A quantum result can be wrong for several reasons. Too few shots can cause an estimate to fluctuate randomly. An excessively deep circuit can systematically lose the intended information. An incorrect mapping can implement the wrong model even on ideal hardware. More shots directly address only the first problem.
What 512 shots do and do not mean
A shot is one execution and measurement of a circuit. For independent repetitions, the usual statistical standard error typically decreases as one divided by the square root of the number of shots. Four times as many shots therefore roughly halve the standard error, rather than making the result four times as accurate.
In our project, 512 is often the number of shots per setting. A job can contain several time points, twirls, training circuits and calibrations. The latest paired run contained 76 PUBs with 512 shots each: 38,912 measurements in total. Describing that complete job as ‘a run with 512 shots’ is therefore incomplete.
If noise has almost erased a spin profile, extra shots may simply confirm very precisely that the noisy profile is nearly flat. In that case, circuit improvements or reliable mitigation are needed, not just more statistics.
Why start with 3×3 and 5×5?
Small lattices allow more exact checks. We can build the fermion Hamiltonian in occupation space, calculate the ideal circuit output and compare the measured quantities site by site. This helps distinguish programming errors from hardware problems.
A preparatory 5×5 check allows us to compare state preparation with a dynamical circuit. A preparation check returning the correct particle numbers does not imply that a long evolution preserves that quality. Nor does a successful non-interacting check establish that the interacting U=8 target is accurate.
Aer as a targeted diagnostic
A noise simulator using saved Nighthawk parameters helps investigate specific questions: how much do readout errors, single-qubit noise and CZ noise contribute individually? What changes with additional folding or more shots? The advantage is that, for the smaller cases, we can also evaluate the same intended circuit without noise.
Such a simulator is not a complete digital twin of the device. Drift, correlated errors and unmodelled effects may be absent. A spin peak in Aer is therefore evidence about the tested noise model, not automatically an explanation for every hardware peak.
Random seeds also require checking. The archive preserves a correction for overlapping seeds: simulations that appear distinct can otherwise be statistically dependent. A fair comparison retains these corrections rather than showing only the most attractive plot.
Sources: AER_NIGHTHAWK_512_PROTOCOL.md, AER_SEED_CORRECTION_2026-09-06.md, HARDWARE_CONTROL_5X5_PROTOCOL.md and HARDWARE_COMPACT_TFLO_PROTOCOL.md.