Add dynamic qreg alloc for cross-qreg gate decomposition

[rniczh]

Context:

Currently, the decomposition pass assumes all qubits involved in a gate operation come from the same quantum register (qreg). However, gates may operate on qubits from different registers, which causes decomposition failures or incorrect behaviour!

Description of the Change:

This PR introduces dynamic qreg allocation logic that automatically created when qubits from different qreg are involved in a gate operation. When such cross-qreg operations are detected:

1. Allocates a new unified quantum register with sufficient capacity
2. Inserts all involved qubits into the new register with sequential indices (0, 1, 2, ...)
3. After the decomposed ops are finished, extracts the results to qubits and deallocates the temporary register. It will run into an error if we deallocate this tmp register

The implementation adds a needAllocQreg flag to the OpSignature struct and implements the allocation logic in prepareCallOperands() and prepareCallResultForQreg()

Exampe:

%reg1 = quantum.alloc(1)
%reg2 = quantum.alloc(1) 
%q1 = quantum.extract %reg1[0]
%q2 = quantum.extract %reg2[0]
%result:2 = quantum.custom "CNOT"() %q1, %q2 

decmopse to

%reg1 = quantum.alloc(1)
%reg2 = quantum.alloc(1)
%q1 = quantum.extract %reg1[0] 
%q2 = quantum.extract %reg2[0]

// new qreg
%tmp = quantum.alloc(2) 
%tmp = quantum.insert %tmp[0], %q1
%tmp = quantum.insert %tmp[1], %q2

// Decomposition happens on tmp qreg:
call @cnot_decomp(%tmp, [0,1]) -> %result_qreg

// Results extracted and cleaned up:
%result1 = quantum.extract %result_qreg[0]
%result2 = quantum.extract %result_qreg[1] 
quantum.dealloc %result_qreg

Benefits:

Possible Drawbacks:

There is a underlying issue if we deallocate the tmp qreg, for running the circuit on lightning, I removed these line. I don't think it's the right way to resolve them.

catalyst/mlir/lib/Quantum/Transforms/DecomposeLoweringPatterns.cpp

Lines 284 to 287 in 2e5d350

	// FIXME: Dealloc should be fine, but it will cause the error in lightning now
	// if (signature.needAllocQreg) {
	// rewriter.create<quantum::DeallocOp>(callOp.getLoc(), qreg);
	// }

Related GitHub Issues:
[sc-100312]

[github-actions]

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 97.48%. Comparing base (64015c1) to head (2e5d350).
⚠️ Report is 2 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #2074   +/-   ##
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  Coverage   97.48%   97.48%           
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  Files          91       91           
  Lines       10594    10594           
  Branches      990      990           
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  Hits        10328    10328           
  Misses        211      211           
  Partials       55       55           

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