用生成模型联合优化量子电路分组、阶数和步长，大幅压缩深度。
Physics Guided Generative Optimization for Trotter Suzuki Decomposition
- 结合扩散模型与图神经网络，端到端学习离散连续混合空间的优化策略。
- 在保真度0.95时，电路深度压缩至原方案的1/19.4，噪声下保真度提升2倍。
- 适合结构化哈密顿量，可灵活调节精度与深度权衡，但对随机哈密顿量无效。
Trotter-Suzuki分解是实现噪声中等规模量子（NISQ）硬件上哈密顿量演化的主要方法，但其精度依赖于三项耦合选择：项分组、公式阶数和时间步分配。分组与阶数为离散变量，导致直接梯度优化不可行，现有编译器依赖静态启发式方法。本文提出P-GONE，结合条件扩散模型（D3PM + DDPM）、图神经网络（GNN）编码器与闭环REINFORCE微调，联合学习混合离散-连续空间中的分组、阶数与时间步优化。在保真度匹配条件（F ≥ 0.95）下，电路深度从Qiskit四阶（未分组，Suzuki-4）的1673降至86，压缩约19.4倍；相较于Paulihedral一阶（141），压缩约1.6倍。在T=0.90时优于Qiskit群交换教师模型（65 vs 103，压缩1.6倍），但在T=0.95时教师仍占优——表明需设计保真度感知微调。在标准去极化噪声模型下，方法实现的噪声保真度约为Qiskit四阶基线（0.380）的两倍（0.743）。消融实验显示：阶数学习 > 时间分配 > 分组。使用Best-of-N采样（N=32为实用最优）和CFG引导，可在推理阶段灵活调节保真度与深度权衡。该方法在结构化哈密顿量（TFIM、Heisenberg）上表现良好，但在随机保罗哈密顿量上于T≥0.95时完全失效——界定了其适用范围。
原文摘要 · Abstract (English)
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 ($F \geq 0.95$), the method achieves circuit depth 86 versus 1673 for Qiskit fourth-order (ungrouped, Suzuki-4), about $19.4\times$ compression, and 141 for Paulihedral (first-order Trotter), about $1.6\times$ compression. At $T=0.90$ the method also beats the Qiskit group-commuting teacher (65 vs 103, $1.6\times$ 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 $2\times$ 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 $T \geq 0.95$ -- a boundary that defines where the method applies.
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