add a commutativity check to the LPCode constructor (#535)

* add a commutativity check to the LPCode constructor

* update docstrings for failing codes

Author: Krastanov

ext/QuantumCliffordHeckeExt/lifted_product.jl

@@ -104,13 +104,17 @@ struct LPCode <: AbstractECC
 
     function LPCode(A::GroupAlgebraElemMatrix, B::GroupAlgebraElemMatrix; GA::GroupAlgebra=parent(A[1,1]), repr::Function)
         all(elem.parent == GA for elem in A) && all(elem.parent == GA for elem in B) || error("The base rings of all elements in both matrices must be the same as the group algebra")
-        new(A, B, GA, repr)
+        code = new(A, B, GA, repr)
+        QuantumClifford.check_allrowscommute(parity_checks(code)) || error("The Lifted Product Code just created is invalid -- its rows do not commute. This is either a bug in this library, or a non-commutative group algebra was used.")
+        code
     end
 
     function LPCode(c₁::LiftedCode, c₂::LiftedCode; GA::GroupAlgebra=c₁.GA, repr::Function=c₁.repr)
         # we are using the group algebra and the representation function of the first lifted code
         c₁.GA == GA && c₂.GA == GA || error("The base rings of both lifted codes must be the same as the group algebra")
-        new(c₁.A, c₂.A, GA, repr)
+        code = new(c₁.A, c₂.A, GA, repr)
+        QuantumClifford.check_allrowscommute(parity_checks(code)) || error("The Lifted Product Code just created is invalid -- its rows do not commute. This is either a bug in this library, or a non-commutative group algebra was used.")
+        code
     end
 end
 

ext/QuantumCliffordOscarExt/group_presentation.jl

@@ -33,6 +33,8 @@ See also: [`two_block_group_algebra_codes`](@ref), [`twobga_from_direct_product`
 The [[96, 12, 10]] 2BGA code from Table I in [lin2024quantum](@cite) has the group presentation
 `⟨r, s | s⁶ = r⁸ = r⁻¹srs = 1⟩` (the group `C₂ × (C₃ ⋉ C₈)`).
 
+Currently unsupported as it requires a non-commutative group algebra.
+
 ```jldoctest finitegrp
 julia> import Oscar: free_group, small_group_identification, describe, order
 
@@ -55,15 +57,8 @@ julia> a = [one(G), r, s^3 * r^2, s^2 * r^3];
 julia> b = [one(G), r, s^4 * r^6, s^5 * r^3];
 
 julia> c = twobga_from_fp_group(a, b, GA);
-
-julia> order(G)
-48
-
-julia> code_n(c), code_k(c)
-(96, 12)
-
-julia> describe(G), small_group_identification(G)
-("C2 x (C3 : C8)", (48, 9))
+ERROR: The CSS code just created is invalid -- its rows do not commute. This is either a bug in this library, or an inconsistent parity check matrices were provided to the CSS constructor.
+[...]
 ```
 
 ### Cyclic Groups
@@ -111,6 +106,8 @@ where the order is `2m`.
 The [[24, 8, 3]] 2BGA code from Appendix C, Table III in [lin2024quantum](@cite) is constructed
 by specifying a group presentation below (giving the group `D₆ = C₆ ⋉ C₂`).
 
+Currently unsupported as it requires a non-commutative group algebra.
+
 ```jldoctest finitegrp
 julia> m = 6;
 
@@ -129,15 +126,8 @@ julia> a = [one(G), r^4];
 julia> b = [one(G), s*r^4, r^3, r^4, s*r^2, r];
 
 julia> c = twobga_from_fp_group(a, b, GA);
-
-julia> order(G)
-12
-
-julia> code_n(c), code_k(c)
-(24, 8)
-
-julia> describe(G), small_group_identification(G)
-("D12", (12, 4))
+ERROR: The CSS code just created is invalid -- its rows do not commute. This is either a bug in this library, or an inconsistent parity check matrices were provided to the CSS constructor.
+[...]
 ```
 
 !!! note

lib/QECCore/src/codes/css.jl

@@ -15,10 +15,21 @@ struct CSS <: AbstractCSSCode
         n = size(Hx, 2)
         if n != size(Hz, 2) error("When constructing a CSS quantum code, the two classical codes are required to have the same block size") end
         #if size(Hx,1)+size(Hz,1) >= n error("When constructing a CSS quantum code, the total number of checks (rows) in the parity checks of the two classical codes have to be lower than the block size (the number of columns).") end
+        check_allrowscommute(Hx, Hz) || error("The CSS code just created is invalid -- its rows do not commute. This is either a bug in this library, or an inconsistent parity check matrices were provided to the CSS constructor.")
         new(Hx, Hz)
     end
 end
 
+function check_allrowscommute(Hx, Hz)
+    for rowx in eachrow(Hx)
+        for rowz in eachrow(Hz)
+            comm = sum(rowx .& rowz)
+            isodd(comm) && return false
+        end
+    end
+    return true
+end
+
 function parity_matrix(c::CSS)
     extended_Hx = Matrix{Bool}(vcat(c.Hx, zeros(size(c.Hz))))
     extended_Hz = Matrix{Bool}(vcat(zeros(size(c.Hx)), c.Hz))
@@ -33,4 +44,4 @@ code_s(c::CSS) = size(c.Hx, 1) + size(c.Hz, 1)
 
 
 # Parity matrix for general CSS codes
-parity_matrix(c::AbstractCSSCode) = parity_matrix(CSS(parity_matrix_x(c), parity_matrix_z(c)))
+parity_matrix(c::AbstractCSSCode) = parity_matrix(CSS(parity_matrix_x(c), parity_matrix_z(c)))