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In the paper by Stamatopoulos et al., the authors say that it is possible to load a distribution on a three qubit state to obtain:

In Qiskit finance this is performed using the uncertainty model function. My question is, how do you encode random numbers on qubit states?

Later is their paper they report that you can use controlled-Y rotations to load a random distribution, this way:

but I don't know how they pick the angle for the controlled rotation in order to obtain the desired number.

Maybe you already know this but I just want to point out that it seems to me that the "Loading random distribution" part of the circuit is coming from the RealAmplitude function: https://qiskit.org/documentation/stubs/qiskit.circuit.library.RealAmplitudes.html Which only generates quantum states with real amplitudes. The question whether this can prepare an arbitrary quantum state with real amplitudes is a good question, see this other question here related to that: https://quantumcomputing.stackexchange.com/questions/14032/preparing-arbitrary-two-and-multi-qubit-states-with-real-amplitudes

– KAJ226 – 2020-11-02T18:26:27.153