Prepare Control Couple Budget - Quantum Computing Physical Bases: Control, Coupling, and Error Signals Step by Step

Start the audit before readout error so the ideal state budget is visible. The toy circuit uses probabilities 3/4 for zero and 1/4 for one, then carries that budget into the calibrated 80-shot count check of 57 and 23; real hardware adds preparation error, drift, decoherence, calibration limits, and shot uncertainty.

The audit starts with the ideal state budget before classical readout error. 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 ideal state budget comes first

Before readout error, the ideal probabilities are 3/4 for zero and 1/4 for one.

p_{\text{zero}}=\frac{3}{4},\quad p_{\text{one}}=\frac{1}{4}

The state budget becomes expected counts

The scan starts with ideal probabilities, then shows the calibrated count budget used by the audit.

\begin{array}{c|c|c|c}\text{row}&\text{zero}&\text{one}&\text{total}\\\text{ideal }p&\frac{3}{4}&\frac{1}{4}&1\\\text{observed }p&\frac{57}{80}&\frac{23}{80}&1\\\text{expected }N&57&23&80\\\end{array}

The expected counts follow from the budget

After the channel, the expected counts over 80 shots are 57 and 23.

N_{\text{zero}}=57,\quad N_{\text{one}}=23