add qubits-truncate optimization

[hhorii]

Summary

This PR truncates qubits in statevector to resolve #147

Details and comments

If some qubits are not used, qasm simulator does not use them in its qubitvector with this change.

• Implement a new circuit optimization
• Implement test cases

[chriseclectic]

@hhorii why did you move the optimization passes out of the controller? It makes the most sense to me there as they are roughly equivalent to transpilation passes in terra and should be able to be applied to circuits regardless of which state they will be executed on (though the state they are intended to be being executed on can obviously effect the optimizations). I think how you had it in your last PR was fine.

With this PR I would say rather than check every op type for remapping you should only specify the op types that need a special case for remapping (like snapshots, multiplexer, multimatrix). For every other instruction all you need to do is remap their qubits parameters and as long as you don't change the relative order of the lists it will be consistent.

Multiplexer and multimatrix are special cases becuase you also need to remap the op.regs fields, and snapshot is a special base where you can only remap some snapshots (the ones that use qubit arguements like probabilities and expectation values), but not others (like statevector, stabilizer). To make it a bit simpler I would say to just not allow remapping for all snapshots for this first implementation.

[hhorii]

OK. I used think that this optimization should be applied only to Statevector::State. Checking a State type in AER::CircuitOptimization is not a good way, so I moved optimization list from Controller to State. Because this my assumption is wrong, I will roll this back.

[chriseclectic]

It will be useful to apply for any state type used in QasmSimulator (like extended stabilizer, stabilizer, and especially density matrix in the future). The point of it is that (except for snapshots) the QasmSimulator only uses the state type to simulate outcomes of measurements, and those measurement outcomes don't change by this remapping of qubits.

[chriseclectic]

Looks good @hhorii, thanks for getting this done quickly!

[ishapoval]

@hhorii The truncation of idle qubits works as expected if I use the execute wrapper, but if I go for transpile/assemble/run chain with seemingly all other parameters being equal I get a bunch of empty results

{'data': {},
'meas_level': <MeasLevel.CLASSIFIED: 2>,
'seed_simulator': 0,
'shots': 0,
'status': 'EMPTY',
'success': False,
'time_taken': 0.0}

from the QasmSimulator with the overall status of

'ERROR: QasmSimulator: Insufficient memory for 65-qubit circuit using "statevector" method. You could try using the "matrix_product_state" or "extended_stabilizer" method instead. '

Do I have to somehow enable fusion explicitly (if truncation is part of it) in the transpile/assemble/run chain?