While I don't have the expertise to know if it's right or wrong, I find Martin Vesely's answer to this question the most intriguing of the bunch:
Martin Vesely: "A measurement leads to collapse of a wave function describing qubits, they get to one particular state and remain in that state. To do reverse operation you have to repeat measurement many times. Based on resulting probability distribution you can reconstruct the state of qubits and prepare it again.
The reconstruction of probability distribution is done with quantum tomography.
Arbitrary state can be prepared with method in this paper: Transformation of quantum states using uniformly controlled rotations (https://arxiv.org/abs/quant-ph/0407010)."
Martin Vesely: "A measurement leads to collapse of a wave function describing qubits, they get to one particular state and remain in that state. To do reverse operation you have to repeat measurement many times. Based on resulting probability distribution you can reconstruct the state of qubits and prepare it again.
The reconstruction of probability distribution is done with quantum tomography.
Arbitrary state can be prepared with method in this paper: Transformation of quantum states using uniformly controlled rotations (https://arxiv.org/abs/quant-ph/0407010)."
Comments?