Model specification: Readout noise and preparation

All apparatus baths and preparation records are fresh and independent of $QSR$.

1. With probability $r_{\mathrm{F}}$, a preparation protocol reports the visible symbol $\mathrm{reset}-\mathrm{failed}$, consumes $Q$, and returns ${\mathrm{Tr}}_{Q}X$ on $S$. Its decoded value is zero.

2. Conditional on readiness, pointer preparation is

   $${\sigma }_A={\underset{j=1}{⨂}}^{b_N}((1-p_{A,j})|0⟩⟨0|+p_{A,j}|1⟩⟨1|).$$

   Its distance from the all-zero pointer is

   $$p_A=1-\prod _j(1-p_{A,j}).$$

3. Before pointer copying, register qubit $j$ undergoes amplitude damping with

   $$r_{D,j}=1-e^{-{\gamma }_j{T}_D},{\gamma }_j\ge 0.$$

   Its Kraus maps are

   $$L_{0,j}=|0⟩⟨0|+\sqrt{1-r_{D,j}}|1⟩⟨1|,L_{1,j}=\sqrt{r_{D,j}}|0⟩⟨1|.$$

   A known residual basis rotation is

   $$V_B=\exp \left(-\frac{\mathrm{i}}{2}\sum _j{\alpha }_j{Y}_{Q_j}\right).$$

4. A separate spectator-coupling interval has a bounded self-adjoint generator $G_X(t)$ on $QS$. Its ideal comparison is the identity.

5. The pointer-copy generator is $H_R+\Delta H_R(t)$, where $\Delta H_R$ is bounded on the finite $QAS$ space. It includes the errors assigned to this interval, but not the separate interval already priced by $G_X$.

6. Computational pointer readout is followed by the fixed matrix $W(y\mid j)$, including any timeout or other declared assignment failures. The raw record or failure label and its decoded value are always retained.