Quantum Physics, Quantum Computing, Quantum Mechanics, Computer Science.
= z|0⟩ + (x + iy)|1⟩ = cosθ|0⟩ + sinθ(cos ϕ+ i sin ϕ)|1⟩ = cosθ|0⟩ + e^(iϕ) sinθ|1⟩ But notice that for θ=0, |ψ⟩ = |0⟩and θ= 90(pie/2), |ψ⟩ = 1⟩. So,we don’t have to consider full angles till 180. Because we get all values in 0 to 90 only so halving θ in above equation will give final equation for