新方法显著降低复数量子态优化中的相位梯度方差，提升训练稳定性与精度。
Low-variance estimators overcome the phase-gradient bottleneck in complex-valued neural quantum states
- 提出低方差估计器，分离幅度与相位梯度计算，避免传统方法的梯度偏差问题。
- 在多种拓扑与费米体系中，将误差从多百分比降至不足1%，突破训练瓶颈。
- 适合研究拓扑量子材料、强关联电子系统及复杂量子态优化的研究者。
当波函数相位包含规范、手性、费米子或拓扑结构时，复数神经量子态的优化面临挑战。我们发现，主要瓶颈并非模型表达能力，而是用于学习该相位的蒙特卡洛估计器。对于分离的幅-相态，固定采样点下对局部能量求导可获得同一变分蒙特卡洛相位力的不同无偏估计，且不改变目标函数。进一步将此构造扩展至耦合双头网络，仅对相位路径使用直接导数，保留幅度梯度贡献。一种自适应最小方差混合策略在训练中动态插值标准与直接估计器。在通量阶梯、手性链、二维通量圆柱、相互作用费米体链、共享网络控制及分数量子霍尔基准测试中，所提估计器显著降低相位梯度方差，抑制初始种子失败，并常将多百分比标准梯度平台推进至亚百分比精度。
原文摘要 · Abstract (English)
Complex neural quantum states are difficult to optimize when their wavefunction phase carries gauge, chiral, fermionic, or topological structure. We show that the major failure mode is not only ansatz expressivity, but the Monte Carlo estimator used to learn this phase. For separated amplitude-phase states, differentiating the local energy at fixed samples gives a different unbiased estimator of the same variational Monte Carlo phase force, without changing the objective. We further extend the construction to coupled two-head networks by keeping the amplitude-gradient contribution and applying the direct derivative only to the phase path. An adaptive minimum-variance mixture interpolates between standard and direct estimators during training. Across flux ladders, chiral chains, two-dimensional flux cylinders, an interacting fermion ladder, shared-network controls, and a fractional quantum Hall benchmark, the resulting estimators reduce phase-gradient variance, suppress seed failures, and often move multi-percent standard-gradient plateaus to sub-percent accuracy.
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