[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)

[github-actions]

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[github-actions]

This pull request has been automatically marked as stale because it has not had any activity for 30 days.

It will be closed in another 7 days if no further activity occurs. Thank you for your contribution. If you'd like to keep this open, leave any comment and the stale label will be removed.

You can always ask for help on the Mahout dev mailing list or in GitHub Discussions.