= Geometric quantum state synthesis by adjacent rotations
{title2=$R_{jk}(\beta)|j\rangle=\cos\beta|j\rangle+\sin\beta|k\rangle$}
On a connected transition chain, independently selected resonant pulses realize embedded two-level rotations with tunable angle and phase. Eliminate target amplitudes from one end of the chain using complex <Givens rotations>, and invert those rotations to prepare the target from a basis state. The pulse angles come from amplitude ratios and the phases from relative complex arguments. Spectator components are unchanged by each embedded rotation. Work in the <interaction picture> and compensate the known drift phases at the chosen final time when the target is specified in the laboratory frame.
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