Equivilance checking for gate scheduler.

[weinbe58]

Currently in order to check of gates can be merged in the scheduler we need to check the equivalence of the gate parameters not including the input qubit:

def same_id_checker(ssa1: ir.SSAValue, ssa2: ir.SSAValue):
    return ssa1 is ssa2

def check_equiv_args(
    args1: Iterable[ir.SSAValue],
    args2: Iterable[ir.SSAValue],
    checker: Callable[[ir.SSAValue, ir.SSAValue], bool] = same_id_checker,
):
    try:
        return all(checker(ssa1, ssa2) for ssa1, ssa2 in zip(args1, args2, strict=True))
    except ValueError:
        return False


def can_merge(stmt1: ir.Statement, stmt2: ir.Statement):
    from bloqade.qasm2.dialects import uop, parallel

    match stmt1, stmt2:
        case (
            (parallel.UGate(), parallel.UGate())
            | (parallel.UGate(), uop.UGate())
            | (uop.UGate(), parallel.UGate())
            | (uop.UGate(), parallel.UGate())
            | (uop.UGate(), parallel.UGate())
            | (parallel.RZ(), parallel.RZ())
        ):
            return check_equiv_args(stmt1.args[1:], stmt2.args[1:])
        case (
            (parallel.CZ(), parallel.CZ())
            | (parallel.CZ, uop.CZ)
            | (uop.CZ, parallel.CZ)
        ):
            return True

Note that the current implementation misses cases where the parameters could point to constant statements that have equivilant values so this code would not be able to merge something like:

qasm2.u(q[0], 0.1, 0.2, 0.3)
qasm2.u(q[1], 0.1, 0.2, 0.3)

Because the constant values have separate SSA values.

[Roger-luo]

this needs GVN (global value numbering) crossref QuEraComputing/kirin#239