[FEATURE] Update the depth calculation to include branching operations with classical registers

[TheGupta2012]

Feature Description

Qiskit Version: 1.2.0

Quantum programs with branching conditions containing classical registers should be considered for depth calculations. For example, the following circuit -

In [41]: from qiskit import QuantumCircuit

In [42]: qasm_str = """
    ...: OPENQASM 2.0;
    ...: include "qelib1.inc";
    ...: qreg q[2];
    ...: creg c0[1];
    ...: creg c1[1];
    ...: h q[0];
    ...: h q[1];
    ...: measure q[0] -> c0[0];
    ...: if(c0==0) x q[1];
    ...: """

In [43]: qc = QuantumCircuit.from_qasm_str(qasm_str)

In [44]: qc.draw()
Out[44]:
      ┌───┐┌─┐
 q_0: ┤ H ├┤M├───────
      ├───┤└╥┘ ┌───┐
 q_1: ┤ H ├─╫──┤ X ├─
      └───┘ ║  └─╥─┘
            ║ ┌──╨──┐
c0: 1/══════╩═╡ 0x0 ╞
            0 └─────┘
c1: 1/═══════════════

In [45]: qc.depth()
Out[45]: 3

has a depth of 3 whereas pyqasm gives a depth of 2 -

In [50]: import pyqasm

In [51]: qasm_str = """
    ...: OPENQASM 2.0;
    ...: include "qelib1.inc";
    ...: qreg q[2];
    ...: creg c0[1];
    ...: creg c1[1];
    ...: h q[0];
    ...: h q[1];
    ...: measure q[0] -> c0[0];
    ...: if(c0==0) x q[1];
    ...: """

In [52]: pyqasm.load(qasm_str).depth()
Out[52]: 2

This is because the classical register depth is not considered during the calculation of qubit depths inside the if block. The depth of c0_0 is 2 when it is used to condition the X gate on q_1.

Implementation (Optional)

• While unrolling the branching conditions, we look at whether the condition contains a set of classical register bits or not. We need to update the depth of all these classical bits to the max depth of this set of bits, eg. -

In [75]: qc.draw(cregbundle=False)
Out[75]:
     ┌─┐     ┌─┐┌─┐
q_0: ┤M├──■──┤M├┤M├─────
     └╥┘┌─┴─┐└╥┘└╥┘
q_1: ─╫─┤ X ├─╫──╫──────
      ║ └───┘ ║  ║ ┌───┐
q_2: ─╫───────╫──╫─┤ H ├
      ║       ║  ║ └─╥─┘
c_0: ═╩═══════╬══╬═══╬══
              ║  ║   ║
c_1: ═════════╩══╬═══╬══
                 ║   ║
c_2: ════════════╩═══■══

c_3: ═══════════════════


In [76]: qc.depth()
Out[76]: 5

Here, if c_0, c_1 and c_2 were used in a branching statement, the depth of each bit would be set to 4 as max depth of bits i.e. c_2 is 4. In above example, since c_2 is used for the classically conditioned H gate, the depth of the circuit is supposed to be 5 but is coming out as 4 with pyqasm -

In [82]: import pyqasm

In [83]: qasm_str = 'OPENQASM 3.0;\ninclude "stdgates.inc";\nbit[4] c;\nqubit[3] q;\nc[0] = m
    ...: easure q[0];\ncx q[0], q[1];\nc[1] = measure q[0];\nc[2] = measure q[0];\nif (c[2])
    ...: {\n  h q[2];\n}\n'

In [84]: pyqasm.load(qasm_str).depth()
Out[84]: 4

• It is not entirely clear how this "max depth of involved classical bits" will be trickled down to the qubits of the if block. A brute force approach is used inside the qbraid sdk's depth function but might not work for a recursive approach used in QasmVisitor.