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 $|+\rangle$, $\alpha = 1/\sqrt{2}$, $\beta = 1/\sqrt{2}$.
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.
The **Global Phase Angle (γ)** represents an overall phase shift that does not affect the qubit's physical state on the Bloch sphere. However, it can be important when combining qubits. When converting from complex numbers, this field will show the original global phase. When converting to complex numbers, this phase will be applied.
Example: For state $|+\rangle$, $\theta = \pi/2$, $\phi = 0$.
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.