[QDP] [feature] Pr5 implicit hadamard engine

[aloha1357]

Related Issues

related #1385

Changes

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

Why

As established in the previous Kronecker Decomposition PR, a significant bottleneck in processing high-qubit circuits ($N \ge 14$) is memory. A traditional $O(4^N)$ matrix representation for the full Dense Hadamard transform completely exhausts modern GPU VRAM limits (causing Out-Of-Memory errors).

Even with the Kronecker Decomposition splitting the matrix into smaller blocks, generating and storing the explicit dense $H$ matrices in memory before applying Tensor Core operations is highly inefficient.

We need a way to perform Dense Matrix Multiplications (GEMM) on the Tensor Cores without ever storing the Hadamard Matrix in Global Memory.

How

This PR introduces the Matrix-Free Implicit Hadamard Ozaki Engine.

• Implicit Matrix Generation: The ImplicitHadamardOzakiEngine leverages the structural properties of the Hadamard matrix ($h_{i,j} = (-1)^{\text{popc}(i & j)}$) to calculate the matrix elements on-the-fly directly inside Shared Memory.
• Ozaki Multi-pass Tensor Core Execution: Using the Ozaki INT8 scheme, we utilize the .m16n8k32.s8 Tensor Core instructions to perform the GEMM natively in hardware. Because the Hadamard values are always $\pm 1$, we experience absolutely zero quantization error despite using the INT8 pipeline.
• Removed Fallback: Replaced the naive_implicit_hadamard_gemm_kernel placeholder from PR 4 with the actual calls to engine.execute_implicit_hadamard.
• Build System Fix: Updated build.rs to drop the unsupported sm_75 (Turing) target fallback, as this specific Tensor Core instruction explicitly requires sm_80 (Ampere) or higher.

Benchmark Results

Environment: Dev Machine (NVIDIA GeForce RTX 4060 Laptop GPU)
Configuration: Batch size 64, 30 iterations, GPU-vs-GPU only (no PyTorch reference)
Script: qdp/qdp-python/benchmark/benchmark_pr5.py
Measured: 2026-06-10
Branch: pr5-implicit-hadamard-engine (ba0376a4f)

Encoding path options (--path)

Value	Description
fwt	engine.encode(..., "iqp") — standard FWT dispatch
tc	engine.encode_batch_tc(...) — Ozaki Kronecker Tensor Core path
both	Run both paths and print FWT/TC speedup

FWT vs Ozaki TC (after PR5)

Qubits	Dim	FWT (ms)	TC (ms)	Speedup (FWT/TC)	Notes
8	256	0.188	0.142	1.33x	Fused shared-memory TC path
10	1024	0.312	0.339	0.92x	Within noise
12	4096	0.821	0.833	0.99x	Parity (fused path)
14	16384	3.060	15.870	0.19x	Kronecker TC-GEMM scaffold
16	65536	21.925	70.723	0.31x	Kronecker TC-GEMM scaffold

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)