Clarify optimization objective type

[ajgpitch]

When reviewing #51 it became apparent that trying to determine the type of optimization, state transfer, gate synth etc., is a little challenging due to the difficulty in qutip of distinguishing between a density matrix and unitary operator (gate).

We should consider forcing the user to specify whether objective is state transfer or gate synth and check inputs (initial, target) accordingly. That is:

• state_transfer: should be ket or dm
• gate_synthesis: should be unitary or CPT map (hopefully can distinguish here to choose correct solver).

[pmenczel]

Just to clarify: it is already possible for the user to specify "state transfer" or "gate synthesis".

If nothing is specified, the code tries to determine the type of problem automatically. It has to determine if the initial and target state are unitaries or density matrices. To do so, the code checks whether the trace of both initial and target state are one. I find it hard to imagine a situation where that could go wrong, in particular since the initial unitary is going to be the identity in most cases. I therefore have doubts about forcing the user to always specify the problem type.

Something I just noticed, though, is that this check "unitary or dm" seems to be only performed for open-system evolution. Since the two problem types should use different fidelity functions also in closed systems (I think), there is probably something wrong somewhere...