physics-guided-generative-optimization - SKILL.md Agent Skill

name: physics-guided-generative-optimization description: Generate-and-evaluate loop for quantum circuit optimization combining conditional diffusion models, physics-informed neural networks, and graph neural networks. Use when optimizing Trotter-Suzuki decompositions, designing quantum circuits with generative models, or applying physics-guided neural optimization to NISQ compilation. Triggered by: generative quantum optimization, Trotter Suzuki decomposition, PINN feedback quantum, diffusion model circuit, NISQ compilation.

Physics-Guided Generative Optimization

Description

Generate-and-evaluate framework for quantum circuit optimization using:

Conditional diffusion model for strategy proposal
Physics-informed neural network (PINN) for fidelity feedback
Graph neural network for commutator structure encoding

Activation Keywords

generative quantum optimization
Trotter Suzuki decomposition
PINN feedback quantum
diffusion model circuit
NISQ compilation
physics-guided optimization

Architecture

Components

Generator: Conditional diffusion model proposes term grouping, product formula order, timestep allocation
Evaluator: PINN supplies differentiable fidelity feedback
Encoder: GNN encodes Hamiltonian commutator structure
Trainer: REINFORCE + Pareto tracker for hybrid discrete-continuous space

Training Loop

for step in training:
    # 1. Generate strategy
    strategy = diffusion_model.sample(condition=hamiltonian)
    
    # 2. Evaluate fidelity
    fidelity = pinn.evaluate(strategy)
    
    # 3. Compute reward
    reward = fidelity - lambda * circuit_depth
    
    # 4. Update via REINFORCE
    diffusion_model.update(reward)
    
    # 5. Track Pareto frontier
    pareto_tracker.update(fidelity, depth)

Key Results

TFIM benchmark: 85.6% fidelity at 21.8% circuit depth vs 4th order Qiskit
Equal depth: 0.9994 fidelity after fine-tuning
19.2% CNOT count vs baseline

Configuration Guidance

CFG (Classifier-Free Guidance) must be tuned jointly with compute budget
Module contributions depend on training recipe and guidance hyperparameters
Discrete grouping and order require REINFORCE (not gradient descent)

Error Handling

Monitor training stability across hybrid spaces
Validate commutator structure encoding accuracy
Track Pareto frontier for fidelity-cost tradeoff

References

Paper: arXiv:2605.13268 (WenBin Yan, 2026-05-13)
Applicable to: TFIM, Heisenberg, Hubbard models