Readout error is a final labeling step, so the lesson applies a calibrated assignment matrix after the state budget rather than mixing it into the quantum part. The fractions are exact for this pinned count model, while real readout rows come from calibration data whose thresholds, drift, and finite-shot noise limit the certainty.

Readout assignment is a separate classical matrix after the quantum state budget. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Readout error has its own calibration rows

The readout assignment rows are 9/10, 1/10 and 1/5, 4/5.

A=[9101101545]A=\begin{bmatrix}\frac{9}{10}&\frac{1}{10}\\\frac{1}{5}&\frac{4}{5}\end{bmatrix}
Readout calibration matrixThe rows come from prepared-state counts.assignment matrixread zeroread onetrue zero9/109 shots1/101 shotstrue one1/52 shots4/58 shots

Readout rows are applied after the state budget

The calibration rows stay separate from the true state probabilities until the prediction step.

rowp(read zero)p(read one)prep zero910110prep one1545true zero3414\begin{array}{c|c|c}\text{row}&p(\text{read zero})&p(\text{read one})\\\text{prep zero}&\frac{9}{10}&\frac{1}{10}\\\text{prep one}&\frac{1}{5}&\frac{4}{5}\\\text{true zero}&\frac{3}{4}&\frac{1}{4}\\\end{array}
Readout row scanThe assignment matrix is the source for both rows.assignment matrixread zeroread onetrue zero9/109 shots1/101 shotstrue one1/52 shots4/58 shots

Assignment error is applied after true probabilities

The readout assignment changes the observed counts to 29 and 11 over 40 shots.

Nread zero=29,Nread one=11N_{\text{read zero}}=29,\quad N_{\text{read one}}=11
Readout predictionThe assignment matrix is applied after the state budget.true probabilitieszero 3/4one 1/4assignmentobserved probszero 29/40one 11/40over 40 shots29 zero reads11 one reads