Measurements with time evolution

[claretgrace0801]

When using the pulse models to simulate the time evolution a state, if there are measurements being done in a circuit, the execution fails.

Could time evolution account for measurements?

A possible approach could be to collapse a state, on measurement, into a mixture (with appropraite probabilities) of all the measurement outcomes (to get a density matrix). Then continue evolution from that point on the resulting density matrix.

[BoxiLi]

It seems that this should now be possible with the new low-level interface solver.step. Similar to the discussion in qutip/qutip#1571, we should be able to evaluate the circuit up to a measurement step, perform the measurement and then start the next step until a second measurement occurs.

Another question that remains to be discussed is how we interpret the measurement:

• Do we project the state to one of the measurement results or
• we branch the simulation and keep all possible measurement results.
  In the gate-level QubitCircuit, we go with the second option by default.