Single-Qubit Quantum Gates on a Bloch Sphere

θ

0

ϕ

0

gate 1

H

X

Y

Z

S

T

add gate 2?

gate 2

H

X

Y

Z

S

T

Using the Bloch sphere, a cubit

ψ=α0+β1=cos(θ/2)0+sin(θ/2)

ϕ

e

1

can be represented as a unit vector (shown in red) from the origin to the point on the unit sphere with spherical coordinates

(θ,ϕ)

. A single-qubit quantum gate

G

1

operating on

ψ〉

produces a rotated qubit

G

1

ψ〉=

ψ

1

〉

, represented by the green vector. Check the box for "add gate 2?" to perform a second operation using gate

G

2

. This produces another qubit

G

2

G

1

ψ〉=

ψ

2

〉

, 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.