isomorphisms for bloch plotting

src/isomorphisms.jl

@@ -12,6 +12,8 @@ export operator_to_iso_vec
 export iso_operator_to_iso_vec
 export iso_operator_to_operator
 export operator_to_iso_operator
+export ket_to_bloch
+export bloch_to_ket
 
 # Do not export Hamiltonian isomorphisms
 
@@ -249,6 +251,42 @@ function var_G(
     return G_0 + G_V
 end
 
+# ----------------------------------------------------------------------------- #
+#                             Bloch Sphere                                      #
+# ----------------------------------------------------------------------------- #
+
+@doc raw"""
+    ket_to_bloch(ψ::AbstractVector{<:Number})
+
+Convert a ket to a Bloch vector representation.
+"""
+function ket_to_bloch(ψ::AbstractVector{<:Number})
+    ρ = ψ * ψ'
+    bloch_vector =  [real(tr(ρ * P)) for P in [PAULIS.X, PAULIS.Y, PAULIS.Z]]
+
+    return bloch_vector / norm(bloch_vector)
+end
+
+@doc raw"""
+    bloch_to_ket(v::AbstractVector{<:Real}; digits=6)
+
+
+Convert a Bloch vector to a ket (up to global phase).
+"""
+function bloch_to_ket(bloch::AbstractVector{<:Number}; digits::Integer=6)
+    x, y, z = bloch  # extract bloch vector components
+
+    # compute angles
+    θ = acos(z)  # polar angle
+    φ = atan(y, x)  # azimuthal angle
+
+    # construct the quantum state
+    ket = [cos(θ/2), exp(im * φ) * sin(θ/2)]
+
+    ket = map(c -> round(real(c), digits=digits) + (isreal(c) ? 0.0 : im * round(imag(c), digits=digits)), ket)
+
+    return ket
+end
 # *************************************************************************** #
 
 @testitem "Test ket isomorphisms" begin
@@ -354,4 +392,19 @@ end
                     1.0 1.0 0.0 0.0 3.0 4.0]
 end
 
+@testitem "Test Bloch vector to ket and ket to Bloch vector" begin
+    using PiccoloQuantumObjects.Isomorphisms: ket_to_bloch, bloch_to_ket
+
+    ψ₁ = [1.0, 0.0]
+    ψ₂ = [0.0, 1.0]
+    ψ₃ = [1 / √2, 1 / √2]
+    ψ₄ = [1 / √2, -1im / √2]
+
+    for ψ in (ψ₁, ψ₂, ψ₃, ψ₄)
+        bloch = ket_to_bloch(ψ)
+        ψ′ = bloch_to_ket(bloch)
+        @test abs2(dot(ψ′, ψ)) ≈ 1.0 atol=1e-10
+    end
+end
+
 end