Extended Data Fig. 4: Shot noise scaling with system size and convergence with number of snapshots.
From: Programmable simulations of molecules and materials with reconfigurable quantum processors
(a) Numerically computed standard deviations of the estimator (7) for the density of states DA(ω) of a spin-1 AFM chain, for different chain lengths and observables. Here, we consider a polarized reference state \(\left\vert S\right\rangle\) and random single-qubit rotations R for the controlled-perturbation. For the bare density of states the standard deviation slowly scales with the chain length (blue circles). For the projectors into the zero (gray diamonds) and three (orange circles) spin-flip sectors the standard deviation is consistent with being independent of system size. (b) Convergence of estimator with number of samples for two different observables. Shaded regions correspond to 2σ error bars around the mean, and decrease with the number of measurements as \(1/\sqrt{M}\). Dark lines are running averages for a specific sampled dataset. The sample complexity is defined as the number of samples needed such that the error bars around the mean do not include zero. After this point, spectral peaks can be reliably distinguished from noise.
