Bad Qubits — Learn Quantum by Doing

Multiple choice

On a real device, the VQE energy

E(\theta)

is estimated from a finite number of measurement shots. How does the statistical uncertainty

\sigma_E

in the energy estimate scale with the number of shots

N

$\sigma_E$ is independent of $N$ once $N > 1$
$\sigma_E \sim \Delta_H \sqrt{N}$ : it grows with the shot count
$\sigma_E \sim \Delta_H / \sqrt{N}$ : it falls as one over the square root of the shot count
$\sigma_E \sim \Delta_H / N$ : it falls linearly with the shot count