Manuscript IX-B-ST@1 · IX-B-ST.tex · section · f6af1523

A fixed-interface evaluation channel

Finite numerical certificates and a destructive clock › A fixed-interface evaluation channel · lines 1702–1727

IX-B-ST@1#eq:evaluation

Let $G$ be the catalogue register, padded to $2^{g}$ labels. Its intended inputs are classical in the basis ${∣ i ⟩}$ . The canonical full-matrix extension pinches that basis. Let $P$ be an arbitrary quantum payload.

For each $(k, i)$ , choose an installed real score $v_{k i} \in [- 1, 1]$ , and put

p_{y} (k, i) = \frac{1 + y v _{k i}}{2}, y = \pm 1,

X_{k i} = (⟨ τ_{k} ∣_{C} ⟨ i ∣_{G} \otimes I_{P}) X (∣ τ_{k} ⟩_{C} ∣ i ⟩_{G} \otimes I_{P}) .

Define

I_{v} (X) = k, i, y \sum ∣ k, i, y, r (k, i)⟩ ⟨ k, i, y, r (k, i) ∣_{W} \otimes p_{y} (k, i) X_{k i} .

Displayed formulas in this passage

IX-B-ST@1#eq:evaluation · line 1721
$I_{v} (X) = k, i, y \sum ∣ k, i, y, r (k, i)⟩ ⟨ k, i, y, r (k, i) ∣_{W} \otimes p_{y} (k, i) X_{k i} .$
unlabeled · line 1711
$p_{y} (k, i) = \frac{1 + y v _{k i}}{2}, y = \pm 1,$
unlabeled · line 1714
$X_{k i} = (⟨ τ_{k} ∣_{C} ⟨ i ∣_{G} \otimes I_{P}) X (∣ τ_{k} ⟩_{C} ∣ i ⟩_{G} \otimes I_{P}) .$

A fixed-interface evaluation channel

Displayed formulas in this passage

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