[QDP] [feature] Pr4 kronecker fwt

[aloha1357]

Related Issues

related #1385

Changes

• Bug fix
• New feature
• Refactoring
• Documentation
• Test
• CI/CD pipeline
• Other

Why

For large qubit counts ($N > 12$), the standard Fast Walsh-Hadamard Transform (FWT) algorithm becomes severely bound by Global Memory bandwidth. The FWT requires $\log_2(N)$ stages of in-place memory access across the entire $2^N$ state vector, which causes cache thrashing and massive DRAM roundtrips.

To overcome this, we mathematically restructure the FWT into a Kronecker Product Decomposition: $H_n = H_{n/2} \otimes H_{n/2}$. This transforms the sparse, memory-bound butterfly operations into standard, dense matrix multiplications (GEMM) using a Blocked architecture.

While the implicit Hadamard engine is not yet introduced (coming in PR 5), this PR establishes the structural memory layout, allocation, and transpose logic necessary for the decomposition.

How

• Kronecker Decomposition Logic: Updated launch_iqp_encode_tc to dynamically split the state vector into two dimensions ($n_1$ and $n_2$).
• Intermediate Allocations: Added temporary memory allocations (d_temp_real, d_temp_imag) to store the transposed matrix blocks during the 4-step blocked algorithm.
• Naive GEMM Placeholder: Introduced naive_implicit_hadamard_gemm_kernel as a fallback structural placeholder. It calculates the Hadamard values on-the-fly ($\text{popc}(k \ &\ i)$) and executes the block multiplication $Z = X \cdot H_{n2}$.
• Matrix Layout Transform: Leveraged the iqp_tc_batch_transpose_kernel (introduced in PR 2) to transpose the blocks between the two GEMM stages, achieving the mathematical equivalent of the $O(N \log N)$ FWT through dense GEMMs.

Checklist

• Added or updated unit tests for all changes (Verified passing against existing CI test suite)
• Added or updated documentation for all changes (Added explanatory inline comments for PR)