🧮 MLIR - Decide and document classical result semantics (SSA vs memory via memref)

[burgholzer]

Background

Frontends like OpenQASM 3, Qiskit, or our own MQT Core IR allow both scalar captures (bit c = measure q;) and writes into bit arrays (c[0] = measure q[0];). MLIR favors SSA values, while QIR and frontends often assume reference/memory semantics for classical bits.

Problem

We need a consistent representation across MQTRef and MQTOpt that enables import, optimization, classical control, and QIR lowering without losing the intended number of observable outputs.
A quantum program requesting a classical register of size N will expect (at least) N classical values to be available.

Proposal:

• Default: measure returns i1 (SSA), as it does at the moment. When a classical register is needed (because it is part of the input program), store the result into a memref<?xi1> at the appropriate index. This keeps MQTOpt value-semantics-friendly and uses MLIR-native memref for storage.
• Alternative: A memory-writing measure form (measure %q, %mem, %idx) for direct stores where desirable (optional extension).

Examples:

• Scalar SSA result

  %c = mqtref.measure %q : !mqtref.qubit -> i1

• Store into classical register

  %cReg = memref.alloc(%n) : memref<?xi1>
  memref.store %c, %cReg[%i] : memref<?xi1>

• Load from classical register for control flow

  %cond = memref.load %cReg[%i] : memref<?xi1>
  scf.if %cond { /* ... */ }

Acceptance criteria:

• Decision note committed in docs (e.g., docs/mlir.md) detailing the rationale behind the decision being made here
• QuantumComputation with classical registers can be faithfully mapped to MLIR

[DRovara]

Just as a quick note: I like the proposed "default" solution here, as it:
(1) does not increase the complexity of transformation passes because it does not introduce new operations/concepts
(2) does not lock us into a specific approach. If we come from another input representation that does not have classical registers, we do not need to use memref