Manuscript En02-D@4 · En02-D-v4.tex · section · e19ec871

Controlled dynamics

Inter-emission dynamics and explicit protocol classes › Controlled dynamics · lines 1091–1121

Use stage A with constant $r$ , localized initialization, and initially perfect transmission. At every opportunity and sector, apply $L$ alternating nearest-neighbour layers before the emission decision. Layer parity alternates with opportunity and layer index.

Each two-qubit gate is

G (θ) = (R_{y} (θ_{1}) \otimes R_{y} (θ_{2})) CZ (R_{x} (θ_{3}) \otimes R_{x} (θ_{4})), R_{P} (θ) = e^{- i θ P /2},

with independent angles uniform on $[- π, π)$ . These are specified entangling gates, not Haar- $U (4)$ samples. The supplement records every angle and gate matrix. Depths are nested using the same preselected layer arrays.

Controls are identity dynamics and initial SWAP transport. The depth parameter in the new family changes actual inter-emission gates, not just initialization.

The proposed first pilot uses $K = 3$ , $L = 0, 1, 2$ , $r = 1, 1/2$ , two declared gate realizations, and horizons $1, \dots, K$ . The $K = 4$ extension is a separate command, not an executed result.

Displayed formulas in this passage

unlabeled · line 1100
$G (θ) = (R_{y} (θ_{1}) \otimes R_{y} (θ_{2})) CZ (R_{x} (θ_{3}) \otimes R_{x} (θ_{4})), R_{P} (θ) = e^{- i θ P /2},$