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Manuscript Oai212-A@1 · Oai212-A.tex · section · 79323841

The local timer rule

Bridge 1: an exact controlled operator-spreading model › The local timer rule · lines 578–589

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Let $U_{τ} (t)$ be the chronological product of all successful CNOTs up to time $t$ , with later gates acting on the left. Define

Z_{x} (t) = U_{τ} (t)^{†} Z_{x} U_{τ} (t), C_{τ} (x, t) = \frac{1}{4 2 ^{∣ V ∣}} Tr ([Z_{x} (t), X_{0}]^{†} [Z_{x} (t), X_{0}]) .

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unlabeled · line 583
$Z_{x} (t) = U_{τ} (t)^{†} Z_{x} U_{τ} (t), C_{τ} (x, t) = \frac{1}{4 2 ^{∣ V ∣}} Tr ([Z_{x} (t), X_{0}]^{†} [Z_{x} (t), X_{0}]) .$

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