Stabilizer Boundary Depth Scans

Round Repeat Boundary Three-Row Scan

Syndrome rounds need a repeated nonbaseline reading before data correction. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Data correction needs repeated nonbaseline rounds

The repeat count ignores the baseline round and counts later nonbaseline readings.

m=r−rmin⁡m=r-r_{\min}
Baseline roundsNo later nonbaseline reading is present.syndrome rounds

Three round patterns bracket the data-error threshold

A one-round blip is still below threshold. Two repeated nonbaseline readings meet it.

rrmin⁡mdecision02−2no error12−1check fault220data error\begin{array}{c|c|c|c}r&r_{\min}&m&\text{decision}\\0&2&-2&\text{no error}\\1&2&-1&\text{check fault}\\2&2&0&\text{data error}\\\end{array}
Check-fault boundaryOne nonbaseline round is not enough.syndrome rounds

The repeated row reaches the data-error threshold

The helper returns the correction index only when the nonbaseline syndrome repeats.

m=0passm=0\quad \text{pass}
Repeated syndromeTwo matching rounds support a data correction.syndrome rounds