研究基底旋转如何影响量子神经态性能，发现优化失败可能源于几何陷阱。
Exploring the Effect of Basis Rotation on NQS Performance
- 通过基底旋转控制参数空间中的精确解位置，分离表示能力与优化难度。
- 旋转后低能量误差仍可能对应错误波函数结构，说明优化失败不等于表达不足。
- 适用于关注变分量子模型设计与优化陷阱的科研人员。
神经量子态（NQS）是强大的量子多体波函数变分表示，但其性能对基底选择极为敏感。我们以一维伊辛模型为例，证明局部基底旋转不改变最小化景观，却会移动精确基态在参数空间中的位置。这提供了一个可控框架，用于分离表示限制与优化引发的可训练性效应。这种几何位移通过信息几何度量量化，可能引导浅层架构优化走向鞍点和高曲率区域。结果表明，即使能量误差较低，波函数结构也可能错误。在同一变分架构下比较能量与保真度优化，发现即便旋转后的目标态仍可表示，优化失败仍可能发生。研究揭示了影响NQS基底依赖性的几何机制，并推动考虑景观特性的变分设计。
原文摘要 · Abstract (English)
Neural Quantum States (NQS) are powerful variational representations of quantum many-body wavefunctions, yet their performance depends sensitively on the chosen basis. Using an exactly solvable one-dimensional Ising model, we show that local basis rotations leave the minimization landscape unchanged while relocating the exact ground state in parameter space. This provides a controlled framework to disentangle representational limitations from optimization-induced trainability effects. This geometric displacement, quantified through information-geometric measures, can steer optimization of shallow architectures toward saddle points and high-curvature regions. As a result, low energy errors may coexist with an incorrect wavefunction structure. By comparing energy and infidelity optimization within the same variational architectures, we show that optimization failure can persist even when the rotated target state remains representable. Our results identify a geometric mechanism contributing to basis dependence in NQS and motivate landscape-aware variational design.
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