Qubit Bloch Sphere Visualizer

Complex Numbers ($\alpha, \beta$)

Alpha (α) Real Part:

Alpha (α) Imaginary Part:

Beta (β) Real Part:

Beta (β) Imaginary Part:

Enter the real and imaginary parts of $\alpha$ and $\beta$. These are the complex amplitudes of the $|0\rangle$ and $|1\rangle$ states.

Remember, for a valid qubit state, the sum of the squares of the magnitudes of $\alpha$ and $\beta$ must be 1: $|\alpha|^2 + |\beta|^2 = 1$.

Example: For state $|+\rangle$, $\alpha = 1/\sqrt{2}$, $\beta = 1/\sqrt{2}$.

Angles ($\theta, \phi$)

Theta (θ) in Radians (0 to π):

Phi (φ) in Radians (0 to 2π):

Enter the polar angle $\theta$ (0 to $\pi$) and azimuthal angle $\phi$ (0 to $2\pi$). These angles define the qubit's position on the Bloch sphere.

The $\theta$ angle determines the probability of measuring $|0\rangle$ or $|1\rangle$. The $\phi$ angle represents the relative phase between the two states.

Example: For state $|+\rangle$, $\theta = \pi/2$, $\phi = 0$.

Qubit State Visualization (Bloch Sphere)

The sphere represents all possible pure states of a single qubit. The North Pole is $|0\rangle$, and the South Pole is $|1\rangle$.

The red arrow points to the current state of the qubit. You can click and drag on the sphere to rotate the view.