Assignment quality is count normalization before it is a prediction input. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A symmetric assignment scan starts with count pairs

Each row uses the same total shots for prepared zero and prepared one. The scan changes the correct count and error count together.

Ncorrect+Nerror=10N_{\text{correct}}+N_{\text{error}}=10
Mild assignment matrixBoth prepared-state rows are normalized from counts.assignment matrixread zeroread onetrue zero4/58 shots1/52 shotstrue one1/52 shots4/58 shots

Three matrix shapes show diagonal strength

The table compresses the symmetric matrix to correct and error columns. The displayed matrix still contains both prepared rows.

NcNeAcAe10010824515643525\begin{array}{c|c|c|c}N_c&N_e&A_c&A_e\\10&0&1&0\\8&2&\frac{4}{5}&\frac{1}{5}\\6&4&\frac{3}{5}&\frac{2}{5}\\\end{array}
Assignment diagonal scanThe mild row keeps a stronger diagonal than off-diagonal.assignment matrixread zeroread onetrue zero4/58 shots1/52 shotstrue one1/52 shots4/58 shots

The soft row is normalized but less decisive

The soft row has correct probability 3/5 and error probability 2/5. The row still sums to one.

35+25=1\frac{3}{5}+\frac{2}{5}=1
Soft assignment rowLess decisive is not the same as unnormalized.assignment matrixread zeroread onetrue zero3/56 shots2/54 shotstrue one2/54 shots3/56 shots

Matrix quality is count normalization here

The scan does not claim a microscopic fidelity model. It only turns prepared-state counts into normalized readout rows.

Ac+Ae=1A_{c}+A_{e}=1
Matrix normalization auditThe helper rejects rows that do not sum to one.assignment matrixread zeroread onetrue zero4/58 shots1/52 shotstrue one1/52 shots4/58 shots