Manuscript Em03-E@1 · Em03-E-v1.tex · section · c4b07e6a

A constructive recovery allowance

Resources, tolerance schedules, and model limitations › A constructive recovery allowance · lines 1968–1998

For a requested recovery tolerance $ϵ > 0$ , it suffices that

\frac{3 - p - 2 p η}{4} \leq ϵ /2, ϵ_{dyn} + ϵ_{acc} + ϵ_{dec} \leq ϵ /2.

A useful sufficient parameter bound is

\frac{3 - p - 2 p η}{4} = \frac{3}{4} (1 - p) + \frac{p}{2} (1 - η) \leq \frac{3}{4} (1 - p) + \frac{1}{2} (1 - η) .

Thus finite pulses with $p, η$ close to one and sufficiently small complete implementation deviations meet the allowance within the declared tunable model family.

Occupation accuracy is a separate allowance:

t_{J} \leq q_{1}^{J_{1} + 1} + q_{2}^{J_{2} + 1} .

For fixed $q_{i} < 1$ , finite $J_{i}$ can meet any positive occupation-state tolerance.

These choices are not arbitrary accuracy on fixed hardware. Pulse selectivity, preparation error floors, storage loss, control bandwidth, and correlated apparatus memory can prevent the required bounds.

Displayed formulas in this passage

unlabeled · line 1971
$\frac{3 - p - 2 p η}{4} \leq ϵ /2, ϵ_{dyn} + ϵ_{acc} + ϵ_{dec} \leq ϵ /2.$
unlabeled · line 1977
$\frac{3 - p - 2 p η}{4} = \frac{3}{4} (1 - p) + \frac{p}{2} (1 - η) \leq \frac{3}{4} (1 - p) + \frac{1}{2} (1 - η) .$
unlabeled · line 1987
$t_{J} \leq q_{1}^{J_{1} + 1} + q_{2}^{J_{2} + 1} .$