Manuscript En02-C@1 · En02-C-v1.tex · corollary · 7549c6df

Corollary: Compiled amplification costs

C5: amplification and the single-copy ledger › Gate-library-dependent reflection costs · lines 1400–1431 · proof included or linked

En02-C@1#cor:HPgates

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Under these library assumptions, a fixed- $r$ programme has

G \leq 2 k + (2 r + 1) g_{U} + r [4 k + 4 d + z (2 k) + z (2 d)] + 2 d,

and

D \leq 5 + (2 r + 1) D_{U} + r [8 + d_{0} (2 k) + d_{0} (2 d)] .

The final measurements of $D D^{'}$ and $C^{'}$ may share one round.

No additional coherent success-flag qubit is required for these direct reflections. If a different implementation computes a predicate into a quantum flag, that flag and all predicate workspace must be added to its ledger.

Proof. Initial Bell preparation costs $2 k$ gates and two rounds. There is an initial conjugate-evolution circuit. Each iteration contains two evolution circuits and the two Bell-subspace reflections. The terminal Bell-basis change costs $2 d$ gates and two rounds; the terminal destructive readouts add one round.

Displayed formulas in this passage

unlabeled · line 1403
$G \leq 2 k + (2 r + 1) g_{U} + r [4 k + 4 d + z (2 k) + z (2 d)] + 2 d,$
unlabeled · line 1410
$D \leq 5 + (2 r + 1) D_{U} + r [8 + d_{0} (2 k) + d_{0} (2 d)] .$

Corollary: Compiled amplification costs

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