Conditionals prevent identifying equivalent circuits/DAGs #3164
Description
The circuit identity check does not distinguish between classical wires used as cargs and classical wires used as conditionals, and so the following two circuits are marked as non-equivalent:
>>> import qiskit as qk
>>> qr = qk.QuantumRegister(2)
>>> cr = qk.ClassicalRegister(1)
>>> qc1 = qk.QuantumCircuit(qr, cr)
>>> qc1.h(0).c_if(cr, 0)
>>> qc1.h(1).c_if(cr, 0)
>>> print(qc1)
┌───┐
q0_0: |0>─┤ H ├────────
└─┬─┘ ┌───┐
q0_1: |0>───┼────┤ H ├─
│ └─┬─┘
┌──┴──┐┌──┴──┐
c0_0: 0 ╡ = 0 ╞╡ = 0 ╞
└─────┘└─────┘
>>> qc2 = qk.QuantumCircuit(qr, cr)
>>> qc2.h(1).c_if(cr, 0)
>>> qc2.h(0).c_if(cr, 0)
>>> print(qc2)
┌───┐
q0_0: |0>────────┤ H ├─
┌───┐ └─┬─┘
q0_1: |0>─┤ H ├────┼───
└─┬─┘ │
┌──┴──┐┌──┴──┐
c0_0: 0 ╡ = 0 ╞╡ = 0 ╞
└─────┘└─────┘
>>> qc1 == qc2
False
Since both gates use c0 as a condition, and there is no gate between them which uses c0 as a carg, it should be possible to determine that the order of the two gates on c0 is not important. Ref. test.python.transpiler.test_cx_direction.TestCXDirection.test_preserves_conditions .