# Physics Guided Generative Optimization for Trotter Suzuki Decomposition

arXiv: https://arxiv.org/abs/2605.13268 · HTML: https://mlsanity.com/paper/2605.13268/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 15 of its 47 references that are in the map.
- First posted on arXiv 13 May 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 15 of 15)

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- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Quantum Graph Neural Networks](https://mlsanity.com/paper/1909.12264/) (2019)
- [Synthesis of discrete-continuous quantum circuits with multimodal diffusion models](https://mlsanity.com/paper/2506.01666/) (2025)
- [Tetris: Re-architecting Convolutional Neural Network Computation for Machine Learning Accelerators](https://mlsanity.com/paper/1811.06841/) (2018)
- [PHOENIX: Pauli-Based High-Level Optimization Engine for Instruction Execution on NISQ Devices](https://mlsanity.com/paper/2504.03529/) (2025)

## Abstract (arXiv)

Trotter Suzuki product formulas are the standard route to Hamiltonian evolution on noisy intermediate-scale quantum (NISQ) hardware, but their accuracy depends on three coupled choices: term grouping, product-formula order, and time-step allocation. Grouping and order are discrete, which makes direct gradient optimization infeasible and forces existing compilers to rely on static heuristics. We describe P-GONE, a method that combines a conditional diffusion model (D3PM + DDPM), a graph neural network (GNN) encoder, and closed-loop REINFORCE fine-tuning to jointly learn grouping, order, and time-step optimization over a mixed discrete-continuous space. Under fidelity-matched conditions (F ≥ 0.95), the method achieves circuit depth 86 versus 1673 for Qiskit fourth-order (ungrouped, Suzuki-4), about 19.4× compression, and 141 for Paulihedral (first-order Trotter), about 1.6× compression. At T=0.90 the method also beats the Qiskit group-commuting teacher (65 vs 103, 1.6× compression), though at T=0.95 the teacher still leads -- a stratified pattern that points toward fidelity-aware fine-tuning. Under a standard depolarizing noise model, the method achieves noisy fidelity roughly 2× the Qiskit fourth-order baseline (0.743 vs 0.380). Ablation shows a clear hierarchy: order learning > time allocation > grouping. Best-of-N sampling (N=32 is a practical sweet spot) and CFG guidance give flexible fidelity-depth trade-offs at inference. The method works well on structured Hamiltonians (TFIM, Heisenberg), but random Pauli Hamiltonians fail entirely at T ≥ 0.95 -- a boundary that defines where the method applies.