Manuscript X-A-conv-ST@1 · X-A-conv-ST.tex · section · 8ca47088

Resource and error ledger

Stage E: scheduled locality and finite report transport › Resource and error ledger · lines 2110–2143

X-A-conv-ST@1#eq:error

If the payload uses $p$ qubits, the route reserves $(n + 1) p$ qubits and uses $n$ register SWAPs. Clock, signal, workspace, supplier, and reference holdings are separately charged. A conservative preallocated bound is

q_{clock} + q_{signal} + q_{workspace} + (n + 1) p .

No optimality is claimed for this bound.

For compatible ideal and implemented complete channels,

d_{⋄} (Γ, Γ) \leq min {1, e_{prep} + e_{clock} + e_{lookup} + e_{read} + j = 1 \sum^{n} e_{j} + e_{decode}}, d_{⋄} (Λ, Γ) = \frac{1}{2} ∥ Λ - Γ ∥_{⋄} .

To prove this, replace one factor at a time and apply diamond-norm contraction under channel composition and the triangle inequality Watrous,En08B. The comparison interfaces include all classical histories and quantum residuals.

A small channel error is not exact causal containment. Nor does it validate a false supplied numerical enclosure or produce a missing field-acquisition map.

Displayed formulas in this passage

X-A-conv-ST@1#eq:error · line 2123
$d_{⋄} (Γ, Γ) \leq min {1, e_{prep} + e_{clock} + e_{lookup} + e_{read} + j = 1 \sum^{n} e_{j} + e_{decode}}, d_{⋄} (Λ, Γ) = \frac{1}{2} ∥ Λ - Γ ∥_{⋄} .$
unlabeled · line 2116
$q_{clock} + q_{signal} + q_{workspace} + (n + 1) p .$