Manuscript Hawk07-B@1 · Hawk07-B.tex · section · b9785538

Fixed residual dimension

Payload-resource tradeoffs before a positive cutoff › Fixed residual dimension · lines 744–755

For fixed $b_{*}$ and $p$ , this construction uses

h = O (d / ε^{2}), r_{*} = O (d^{2} / ε^{2}), dim R_{*} = O (d^{3} / ε^{4}) .

The logarithms of these dimensions count qubits. A polynomial Hilbert-space dimension does not imply a polynomial algorithm in the payload qubit count $ℓ = lo g_{2} d$ .

Displayed formulas in this passage

unlabeled · line 747
$h = O (d / ε^{2}), r_{*} = O (d^{2} / ε^{2}), dim R_{*} = O (d^{3} / ε^{4}) .$

Nearby in this section

section: Fixed residual dimension
theorem: Theorem: Explicit multi-cut design for any qubit payload