Shot Total Scaling Three-Row Scan - Quantum Hardware Readout: Signals and Calibration Step by Step

A shot-total scaling scan holds the true state and assignment matrix fixed, then scales only the number of shots to show how expected counts grow proportionally. The observed probabilities (13/20, 7/20) stay constant while shot totals 20, 40, and 80 give expected counts (13, 7), (26, 14), and (52, 28) exactly for the stated toy readout model; real hardware readout has shot noise, calibration drift, assignment-matrix uncertainty, and threshold variation.

Changing the shot total scales expected counts after the observed probabilities are fixed. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Shot totals scale counts after probabilities are fixed

The true state and assignment matrix stay fixed. The observed probabilities are computed once, then shot totals scale expected counts.

p_{\text{obs}}=\left(\frac{13}{20},\frac{7}{20}\right)

Three shot totals keep the same observed fractions

The first two columns stay fixed across the scan. Only the count columns scale with the number of shots.

\begin{array}{c|c|c|c}p_z&p_o&N_z&N_o\\\frac{13}{20}&\frac{7}{20}&13&7\\\frac{13}{20}&\frac{7}{20}&26&14\\\frac{13}{20}&\frac{7}{20}&52&28\\\end{array}

The largest shot row keeps the same proportions

The large row has 52 expected zero reads and 28 expected one reads.

\frac{13}{20}\cdot80=52

More shots do not change the calibration matrix

This scan claims expected counts only. It does not add sampling variance, Bayesian updating, or detector drift.

\frac{13}{20}+\frac{7}{20}=1