Stabilizer Audit

Code Syndrome Correction Chain

Read the audit as a chain of labels that must all point to the same protected word. In this pinned stabilizer toy model, the code source starts at 111, the syndrome 11 names the repair row for error word 101, and the correction closes back to 111; real syndrome chains also carry readout and calibration errors.

A stabilizer audit is a source-ref chain, not a final caption. 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 audit begins from a source-checked code word

The code source says the protected word is 111.

w=111w=111
Code sourceThe audit will cite this source field.repetition code

The syndrome source names the repair row

The error word is 101 with syndrome 11.

s=11c=1s=11\quad c=1
Syndrome sourceThe syndrome and correction index agree.syndrome check

The correction source closes the repaired word

The lookup repairs the word to 111.

wfixed=111w_{\mathrm{fixed}}=111
Correction sourceThe fixed word is a checked field.correction lookup