Revise SSA transformation for OpenQASM 3 variables

[mhillenbrand]

Description

qss-compiler expresses variable references and assignments in OpenQASM 3 source code as MLIR operations that directly reflect these references and assignments in the initial MLIR -- that is, the initial MLIR uses memory semantics for variables. For later optimization, it is beneficial to resolve these operations with memory semantics such that the use of a variable directly uses the SSA value that has been assigned to the variable at that point.

Currently, the compiler uses the pass VariableElimination towards that goal. That pass takes a detour through the affine dialect and its scalar replacement pass. As a downside, that approach currently cannot resolve variable memory semantics around control flow.

We should revise the VariableElimination pass to fully resolve the OpenQASM 3 variable operations into SSA form.

Tasks

• Identify test cases first.
• Revise the VariableElimination pass.

Acceptance Criteria

• New test cases check corner cases.

Proposal

• The transformation could be integrated into quirgen. Yet, it should remain its own pass to facilitate debugging and unit testing.
• Consider Marc M. Brandis, Hanspeter Mössenböck

Notes

• The paper Marc M. Brandis, Hanspeter Mössenböck: Single-pass generation of static single-assignment form for structured languages describes an algorithm for transforming structured control flow into SSA form in a single pass and may serve as a starting point. The algorithm generates "classical SSA" with phi nodes, while MLIR has block and region arguments (and yield values), so there's some transformation required.