QML intuition,
made visible.
Change a qubit state, inspect a fidelity kernel, and see how measurement budgets constrain precision. These analytic demos are educational visualizations, not remote quantum hardware.
01 · A qubit on the Bloch sphere
Prepare $|\psi\rangle=\cos(\theta/2)|0\rangle+e^{i\phi}\sin(\theta/2)|1\rangle$. The projection on Z determines $P(0)$ and the expectation $\langle Z\rangle$.
The sphere diagram is a 2D projection; the readout is calculated from the exact one-qubit formula.
02 · Fidelity quantum kernel
For the simple feature map $R_y(x)|0\rangle$, the state-overlap kernel is $K(x,z)=\cos^2((x-z)/2)$.
Notice the periodicity. A feature map can identify distinct classical inputs as similar quantum states.
03 · Shot noise budget
For a ±1-valued observable, the worst-case standard error of its sample mean is at most $1/\sqrt M$.
Increasing shots improves statistical precision but also increases circuit executions.