Manuscript Hawk07-A@1 · Hawk07-A.tex · example · f9c0f5da

Example: An analytic numerical certificate

Existence with a nontrivial window and turnover · lines 1410–1438

Let

ε = \frac{1}{5}, ζ = \frac{1}{200}, m = 17, h = 131072.

The size requirement is $h \geq 102400$ . The vault has $21$ qubits, and the early receiver has $17$ . The retained cuts are:

cut k_{*} = 18 k_{peak} = 19 K = 20 late qubits 181920 active residual qubits 321 total receiver qubits 353637

The full-diamond allowance is $0.2$ , not $0.1$ . The fixed decoder core has input dimension $2^{35}$ ; its Kraus rank is at most $2^{39}$ . Equation (eq:workspace) gives a conservative batch peak of $80$ live decoder qubits at the last cut.

This is an exact parameter calculation. No Haar sample, decoder optimization, or hardware execution is reported.

Displayed formulas in this passage

unlabeled · line 1412
$ε = \frac{1}{5}, ζ = \frac{1}{200}, m = 17, h = 131072.$
unlabeled · line 1420
$cut k_{*} = 18 k_{peak} = 19 K = 20 late qubits 181920 active residual qubits 321 total receiver qubits 353637$

Example: An analytic numerical certificate

Displayed formulas in this passage

Nearby in this section