Phase Errors and Rounds

Repeated Syndromes Mark Data Error

A repeated nonbaseline syndrome supports a data-error 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

Repeated nonzero syndrome marks a data error

The three readings are 00, 11, and 11.

s0=00s1=11s2=11s_{0}=00\quad s_{1}=11\quad s_{2}=11
Repeated syndromeThe stage order is baseline, first, second.syndrome rounds

The repeated syndrome chooses a correction index

The repeated nonbaseline readings choose correction index 1.

c=1c=1
Data-error decisionTwo matching nonbaseline rounds are required.syndrome rounds