A checked swap exchanges the upper and lower rail labels. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A swap sends upper occupation to the lower rail

Starting from logical 0, the checked swap gives output logical 1.

0swap10\xrightarrow{\text{swap}}1
Swap from zeroThe output rail binding is checked.0upper1lowerdual rail

The same swap sends lower occupation to upper

Starting from logical 1, the checked swap gives output logical 0.

1swap01\xrightarrow{\text{swap}}0
Swap from oneBoth swap directions use the same checked rule.1upper0lowerdual rail