Close to your suggestion #2. There are electronics running software, plus a set of entangled qubits whose output probabilities are influenced by the machinery which the above mentioned software controls, and the software also interprets the output and decides when a sufficiently accurate answer has been found.

The particular configuration that the software defines for the controlling machinery (and how it sets up the qubit entanglement) is meant to implement the chosen quantum computing algorithms and to encode the chosen inputs.

For example, for a given instance of Shor's algorithm and for one given public key, you'd first calculate how to encode this configuration into the qubits, then load it up, to then run it over and over and interpret all of the outputs to look for a useful answer.

I've got no idea how the qubit programming is practically implemented.