Exploring the Effect of Basis Rotation on NQS Performance

Part of data pertaining to the paper "Exploring the Effect of Basis Rotation on NQS Performance".

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 train-
ability 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 en-
ergy 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.