A declared control set and an exact pulse sequence

The constant-pulse version is the Hamiltonian

on each pair, as a special case.

-energy convention. A memory Hamiltonian ${\Omega }_c{N}_c$, ${\Omega }_c>0$, may be specified, with degenerate computational register levels. The displayed controls are in its interaction picture. Their laboratory-frame version contains the corresponding number-dependent phase modulation. The required frequency range grows with $K{\Omega }_c$; it is not hidden in the envelope derivative bound. No field packet Hamiltonian is identified with ${\Omega }_c{N}_h$, and extraction is not asserted to conserve the memory's free energy without work exchange.