✨ Integrate registers

[denialhaag]

Description

After #1542 has added support for linear tensors, this PR integrates registers deeper into our infrastructure. Furthermore, it updates our QIR code to use the dynamic allocations introduced in qir-alliance/qir-spec#60.

Some known shortcomings at this point:

• Vast majority of failing tests are due to the conversion between QCO and Jeff. The problem is that Jeff's QuregType does not have any information about the register size. I will create an issue and/or follow up on Slack.
• The remaining (15 or so) failing tests either have an easy solution that I already have in mind, or I haven't looked at them yet. That said, I don't expect bigger issues at this point.
• Existing docstrings are outdated or missing, especially for the conversion from QC to QIR where a lot had changed.
• At the moment, the QIR code do not support static qubits. I will look into this once ✨ Improve Static Qubit Handling #1569 is merged.
• There will probably be a good amount of linter issues.

Checklist

• The pull request only contains commits that are focused and relevant to this change.
• I have added appropriate tests that cover the new/changed functionality.
• I have updated the documentation to reflect these changes.
• I have added entries to the changelog for any noteworthy additions, changes, fixes, or removals.
• I have added migration instructions to the upgrade guide (if needed).
• The changes follow the project's style guidelines and introduce no new warnings.
• The changes are fully tested and pass the CI checks.
• I have reviewed my own code changes.

[github-actions]

Cpp-Linter Report ⚠️

Some files did not pass the configured checks!

clang-tidy (v22.1.3) reports: 13 concern(s)

• mlir/lib/Conversion/QCOToQC/QCOToQC.cpp:68:25: warning: [misc-include-cleaner]

  no header providing "mlir::RankedTensorType" is directly included

     25 |     addConversion([ctx](RankedTensorType type) -> Type {
        |                         ^

• mlir/lib/Conversion/QCOToQC/QCOToQC.cpp:71:16: warning: [misc-include-cleaner]

  no header providing "mlir::MemRefType" is directly included

     71 |         return MemRefType::get({ShapedType::kDynamic}, qc::QubitType::get(ctx));
        |                ^

• mlir/lib/Conversion/QCToQCO/QCToQCO.cpp:167:21: warning: [misc-include-cleaner]

  no header providing "mlir::ShapedType" is directly included

     26 |     if (shape[0] == ShapedType::kDynamic) {
        |                     ^

• mlir/lib/Conversion/QCToQIR/QCToQIR.cpp:236:21: warning: [misc-include-cleaner]

  no header providing "mlir::ShapedType" is directly included

     36 |     if (shape[0] == ShapedType::kDynamic) {
        |                     ^

• mlir/lib/Conversion/QCToQIR/QCToQIR.cpp:433:28: warning: [misc-unused-parameters]

  parameter 'op' is unused

    433 |   matchAndRewrite(StaticOp op, OpAdaptor adaptor,
        |                            ^~
        |                             /*op*/

• mlir/lib/Conversion/QCToQIR/QCToQIR.cpp:433:42: warning: [misc-unused-parameters]

  parameter 'adaptor' is unused

    433 |   matchAndRewrite(StaticOp op, OpAdaptor adaptor,
        |                                          ^~~~~~~
        |                                           /*adaptor*/

• mlir/lib/Conversion/QCToQIR/QCToQIR.cpp:434:46: warning: [misc-unused-parameters]

  parameter 'rewriter' is unused

    434 |                   ConversionPatternRewriter& rewriter) const override {
        |                                              ^~~~~~~~
        |                                               /*rewriter*/

• mlir/lib/Dialect/QC/Builder/QCProgramBuilder.cpp:99:57: warning: [misc-unused-parameters]

  parameter 'name' is unused

     99 |                                      const std::string& name) {
        |                                                         ^~~~
        |                                                          /*name*/

• mlir/lib/Dialect/QCO/Builder/QCOProgramBuilder.cpp:105:58: warning: [misc-unused-parameters]

  parameter 'name' is unused

    105 |                                       const std::string& name) {
        |                                                          ^~~~
        |                                                           /*name*/

• mlir/lib/Dialect/QIR/Builder/QIRProgramBuilder.cpp:103:26: warning: [readability-convert-member-functions-to-static]

  method 'staticQubit' can be made static

    103 | Value QIRProgramBuilder::staticQubit(const int64_t index) {
        |                          ^

• mlir/lib/Dialect/QIR/Builder/QIRProgramBuilder.cpp:103:52: warning: [misc-unused-parameters]

  parameter 'index' is unused

    103 | Value QIRProgramBuilder::staticQubit(const int64_t index) {
        |                                                    ^~~~~
        |                                                     /*index*/

• mlir/lib/Dialect/QTensor/IR/Operations/AllocOp.cpp:43:8: warning: [clang-analyzer-deadcode.DeadStores]

  Value stored to 'resultSize' during its initialization is never read

     43 |   auto resultSize = resultType.getShape()[0];
        |        ^~~~~~~~~~   ~~~~~~~~~~~~~~~~~~~~~~~~
  /home/runner/work/core/core/mlir/lib/Dialect/QTensor/IR/Operations/AllocOp.cpp:43:8: note: Value stored to 'resultSize' during its initialization is never read
     43 |   auto resultSize = resultType.getShape()[0];
        |        ^~~~~~~~~~   ~~~~~~~~~~~~~~~~~~~~~~~~

• mlir/lib/Dialect/QTensor/IR/Operations/InsertOp.cpp:31:5: warning: [readability-else-after-return]

  do not use 'else' after 'return'

     31 |   } else if (llvm::isa<InsertOp>(definingOp)) {
        |     ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
     32 |     auto nestedInsertOp = llvm::cast<InsertOp>(definingOp);
        |     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
     33 |     return findExtractOp(nestedInsertOp);
        |     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
     34 |   }
        |   ~

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