Shot Noise Explorer
Finite measurement statistics in quantum estimation
Prepare a 1-qubit state Ry(theta)|0> and estimate the Pauli-Z expectation from finite measurement shots. Run 100 independent estimates to see the sampling distribution. Observe that variance scales as 1/N with shot count, and that noise is state-dependent: zero at eigenstates, maximal at equal superpositions.
0 (|0⟩)pi/2 (|+⟩)pi (|1⟩)
true <Z> = 0.5000Var(Z) = 0.7500Var(est) = Var/N = 7.500e-3
Estimation variance vs shot count
State-dependent noise: Var(Z) vs theta
Measurement noise is state-dependent: zero at eigenstates (theta = 0 or pi), maximal at superpositions (theta = pi/2). Estimation variance scales as 1/N with shot count. This is the fundamental noise floor of any VQA.