multiplexer

Call MultiplexerAlgorithm().run(Psi=psi, target_qubits=n, target_error=1e-6) with a nonzero complex vector. The algorithm normalizes and pads the vector, builds a recursive probability tree of RY/CRY/MCRY gates, applies basis-selective phase gates, and returns the prepared state with a total error.

Multiplexer state preparation is a recursive construction that splits probability mass down a binary tree using controlled RY rotations, then loads complex phases onto individual basis states with mixed-control phase gates. It prepares arbitrary n-qubit states from elementary gates.

Correct magnitudes with wrong phases usually indicate a phase-loading issue: check the basis-index bit strings, the last-wire target flip for zero bits, and the mixed control values. Also verify the single internal bit reversal was applied exactly once before building the schedule.

Yes, vectors shorter than 2**target_qubits are trailing-zero padded after normalization, with a RuntimeWarning. Vectors longer than the target Hilbert-space dimension raise a ValueError, and the norm must exceed 1e-12.

The implementation uses dense matrix simulation, so memory and time grow exponentially with qubit count, limiting practical register sizes. It also emits one gate per nonzero tree node and phase, producing deep circuits for large registers.

The error is a global-phase-invariant Euclidean distance: the overlap between target and prepared state is computed, the prepared state is rotated by the conjugate unit-modulus phase factor when the overlap exceeds 1e-12, and the norm of the difference is reported.