Stabilizer Decision Cross Scans

Round Decision Three-Row Scan

Three syndrome-round patterns separate no error, check fault, and data 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

Baseline readings choose no correction

Readings 00, 00, and 00 keep correction index negative 1.

s: 00,00,00c=−1s:\ 00,00,00\quad c=-1
Round decision scan rowAll baseline readings mean no data correction.syndrome rounds

A one-round blip is a check fault

Readings 00, 11, and 00 return to baseline, so correction index remains negative 1.

s: 00,11,00c=−1s:\ 00,11,00\quad c=-1
Round decision scan rowOne nonbaseline round does not move the data.syndrome rounds

Repeated nonbaseline readings choose data correction

Readings 00, 11, and 11 repeat the nonbaseline syndrome, so correction index 1 is checked.

s: 00,11,11c=1s:\ 00,11,11\quad c=1
Round decision scan rowTwo matching nonbaseline rounds support a repair.syndrome rounds