Faithfully empirical from https://qiskit.org/textbook/ch-quantum-hardware/measuring-quantum-volume.html

Each column in the first table is 1000 independent trials, 1024 shots per cell per trial

"Integrated noisy heavy output generation rate" ("INHOGR") requires a Riemann sum over depth and noise, to prove and predict average fidelity.

If you want to use this for a single specific circuit in the class of heavy output generation problems:

1. Find your "minimum attainable rounding parameter" ("MARP") by repeating simulation with different rounding parameter values until it barely successfully completes the calculation.

2. Look up the heavy output rate excess (above 0.5) after the final preprocessing step of this calibration, at bottom in row 105 and down.

(The square root of the fraction of your HOG rate cell over HOG rate for 0 noise in the same row is a pessimistic estimator for "square fidelity." "Infidelity" is 1 minus fidelity.)

[Fidelity] >= SQRT([Noisy HOG rate]/[Ideal HOG rate])

3. (If your MARP is greater than 0,) apply the excess circuit width correction model, ln([square circuit infidelity]) / ln([infidelity of your circuit]) = ln([width]) / ln([depth]). (0 MARP needs no excess width correction.)

4. Algebra gets you from step 3 to estimates for "fidelity" and HOG rate.

"0" rounding parameter is rather floating-point "epsilon," dependent on floating-point type precision.

Observed heavy output rate as a function of Qrack Schmidt decomposition rounding parameter

100 trials for 22, 0 above 0.3375

Log-scale heavy output rate as a function of Qrack Schmidt decomposition rounding parameter

Smoothed heavy output rate as a function of Qrack Schmidt decomposition rounding parameter

Mean-adjusted and smoothed heavy output rate as a function of Qrack Schmidt decomposition rounding parameter