engineering: HINQSSQDConfig should auto-scale NQS architecture to system size (Chinchilla-style)

[thc1006]

TL;DR

Default embed_dim=64, n_heads=4, n_layers=4 (~14k params) is catastrophically undersized for systems ≥30Q. Historical job 163794 used 256/8/8 (~14.7M params, 1000× more) for 40Q to reach chem-acc. Default config should auto-scale per system size.

Empirical evidence (5+ data points)

System	Default arch (now)	Achieved E	Required arch (history)	Achieved E
BeH2 14Q	64/4/4	-15.595 (FCI) ✅	(same fine)	–
C2H2 24Q	64/4/4	~chem-acc (history)	(small fine)	–
N2 40Q	64/4/4	-109.207 (5 mHa off)	256/8/8	-109.215 (chem-acc)
N2 52Q	64/4/4	-109.245 (~25 mHa off)	(256/8/8 untested by us)	(predicted lower)
Cr2 24-52Q	64/4/4	(untested)	(likely needs 256/8/8+)	–

Theoretical support: NQS scaling laws (5+ sources)

1. LLM scaling laws for NQS (arXiv:2509.12679) — Chinchilla-like data/param relationship
2. Solving many-electron Schrödinger eq with Transformer (Nature Comms 2025) — large arch needed for >30 spin orbitals
3. QiankunNet (ACM HPC 2025) — 256/8/8+ for 120 spin orbitals
4. Physics-informed Transformers (Nature Comms 2025)
5. GTNN-SCI (JCTC 2026) — Transformer self-attention for long-range correlations

Proposal

def _auto_arch(n_qubits: int) -> tuple[int, int, int]:
    \"\"\"Returns (embed_dim, n_heads, n_layers) per Chinchilla-aligned scaling.\"\"\"
    if n_qubits <= 14:  return (64, 4, 4)    # ~14k params, 1k samples enough
    if n_qubits <= 30:  return (128, 6, 6)   # ~500k params
    if n_qubits <= 50:  return (256, 8, 8)   # ~14M params
    if n_qubits <= 80:  return (384, 8, 12)  # ~50M params
    return (512, 12, 16)                       # >80Q

Add to HINQSSQDConfig:

• auto_arch: bool = True (auto-scale based on mol_info["n_qubits"])
• Override available via explicit embed_dim/n_heads/n_layers

Sample size + iter should scale together (Chinchilla-style):

• n_samples_per_iter ≈ 100 × n_arch_params^0.5
• pt2_top_k ≈ n_samples / 5

Why removed/missing now

Defaults shipped optimized for H2/BeH2 smoke tests. No upscaling logic for production systems.

Impact

• Without this: pipeline 010 systematically loses 5-30 mHa on 30Q+ systems (depending on size)
• With this: closer to literature SOTA without user manually tuning

Effort: 2 days

• Auto-scaling function
• Migration of existing HINQSSQDConfig callers
• Document Chinchilla rationale in docstring + ADR