Canonicalization does not recognize extracts from different indices on the same qreg

[paul0403]

Consider the circuit X(0)-Z(1):

  %0 = quantum.alloc( 2) : !quantum.reg

  %1 = quantum.extract %0[ 0] : !quantum.reg -> !quantum.bit
  %out_qubits = quantum.custom "PauliX"() %1 : !quantum.bit
  %2 = quantum.insert %0[ 0], %out_qubits : !quantum.reg, !quantum.bit

  %3 = quantum.extract %2[ 1] : !quantum.reg -> !quantum.bit
  %out_qubits_0 = quantum.custom "PauliZ"() %3 : !quantum.bit
  %4 = quantum.insert %2[ 1], %out_qubits_0 : !quantum.reg, !quantum.bit

  quantum.dealloc %4 : !quantum.reg

After --canonicalize, the IR stays unchanged.

Proposed improvement:
Since the 0th and 1st qubits are from the same register, it should be possible to make them extract from the same SSA qreg value:

  %0 = quantum.alloc( 2) : !quantum.reg

  %1 = quantum.extract %0[ 0] : !quantum.reg -> !quantum.bit
  %out_qubits = quantum.custom "PauliX"() %1 : !quantum.bit

  %3 = quantum.extract %0[ 1] : !quantum.reg -> !quantum.bit
  %out_qubits_0 = quantum.custom "PauliZ"() %3 : !quantum.bit

  %2 = quantum.insert %0[ 0], %out_qubits : !quantum.reg, !quantum.bit
  %4 = quantum.insert %2[ 1], %out_qubits_0 : !quantum.reg, !quantum.bit

  quantum.dealloc %4 : !quantum.reg

This makes it easier to see if two qubits are from the same register.

Also, in the original version's dataflow, the 1st qubit is in the forward slice of the 0th qubit (through the in-between insert %2), but this is not the most optimal description of the circuit: the two starting qubit values on the two wires should ideally be independent dataflow-wise.

[rylanmalarchick]

I'd like to take this one. Plan: extend ExtractOp::canonicalize to cover the case where the extract index and the defining quantum.insert index are statically distinct constants. There the extract can read from the insert's source register instead, which drops the false dependency between the two wires. I'll add a lit test to CanonicalizationTest.mlir and update test_extract_insert_no_fold_static, which currently pins the old behavior. Let me know if that is the approach you had in mind.

[dime10]

Hi @rylanmalarchick, that sounds great, please go ahead :)