# Single-Qubit Quantum Gates on a Bloch Sphere

Single-Qubit Quantum Gates on a Bloch Sphere

Using the Bloch sphere, a cubit can be represented as a unit vector (shown in red) from the origin to the point on the unit sphere with spherical coordinates . A single-qubit quantum gate operating on produces a rotated qubit , represented by the green vector. Check the box for "add gate 2?" to perform a second operation using gate . This produces another qubit , which is represented by the blue vector. You can choose from the gates H, X, Y, Z, S and T as defined in the Details.

ψ〉=α0〉+β1〉=cos(θ/2)0〉+sin(θ/2)e1〉

ϕ

(θ,ϕ)

G

1

ψ〉

Gψ〉=ψ〉

1

1

G

2

GGψ〉=ψ〉

2

1

2