add code review suggestions

Author: Fe-r-oz

Manifest.toml

@@ -1027,9 +1027,9 @@ version = "0.12.1+0"
 
 [[deps.libsingular_julia_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Singular_jll", "libcxxwrap_julia_jll"]
-git-tree-sha1 = "ab24eb5706b1d1a1b5037951a382b0c4fd6edf5b"
+git-tree-sha1 = "436efe88c41337fd128062555fe8f8ea6c0e7309"
 uuid = "ae4fbd8f-ecdb-54f8-bbce-35570499b30e"
-version = "0.45.5+0"
+version = "0.45.6+0"
 
 [[deps.lrslib_jll]]
 deps = ["Artifacts", "GMP_jll", "JLLWrappers", "Libdl", "Pkg"]

docs/src/Quantum/product_codes.md

@@ -6,6 +6,8 @@
 - [Generealized bicycle](https://errorcorrectionzoo.org/c/generalized_bicycle): [pryadko2013quantum](@cite), [Kovalev_2013](@cite), [panteleev2021degenerate](@cite)
 - Generalized hypergraph product: [panteleev2021degenerate](@cite)
 - Bias-tailored lifted product: [roffe2023bias](@cite)
+- Bivariate bicycle: [wang2024coprime](@cite)
+- Coprime bivarate bicycle: [wang2024coprime](@cite)
 
 
 ```@autodocs

docs/src/references.bib

@@ -183,3 +183,21 @@ @inproceedings{yao2024belief
   year={2024},
   organization={IEEE}
 }
+
+@article{bravyi2024high,
+  title={High-threshold and low-overhead fault-tolerant quantum memory},
+  author={Bravyi, Sergey and Cross, Andrew W and Gambetta, Jay M and Maslov, Dmitri and Rall, Patrick and Yoder, Theodore J},
+  journal={Nature},
+  volume={627},
+  number={8005},
+  pages={778--782},
+  year={2024},
+  publisher={Nature Publishing Group UK London}
+}
+
+@article{wang2024coprime,
+  title={Coprime Bivariate Bicycle Codes and their Properties},
+  author={Wang, Ming and Mueller, Frank},
+  journal={arXiv preprint arXiv:2408.10001},
+  year={2024}
+}

src/CodingTheory.jl

@@ -378,7 +378,7 @@ export HypergraphProductCode, GeneralizedShorCode, BaconCasaccinoConstruction,
     GeneralizedHypergraphProductCode, LiftedProductCode, bias_tailored_lifted_product_matrices,
     BiasTailoredLiftedProductCode, SPCDFoldProductCode, SingleParityCheckDFoldProductCode,
     Quintavalle_basis, asymmetric_product, symmetric_product, random_homological_product_code,
-    homological_product, ⊠, BivariateBicycleCode, CoPrimeBivariateBicycleCode
+    homological_product, ⊠, BivariateBicycleCode, CoprimeBivariateBicycleCode
 
 #############################
 #   Quantum/simulation.jl

src/Quantum/product_codes.jl

@@ -956,7 +956,7 @@ Return the coprime bivariate bicycle code defined by the residue ring elements `
 # Note
 - This is defined in https://arxiv.org/pdf/2408.10001v1.
 """
-function CoPrimeBivariateBicycleCode(a::T, b::T, l::Int, m::Int) where T <: Union{MPolyQuoRingElem{FqMPolyRingElem}, MPolyQuoRingElem{fpMPolyRingElem}}
+function CoprimeBivariateBicycleCode(a::T, b::T, l::Int, m::Int) where T <: Union{MPolyQuoRingElem{FqMPolyRingElem}, MPolyQuoRingElem{fpMPolyRingElem}}
     R = parent(a)
     R == parent(b) || throw(DomainError("Polynomials must have the same parent."))
     F = base_ring(base_ring(a))
@@ -968,26 +968,18 @@ function CoPrimeBivariateBicycleCode(a::T, b::T, l::Int, m::Int) where T <: Unio
     gcd([l, m]) == 1 || throw(DomainError("l and m must be coprime numbers."))
     x = matrix(F, [mod1(i + 1, l) == j ? 1 : 0 for i in 1:l, j in 1:l]) ⊗ identity_matrix(F, m)
     y = identity_matrix(F, l) ⊗ matrix(F, [mod1(i + 1, m) == j ? 1 : 0 for i in 1:m, j in 1:m])
-
+    P = x*y
     A = zero_matrix(F, l * m, l * m)
     for ex in exponents(lift(a))
-        power, which = findmax(ex)
-        if which == 1
-            A += x^power
-        elseif which == 2
-            A += y^power
-        end
+        power, _ = findmax(ex)
+        A += P^power
     end
 
     B = zero_matrix(F, l * m, l * m)
     for ex in exponents(lift(b))
-        power, which = findmax(ex)
-        if which == 1
-            B += x^power
-        elseif which == 2
-            B += y^power
-        end
+        power, _ = findmax(ex)
+        B += P^power
     end
 
     return CSSCode(hcat(A, B), hcat(transpose(B), transpose(A)))
-end
+end

test/Quantum/product_codes_test.jl

@@ -607,60 +607,61 @@
         @test dimension(Q) == 12
         @test_broken minimum_distance(S) == 8
 
-        # co-prime bivariate bicycle codes
+        # Coprime Bivariate Bicycle codes
+        # Table 2 of https://arxiv.org/pdf/2408.10001v1
         # [[30, 4, 6]]
-        S, (π) = polynomial_ring(Oscar.Nemo.Native.GF(2), [:π])
+        S, (P) = polynomial_ring(Oscar.Nemo.Native.GF(2), [:P])
         l = 3
         m = 5
-        R, _ = quo(S, ideal(S, [π[1]^(l*m)]))
-        a = R(1 + π[1] + π[1]^2)
-        b = R(π[1] + π[1]^3 + π[1]^8)
-        Q = CoPrimeBivariateBicycleCode(a, b, l, m)
+        R, _ = quo(S, ideal(S, [P[1]^(l*m)]))
+        a = R(1 + P[1] + P[1]^2)
+        b = R(P[1] + P[1]^3 + P[1]^8)
+        Q = CoprimeBivariateBicycleCode(a, b, l, m)
         @test length(Q) == 30
-        @test_broken  dimension(code) == 4
+        @test dimension(Q) == 4
         @test_broken  minimum_distance(S) == 6
-        
+
         # [[42, 6, 6]]
         l = 3
         m = 7
-        R, _ = quo(S, ideal(S, [π[1]^(l*m)]))
-        a = R(1 + π[1]^2 + π[1]^3)
-        b = R(π[1] + π[1]^3 + π[1]^11)
-        Q = CoPrimeBivariateBicycleCode(a, b, l, m)
+        R, _ = quo(S, ideal(S, [P[1]^(l*m)]))
+        a = R(1 + P[1]^2 + P[1]^3)
+        b = R(P[1] + P[1]^3 + P[1]^11)
+        Q = CoprimeBivariateBicycleCode(a, b, l, m)
         @test length(Q) == 42
-        @test_broken dimension(Q) == 6
+        @test dimension(Q) == 6
         @test_broken minimum_distance(S) == 6
 
         # [[70, 6, 8]]
         l = 5
         m = 7
-        R, _ = quo(S, ideal(S, [π[1]^(l*m)]))
-        a = R(1 + π[1]^2 + π[1]^5)
-        b = R(1 + π[1] + π[1]^12)
-        Q = CoPrimeBivariateBicycleCode(a, b, l, m)
+        R, _ = quo(S, ideal(S, [P[1]^(l*m)]))
+        a = R(1 + P[1] + P[1]^5)
+        b = R(1 + P[1] + P[1]^12)
+        Q = CoprimeBivariateBicycleCode(a, b, l, m)
         @test length(Q) == 70
-        @test_broken dimension(Q) == 6
+        @test dimension(Q) == 6
         @test_broken minimum_distance(S) == 8
 
         # [[108, 12, 6]]
         l = 2
         m = 27
-        R, _ = quo(S, ideal(S, [π[1]^(l*m)]))
-        a = R(π[1]^2 + π[1]^5 + π[1]^44)
-        b = R(π[1]^8 + π[1]^14 + π[1]^47)
-        Q = CoPrimeBivariateBicycleCode(a, b, l, m)
+        R, _ = quo(S, ideal(S, [P[1]^(l*m)]))
+        a = R(P[1]^2 + P[1]^5 + P[1]^44)
+        b = R(P[1]^8 + P[1]^14 + P[1]^47)
+        Q = CoprimeBivariateBicycleCode(a, b, l, m)
         @test length(Q) == 108
-        @test_broken dimension(Q) == 12
+        @test dimension(Q) == 12
         @test_broken minimum_distance(S) == 6
 
         # [126, 12, 10]]
         l = 7
         m = 9
-        R, _ = quo(S, ideal(S, [π[1]^(l*m)]))
-        a = R(1 + π[1] + π[1]^58)
-        b = R(π[1]^3 + π[1]^16 + π[1]^44)
-        Q = CoPrimeBivariateBicycleCode(a, b, l, m)
+        R, _ = quo(S, ideal(S, [P[1]^(l*m)]))
+        a = R(1 + P[1] + P[1]^58)
+        b = R(P[1]^3 + P[1]^16 + P[1]^44)
+        Q = CoprimeBivariateBicycleCode(a, b, l, m)
         @test length(Q) == 126
-        @test_broken dimension(Q) == 12
+        @test dimension(Q) == 12
         @test_broken dimension(Q) == 10
 end