Error Signals

Readout Channel Changes Counts

assignment is applied last

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