[[2ʲ, 2ʲ - 2j - 2, 4]] Gottesman code

src/ecc/ECC.jl

@@ -397,6 +397,8 @@ include("codes/util.jl")
 include("codes/concat.jl")
 include("codes/random_circuit.jl")
 include("codes/classical/bch.jl")
+include("codes/gottesman4.jl")
+
 
 # qLDPC
 include("codes/classical/lifted.jl")

src/ecc/codes/gottesman4.jl

@@ -0,0 +1,25 @@
+"""The family of `[[2ʲ, 2ʲ - 2j - 2, 4]]` Gottesman codes, also known as a 'Class of Distance Four Codes', as described in [Gottesman's 1997 PhD thesis](@cite gottesman1997stabilizer) and in [gottesman1996class](@cite).
+
+The stabilizer generators of the original `[[2ʲ, 2ʲ - j - 2, 3]]` Gottesman codes are incorporated to create a set of generators for this distance-four code. The resulting stabilizer set, denoted by S, incorporates the following elements: The first two generators are the Pauli-`X` and Pauli-`Z` operators acting on all qubits, represented by `Mₓ` and `Mz`, respectively. The next `j` generators correspond to `M₁` through `Mⱼ`, which are directly inherited from the `[[2ʲ, 2ʲ - j - 2, 3]]` Gottesman  code's stabilizers. This inclusion ensures that `S` retains the inherent distance-three property of the original Gottesman code. The final `j` generators are defined as `Nᵢ = RMᵢR`, where `i` ranges from `1` to `j`. Here, `R` signifies a Hadamard Rotation operation applied to all `2ʲ` qubits, and `Mᵢ` refers to one of the existing generators from the second set `(M₁ to Mⱼ)`. By incorporating the stabilizers of a distance-three code, the constructed set `S` inherently guarantees a minimum distance of three for the resulting distance-four Gottesman code.
+"""
+struct Gottesman4 <: AbstractECC
+    j::Int
+    function Gottesman4(j)
+        (j >= 3 && j < 21) || error("In `Gottesman4(j)`, `j` must be ≥  3 in order to obtain a valid code and < 21 to remain tractable")
+        new(j)
+    end
+end
+
+code_n(c::Gottesman4) = 2^c.j
+code_k(c::Gottesman4) = 2^c.j - 2*c.j - 2
+distance(c::Gottesman4) = 4
+
+function parity_checks(c::Gottesman4)
+    H₁ = parity_checks(Gottesman(c.j))
+    Hⱼ = H₁[3:end]
+    for qᵢ in 1:nqubits(Hⱼ)
+        apply!(Hⱼ, sHadamard(qᵢ))
+    end
+    H = vcat(H₁, Hⱼ)
+    Stabilizer(H)
+end

test/test_ecc_base.jl

@@ -1,8 +1,9 @@
 using Test
 using QuantumClifford.ECC.QECCore
 using QuantumClifford
-using QuantumClifford.ECC
-using QuantumClifford.ECC: check_repr_commutation_relation, check_repr_regular_linear
+using QuantumClifford.ECC: 
+using QuantumClifford.ECC: check_repr_commutation_relation, check_repr_regular_linear, Gottesman4
+
 using InteractiveUtils
 using SparseArrays
 
@@ -325,9 +326,9 @@ const code_instance_args = Dict(
     :QuantumTannerGraphProduct => [(H1, H2),(H2, H2), (H1, H1), (H2, H1)],
     :CyclicQuantumTannerGraphProduct => [1, 2, 3, 4, 5],
     :DDimensionalSurfaceCode => [(2, 2), (2, 3), (3, 2), (3, 3), (4, 2)],
-    :DDimensionalToricCode => [(2, 2), (2, 3), (3, 2), (3, 3), (4, 2)]
+    :DDimensionalToricCode => [(2, 2), (2, 3), (3, 2), (3, 3), (4, 2)],
+    :Gottesman4 => [4, 5, 6, 7, 8]
 )
-
 function all_testablable_code_instances(;maxn=nothing)
     codeinstances = []
     i = 1