[[2ʲ, 2ʲ - 2j - 2, 4]] Gottesman code

src/ecc/ECC.jl

@@ -380,6 +380,7 @@ include("codes/classical/reedmuller.jl")
 include("codes/classical/recursivereedmuller.jl")
 include("codes/classical/bch.jl")
 include("codes/quantumreedmuller.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

@@ -1,6 +1,6 @@
 using Test
 using QuantumClifford
-using QuantumClifford.ECC
+using QuantumClifford.ECC: Gottesman4
 using InteractiveUtils
 
 import Nemo: GF
@@ -60,11 +60,13 @@ const code_instance_args = Dict(
     Toric => [(3,3), (4,4), (3,6), (4,3), (5,5)],
     Surface => [(3,3), (4,4), (3,6), (4,3), (5,5)],
     Gottesman => [3, 4, 5],
+    CSS => (c -> (parity_checks_x(c), parity_checks_z(c))).([Shor9(), Steane7(), Toric(4,4)]),
     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,
     LPCode => (c -> (c.A, c.B)).(vcat(LP04, LP118, test_gb_codes, other_lifted_product_codes)),
-    QuantumReedMuller => [3, 4, 5]
+    QuantumReedMuller => [3, 4, 5],
+    Gottesman4 => [4, 5, 6, 7, 8]
 )
 
 function all_testablable_code_instances(;maxn=nothing)