Qualtran to QIR conversion

[skushnir123]

This is an issue to track progress on the Qualtran to QIR Compiler.

The primary motivation for converting Qualtran circuits to QIR is to:
Enhance Interoperability: QIR-compatible Qualtran circuits can be seamlessly integrated with a wider range of quantum computing frameworks, toolchains, and services.

Facilitate Resource Estimation: Resource estimation tools, such as those available on Microsoft Azure, often accept QIR as input. Converting Qualtran circuits to QIR allows us to leverage these tools to reproduce and verify the resource estimates (e.g., runtime, gate counts) reported in research papers.

It is unclear how we will move forward with this project at the moment given the following issues we've faced with PyQIR. For more details, take a look at the following github issues: Issue #1, Issue #2, Issue #3.

Example notebook using PyQIR with Microsoft Resource Estimation: Colab

Example Notebook using open-source resource estimator: Notebook

[anurudhp]

This may be of interest: https://docs.pennylane.ai/projects/catalyst/en/latest/modules/mlir.html
It is an LLVM-MLIR based compiler, which then lowers to QIR (LLVM). MLIR is closer to qualtran in representation, with more high-level constructs, so might be easier to convert to.

I've worked on an MLIR-based quantum IR in the past, and am happy to chat more if it helps!