New commutation passes

[godott]

Summary

1. A commutation analysis pass and a commutation transformation are added.
2. Test cases for commutation passes are added.
3. An example is added.

Details and comments

The commutation analysis pass figures out the commutation relations for gates in DAGCircuit, all the 1&2 qubit gates are supported now.

Here are some examples:

1. Test all the gates

Circuit:

DAG before:

DAG after:

2. An example of Quantum Instantaneous Polynomial Time(all gates commute)

Circuit:

DAG_before:

DAG_after:

3. Circuits produced by Jordan-Wigner transformation

Circuit:

DAG before:

DAG after:

[jaygambetta]

is nice that we show the dag before and after but can we also show the circuit. It would also be nice to have the circuit in the example

[godott]

is nice that we show the dag before and after but can we also show the circuit. It would also be nice to have the circuit in the example

For that, I think a DAG_to_circuit() method is needed. Right now, we have functions to convert DAG to openQASM and convert openQASM to QuantumCircuit, but the two functions don't work together.

[ajavadia]

is nice that we show the dag before and after but can we also show the circuit. It would also be nice to have the circuit in the example

For that, I think a DAG_to_circuit() method is needed. Right now, we have functions to convert DAG to openQASM and convert openQASM to QuantumCircuit, but the two functions don't work together.

you can use

from qiskit.converters import dag_to_circuit
circuit = dag_to_circuit(dag)
circuit.draw()

but i don't think drawing the circuit shows much. this pass modifies DAG edges, to make them more amenable to scheduling, optimization, etc. The circuit drawer may just move some boxes around.

[jaygambetta]

@ajavadia and @godott i have already done that i push a pr into your branch dealing with some linting.