Matrix Quality Prediction Three-Row Scan - Quantum Hardware Readout: Signals and Calibration Step by Step

A matrix-quality prediction scan holds the true state and shot total fixed, then changes the assignment matrix to show how readout quality shifts observed counts. With true state (3/4, 1/4) and 20 shots, the perfect, mild, and soft matrices give observed counts (15, 5), (13, 7), and (11, 9) exactly for the stated toy matrix model; real hardware readout has calibration error, threshold drift, assignment-matrix estimation uncertainty, and shot noise.

Changing the assignment matrix moves the observed readout budget for the same true state. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Matrix quality changes what the same state looks like

The true state is fixed at 3/4 zero and 1/4 one. Only the assignment matrix changes.

p_{\text{true}}=\left(\frac{3}{4},\frac{1}{4}\right)

Three matrix qualities move the observed budget

The table shows perfect, mild, and soft assignment rows. The shot total stays fixed, so count changes come from matrix quality.

\begin{array}{c|c|c|c|c|c}A_c&A_e&p_z&p_o&N_z&N_o\\1&0&\frac{3}{4}&\frac{1}{4}&15&5\\\frac{4}{5}&\frac{1}{5}&\frac{13}{20}&\frac{7}{20}&13&7\\\frac{3}{5}&\frac{2}{5}&\frac{11}{20}&\frac{9}{20}&11&9\\\end{array}

The soft matrix pulls the result toward ambiguity

With the soft matrix, expected zero reads drop to 11 while expected one reads rise to 9.

\frac{11}{20}+\frac{9}{20}=1

This is readout accounting, not error correction

The scan makes no correction claim. It shows how calibrated assignment rows change observed probabilities and expected counts.

A\,p_{\text{true}}=p_{\text{observed}}