}([ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0;
+                                                               1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0;
+                                                               1 1 1 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1])
+end

test/test_ecc_throws.jl

@@ -7,6 +7,7 @@
     @test_throws ArgumentError ReedMuller(4, 2)
 
     @test_throws ArgumentError BCH(2, 2)
+    @test_throws ArgumentError BCH(3, 3)
     @test_throws ArgumentError BCH(3, 4)
 
     @test_throws ArgumentError RecursiveReedMuller(-1, 3)