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QuantumSavory · Nov 5, 2024 · 27d9897 · 27d9897
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diff --git a/docs/src/references.bib b/docs/src/references.bib
@@ -513,16 +513,6 @@ @article{anderson2014fault
   publisher={APS}
 }
 
-@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{lin2024quantum,
   title={Quantum two-block group algebra codes},
   author={Lin, Hsiang-Ku and Pryadko, Leonid P},
@@ -533,3 +523,14 @@ @article{lin2024quantum
   year={2024},
   publisher={APS}
 }
+
+@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}
+}
diff --git a/docs/src/references.md b/docs/src/references.md
@@ -40,6 +40,8 @@ For quantum code construction routines:
 - [steane1999quantum](@cite)
 - [campbell2012magic](@cite)
 - [anderson2014fault](@cite)
+- [lin2024quantum](@cite)
+- [bravyi2024high](@cite)
 
 For classical code construction routines:
 - [muller1954application](@cite)

diff --git a/ext/QuantumCliffordHeckeExt/QuantumCliffordHeckeExt.jl b/ext/QuantumCliffordHeckeExt/QuantumCliffordHeckeExt.jl
@@ -5,8 +5,7 @@ using DocStringExtensions
 import QuantumClifford, LinearAlgebra
 import Hecke: Group, GroupElem, AdditiveGroup, AdditiveGroupElem,
     GroupAlgebra, GroupAlgebraElem, FqFieldElem, representation_matrix, dim, base_ring,
-    multiplication_table, coefficients, abelian_group, group_algebra, rand,
-    FinGenAbGroup, FinGenAbGroupElem, one
+    multiplication_table, coefficients, abelian_group, group_algebra, rand, one
 import Nemo
 import Nemo: characteristic, matrix_repr, GF, ZZ, lift
 

diff --git a/ext/QuantumCliffordHeckeExt/lifted_product.jl b/ext/QuantumCliffordHeckeExt/lifted_product.jl
@@ -238,19 +238,17 @@ julia> GA = group_algebra(GF(2), abelian_group([l, m]));
 
 julia> x, y = gens(GA);
 
-julia> A = [x^3 , y^10 , y^17];
+julia> A = x^3 + y^10 + y^17;
 
-julia> B = [y^5 , x^3  , x^19];
+julia> B = y^5 + x^3  + x^19;
 
-julia> c = bivariate_bicycle_codes(A,B,GA);
+julia> c = bivariate_bicycle_codes(A,B);
 
 julia> code_n(c), code_k(c)
 (756, 16)
 ```
 """
-function bivariate_bicycle_codes(A::VectorGroupAlgebraElem, B::VectorGroupAlgebraElem, GA::FqFieldFinGenAbGroupElemGroupAlgebra)
-    a = sum(GA(x) for x in A)
-    b = sum(GA(x) for x in B)
-    c = two_block_group_algebra_codes(a,b)
+function bivariate_bicycle_codes(A::GroupAlgebraElem, B::GroupAlgebraElem)
+    c = two_block_group_algebra_codes(A,B)
     return c
 end
diff --git a/ext/QuantumCliffordHeckeExt/types.jl b/ext/QuantumCliffordHeckeExt/types.jl
@@ -10,10 +10,6 @@ const FqFieldGroupAlgebraElemMatrix = Union{
     LinearAlgebra.Adjoint{<:GroupAlgebraElem{FqFieldElem,<:GroupAlgebra},<:Matrix{<:GroupAlgebraElem{FqFieldElem,<:GroupAlgebra}}}
 }
 
-const VectorGroupAlgebraElem = Vector{GroupAlgebraElem{FqFieldElem, GroupAlgebra{FqFieldElem, FinGenAbGroup, FinGenAbGroupElem}}}
-
-const FqFieldFinGenAbGroupElemGroupAlgebra = GroupAlgebra{FqFieldElem, FinGenAbGroup, FinGenAbGroupElem}
-
 """
 Compute the conjugate of a group algebra element.
 The conjugate is defined by inversing elements in the associated group.

diff --git a/test/test_ecc_base.jl b/test/test_ecc_base.jl
@@ -6,7 +6,7 @@ using InteractiveUtils
 
 import Nemo: GF
 import LinearAlgebra
-import Hecke: group_algebra, abelian_group, gens, one
+import Hecke: group_algebra, abelian_group, gens
 
 # generate instances of all implemented codes to make sure nothing skips being checked
 
@@ -62,25 +62,25 @@ push!(other_lifted_product_codes, LPCode(A, B))
 l=6; m=6
 GA = group_algebra(GF(2), abelian_group([l, m]))
 x, y = gens(GA)
-A = [x^3, y, y^2]
-B = [y^3, x, x^2]
-bb1 = bivariate_bicycle_codes(A,B,GA)
+A = x^3 + y + y^2
+B = y^3 + x + x^2
+bb1 = bivariate_bicycle_codes(A,B)
 
 # A [[90, 8, 10]] code from Table 3 of [bravyi2024high](@cite).
 l=15; m=3
 GA = group_algebra(GF(2), abelian_group([l, m]))
 x, y = gens(GA)
-A = [x^9   , y   , y^2]
-B = [one(x), x^2 , x^7]
-bb2 = bivariate_bicycle_codes(A,B,GA)
+A = x^9 + y   + y^2
+B = 1   + x^2 + x^7
+bb2 = bivariate_bicycle_codes(A,B)
 
 # A [[360, 12, ≤ 24]]  code from Table 3 of [bravyi2024high](@cite).
 l=30; m=6
 GA = group_algebra(GF(2), abelian_group([l, m]))
 x, y = gens(GA)
-A = [x^9 , y    ,  y^2]
-B = [y^3 , x^25 , x^26]
-bb3 = bivariate_bicycle_codes(A,B,GA)
+A = x^9 + y    + y^2
+B = y^3 + x^25 + x^26
+bb3 = bivariate_bicycle_codes(A,B)
 
 test_bb_codes = [bb1, bb2, bb3]
 

diff --git a/test/test_ecc_bivaraite_bicycle_as_twobga.jl b/test/test_ecc_bivaraite_bicycle_as_twobga.jl
@@ -8,63 +8,63 @@
         l=6; m=6
         GA = group_algebra(GF(2), abelian_group([l, m]))
         x, y = gens(GA)
-        A = [x^3, y, y^2]
-        B = [y^3, x, x^2]
-        c = bivariate_bicycle_codes(A,B,GA)
+        A = x^3 + y + y^2
+        B = y^3 + x + x^2
+        c = bivariate_bicycle_codes(A,B)
         @test code_n(c) == 72 &&  code_k(c) == 12
 
         # [[90, 8, 10]]
         l=15; m=3
         GA = group_algebra(GF(2), abelian_group([l, m]))
         x, y = gens(GA)
-        A = [x^9   , y   , y^2]
-        B = [one(x), x^2 , x^7]
-        c = bivariate_bicycle_codes(A,B,GA)
+        A = x^9 + y   + y^2
+        B = 1   + x^2 + x^7
+        c = bivariate_bicycle_codes(A,B)
         @test code_n(c) == 90 &&  code_k(c) == 8
 
         # [[108, 8, 10]]
         l=9; m=6
         GA = group_algebra(GF(2), abelian_group([l, m]))
         x, y = gens(GA)
-        A = [x^3 , y , y^2]
-        B = [y^3 , x , x^2]
-        c = bivariate_bicycle_codes(A,B,GA)
+        A = x^3 + y + y^2
+        B = y^3 + x + x^2
+        c = bivariate_bicycle_codes(A,B)
         @test code_n(c) == 108 &&  code_k(c) == 8
 
         # [[144, 12, 12]]
         l=12; m=6
         GA = group_algebra(GF(2), abelian_group([l, m]))
         x, y = gens(GA)
-        A = [x^3 , y , y^2]
-        B = [y^3 , x , x^2]
-        c = bivariate_bicycle_codes(A,B,GA)
+        A = x^3 + y + y^2
+        B = y^3 + x + x^2
+        c = bivariate_bicycle_codes(A,B)
         @test code_n(c) == 144 &&  code_k(c) == 12
 
         # [[288, 12, 12]]
         l=12; m=12
         GA = group_algebra(GF(2), abelian_group([l, m]))
         x, y = gens(GA)
-        A = [x^3 , y^2, y^7]
-        B = [y^3 , x  , x^2]
-        c = bivariate_bicycle_codes(A,B,GA)
+        A = x^3 + y^2 + y^7
+        B = y^3 + x   + x^2
+        c = bivariate_bicycle_codes(A,B)
         @test code_n(c) == 288 &&  code_k(c) == 12
 
         # [[360, 12, ≤ 24]]
         l=30; m=6
         GA = group_algebra(GF(2), abelian_group([l, m]))
         x, y = gens(GA)
-        A = [x^9 , y    ,  y^2]
-        B = [y^3 , x^25 , x^26]
-        c = bivariate_bicycle_codes(A,B,GA)
+        A = x^9 + y    + y^2
+        B = y^3 + x^25 + x^26
+        c = bivariate_bicycle_codes(A,B)
         @test code_n(c) == 360 &&  code_k(c) == 12
 
         # [[756, 16, ≤ 34]]
         l=21; m=18
         GA = group_algebra(GF(2), abelian_group([l, m]))
         x, y = gens(GA)
-        A = [x^3 , y^10 , y^17]
-        B = [y^5 , x^3  , x^19]
-        c = bivariate_bicycle_codes(A,B,GA)
+        A = x^3 + y^10 + y^17
+        B = y^5 + x^3  + x^19
+        c = bivariate_bicycle_codes(A,B)
         @test code_n(c) == 756 &&  code_k(c) == 16
     end
 
@@ -73,45 +73,45 @@
         l=12; m=3
         GA = group_algebra(GF(2), abelian_group([l, m]))
         x, y = gens(GA)
-        A = [x^9   , y ,  y^2]
-        B = [one(x), x , x^11]
-        c = bivariate_bicycle_codes(A,B,GA)
+        A = x^9 + y + y^2
+        B = 1   + x + x^11
+        c = bivariate_bicycle_codes(A,B)
         @test code_n(c) == 72 &&  code_k(c) == 8
 
         # [[90, 8, 6]]
         l=9; m=5
         GA = group_algebra(GF(2), abelian_group([l, m]))
         x, y = gens(GA)
-        A = [x^8 , y^4 ,  y]
-        B = [y^5 , x^8 , x^7]
-        c = bivariate_bicycle_codes(A,B,GA)
+        A = x^8 + y^4 + y
+        B = y^5 + x^8 + x^7
+        c = bivariate_bicycle_codes(A,B)
         @test code_n(c) == 90 &&  code_k(c) == 8
 
         # [[120, 8, 8]]
         l=12; m=5
         GA = group_algebra(GF(2), abelian_group([l, m]))
         x, y = gens(GA)
-        A = [x^10  , y^4,   y]
-        B = [one(x), x  , x^2]
-        c = bivariate_bicycle_codes(A,B,GA)
+        A = x^10 + y^4 + y
+        B = 1    + x   + x^2
+        c = bivariate_bicycle_codes(A,B)
         @test code_n(c) == 120 &&  code_k(c) == 8
 
         # [[150, 8, 8]]
         l=15; m=5
         GA = group_algebra(GF(2), abelian_group([l, m]))
         x, y = gens(GA)
-        A = [x^5 , y^2 , y^3]
-        B = [y^2 , x^7 , x^6]
-        c = bivariate_bicycle_codes(A,B,GA)
+        A = x^5 + y^2 + y^3
+        B = y^2 + x^7 + x^6
+        c = bivariate_bicycle_codes(A,B)
         @test code_n(c) == 150 &&  code_k(c) == 8
 
         # [[196, 12, 8]]
         l=14; m=7
         GA = group_algebra(GF(2), abelian_group([l, m]))
         x, y = gens(GA)
-        A = [x^6   , y^5 ,  y^6]
-        B = [one(x), x^4 , x^13]
-        c = bivariate_bicycle_codes(A,B,GA)
+        A = x^6 + y^5 + y^6
+        B = 1   + x^4 + x^13
+        c = bivariate_bicycle_codes(A,B)
         @test code_n(c) == 196 &&  code_k(c) == 12
     end
 
@@ -120,54 +120,54 @@
         l=3; m=9
         GA = group_algebra(GF(2), abelian_group([l, m]))
         x, y = gens(GA)
-        A = [one(x), y^2, y^4]
-        B = [y^3   , x  , x^2]
-        c = bivariate_bicycle_codes(A,B,GA)
+        A = 1   + y^2 + y^4
+        B = y^3 + x   + x^2
+        c = bivariate_bicycle_codes(A,B)
         @test code_n(c) == 54 &&  code_k(c) == 8
 
         # [[98, 6, 12]]
         l=7; m=7
         GA = group_algebra(GF(2), abelian_group([l, m]))
         x, y = gens(GA)
-        A = [x^3 , y^5 , y^6]
-        B = [y^2 , x^3 , x^5]
-        c = bivariate_bicycle_codes(A,B,GA)
+        A = x^3 + y^5 + y^6
+        B = y^2 + x^3 + x^5
+        c = bivariate_bicycle_codes(A,B)
         @test code_n(c) == 98 &&  code_k(c) == 6
 
         # [[126, 8, 10]]
         l=3; m=21
         GA = group_algebra(GF(2), abelian_group([l, m]))
         x, y = gens(GA)
-        A = [one(x), y^2, y^10]
-        B = [y^3   , x  ,  x^2]
-        c = bivariate_bicycle_codes(A,B,GA)
+        A = 1   + y^2 + y^10
+        B = y^3 + x  +  x^2
+        c = bivariate_bicycle_codes(A,B)
         @test code_n(c) == 126 &&  code_k(c) == 8
 
         # [[150, 16, 8]]
         l=5; m=15
         GA = group_algebra(GF(2), abelian_group([l, m]))
         x, y = gens(GA)
-        A = [one(x), y^6, y^8]
-        B = [y^5   , x  , x^4]
-        c = bivariate_bicycle_codes(A,B,GA)
+        A = 1   + y^6 + y^8
+        B = y^5 + x   + x^4
+        c = bivariate_bicycle_codes(A,B)
         @test code_n(c) == 150 &&  code_k(c) == 16
 
         # [[162, 8, 14]]
         l=3; m=27
         GA = group_algebra(GF(2), abelian_group([l, m]))
         x, y = gens(GA)
-        A = [one(x), y^10, y^14]
-        B = [y^12  , x   ,  x^2]
-        c = bivariate_bicycle_codes(A,B,GA)
+        A = 1    + y^10 + y^14
+        B = y^12 + x    + x^2
+        c = bivariate_bicycle_codes(A,B)
         @test code_n(c) == 162 &&  code_k(c) == 8
 
         # [[180, 8, 16]]
         l=6; m=15
         GA = group_algebra(GF(2), abelian_group([l, m]))
         x, y = gens(GA)
-        A = [x^3 , y   , y^2]
-        B = [y^6 , x^4 , x^5]
-        c = bivariate_bicycle_codes(A,B,GA)
+        A = x^3 + y   + y^2
+        B = y^6 + x^4 + x^5
+        c = bivariate_bicycle_codes(A,B)
         @test code_n(c) == 180 &&  code_k(c) == 8
     end
 end