Resources and complete-output errors

For an inherited $n_C$-qubit clock, $p$-qubit payloads, $b$-bit report reserves, and lookup workspace $w_{\mathrm{lookup}}$, a conservative preallocated quantum reserve is

Any additional description register is separately added to the ledger. The final qubit is an optional table probe. Classical table storage, external reference storage, gate counts, and durations are separately declared.

The route uses $n$ register SWAPs and $n$ classical report transmissions. Readout, lookup, and the buffer are charged before departure. The consumed clock names are not returned. All retained record copies and any discarded blank factors are specified in the complete interface.

For compatible implemented complete channels, factorwise replacement gives

Indeed, telescope the difference of the two compositions and use diamond-norm contraction under pre- and postcomposition by channels Watrous. An arrival or failure probability is controlled only when its flag belongs to the compared complete output. A channel-error bound is not itself exact causal containment of an erroneous implementation.