Stabilizer Decision Cross Scans

Syndrome Index Three-Row Scan

The three single-carrier flips make the syndrome table visible as exact rows. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Left-carrier flip gives syndrome ten

A flip at index 0 changes the word to 011. The syndrome is 10 and the correction index is 0.

s=10c=0s=10\quad c=0
Syndrome index scan rowThe left parity bit is the first syndrome bit.syndrome check

Middle flip makes both parity checks fire

A flip at index 1 changes the word to 101. Syndrome 11 maps to correction index 1.

s=11c=1s=11\quad c=1
Syndrome index scan rowBoth parity checks identify the middle carrier.syndrome check

Right-carrier flip gives syndrome one

A flip at index 2 changes the word to 110. Syndrome 01 maps to correction index 2.

s=01c=2s=01\quad c=2
Syndrome index scan rowThree rows show the full single-error table.syndrome check