Migrate `control-lowering` pass to QRef

Design

For this example:

def controlled_gate_circuit(angle):
   qp.PauliX(0) #Flip to |1> for RX to act on the second wire
   qp.ctrl(qp.RX, control = (0), control_values=(1))(angle, wires=[1])
   return qp.state()

Current Flow

The mlir generated is:

      qref.custom "PauliX"() %1 : !qref.bit
      %2 = qref.get %0[ 0] : !qref.reg<2> -> !qref.bit
      qref.ctrl(%2) ctrlvals(%true) {
        %5 = qref.get %0[ 1] : !qref.reg<2> -> !qref.bit
        %extracted = tensor.extract %arg0[] : tensor<f64>
        qref.custom "RX"(%extracted) %5 : !qref.bit
      }

Instead of this going through the convert-to-value-semantics turning into:

      %out_ctrl_qubits, %results = quantum.ctrl(%3) ctrlvals(%true) (%4) : !quantum.bit -> !quantum.bit {
      ^bb0(%arg1: !quantum.bit):
        %extracted = tensor.extract %arg0[] : tensor<f64>
        %out_qubits_0 = quantum.custom "RX"(%extracted) %arg1 : !quantum.bit
        quantum.yield %out_qubits_0 : !quantum.bit
      }

which gets folded into this in the ctrl-lowering pass

%out_qubits_0, %out_ctrl_qubits = quantum.custom "RX"(%extracted) %2 ctrls(%out_qubits) ctrlvals(%true) : !quantum.bit ctrls !quantum.bit

We want to move this process earlier in the pipeline in reference semantics as it is easier and more intuitive there.

New Flow

Now we want to go directly from the original mlir:

      qref.custom "PauliX"() %1 : !qref.bit
      %2 = qref.get %0[ 0] : !qref.reg<2> -> !qref.bit
      qref.ctrl(%2) ctrlvals(%true) {
        %5 = qref.get %0[ 1] : !qref.reg<2> -> !qref.bit
        %extracted = tensor.extract %arg0[] : tensor<f64>
        qref.custom "RX"(%extracted) %5 : !qref.bit
      }

To the Qref instructions:

%5 = qref.get %0[ 1] : !qref.reg<2> -> !qref.bit
%extracted = tensor.extract %arg0[] : tensor<f64>
qref.custom "RX"(%extracted) %5 ctrls(%2) ctrlvals(%true) : !qref.bit

Then after convert-to-value-semantics is called,

qref.custom "RX"(%extracted) %5 ctrls(%2) ctrlvals(%true) : !qref.bit

gets folded into

%out_qubits_0, %out_ctrl_qubits = quantum.custom "RX"(%extracted) %q1 ctrls(%q0) ctrlvals(%true) : !quantum.bit ctrls !quantum.bit

The test for this behaviour is in TestFlatCircuits.mlir:

    // CHECK: [[ROT:%.+]], [[ROTctrl:%.+]] = quantum.custom "some_gate"(%arg0, %arg1) [[RX]] adj ctrls([[CNOT]]#1) ctrlvals(%arg2) : !quantum.bit ctrls !quantum.bit
    qref.custom "some_gate"(%arg0, %arg1) %q0 adj ctrls (%q1) ctrlvals (%arg2) : !qref.bit ctrls !qref.bit

The idea is to call --convert-to-reference-semantics on entering the control-lowering pass, do the lowering described above, then call --convert-to-value-semantics on exit.
Then for any pass that breaks, call conver-to-value-semantics at the beginning to fix it.

Start by inspecting the control-lowering pass and the reference- and value-semantics conversion pipeline. Use the control-lowering case in TestFlatCircuits.mlir as the first test to run and trace. Done means controlled qref.custom operations are lowered before value semantics, with the expected quantum.custom output and no downstream pass regressions.