Circuit Source-Factor Scans

Error Channel Shot-Scale Three-Row Scan

The shot-scale scan keeps the same calibrated error model and changes only the total number of shots. The expected counts scale from 57/23 at 80 shots to 114/46 at 160 and 171/69 at 240, so the row arithmetic separates model probabilities from sample size. Real count predictions include binomial fluctuation, calibration uncertainty, drift, thresholding, and finite-shot noise.

A fixed readout model is evaluated at three shot totals to make scaling explicit. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The eighty-shot row is the source prediction

The calibrated probabilities give 57 zero reads and 23 one reads.

Nzero=57,None=23N_{\text{zero}}=57,\quad N_{\text{one}}=23
Eighty-shot predictionThe count row is computed from the calibrated probabilities.true probabilitieszero 3/4one 1/4assignmentobserved probszero 57/80one 23/80over 80 shots57 zero reads23 one reads

Shot total scales both expected counts

The assignment matrix and true probabilities stay fixed. The shot total is the only source that changes.

SNzeroNone8057231601144624017169\begin{array}{c|c|c}S&N_{\text{zero}}&N_{\text{one}}\\80&57&23\\160&114&46\\240&171&69\\\end{array}
Scaled shot predictionThe middle row doubles the baseline shot total.true probabilitieszero 3/4one 1/4assignmentobserved probszero 57/80one 23/80over 160 shots114 zero reads46 one reads

The largest row is still the same calibrated model

Tripling the shot total triples the expected counts. No new readout matrix is introduced.

Nzero=171,None=69N_{\text{zero}}=171,\quad N_{\text{one}}=69
Two-hundred-forty shotsThe largest row remains source-bound to the same matrix.true probabilitieszero 3/4one 1/4assignmentobserved probszero 57/80one 23/80over 240 shots171 zero reads69 one reads