Exploring the Effect of Basis Rotation on NQS Performance

Researchers demonstrate that basis rotations in Neural Quantum States (NQS) alter the optimization landscape geometry without changing the underlying physics, causing optimization algorithms to converge toward saddle points rather than true ground states. This finding reveals a fundamental geometric mechanism explaining why NQS performance depends on basis choice, with implications for quantum computing and variational algorithms.

Neural Quantum States represent a convergence of machine learning and quantum physics, leveraging neural networks to approximate complex quantum wavefunctions. This research exposes a critical vulnerability in current NQS implementations: the choice of mathematical basis—essentially the coordinate system used to describe quantum states—fundamentally affects whether training algorithms successfully find optimal solutions, even when solutions theoretically exist.

The study uses an exactly solvable one-dimensional Ising model as a controlled laboratory, proving that basis rotations preserve the underlying physics while geometrically displacing the target solution through parameter space. This displacement introduces high-curvature regions and saddle points that trap shallow neural network architectures during optimization. Critically, the researchers demonstrate that low energy errors can mask fundamentally incorrect wavefunction structures, meaning systems appear to be training successfully when they're actually learning wrong quantum representations.

For the quantum computing and variational algorithm community, this work identifies a previously underestimated source of training failure. The findings challenge assumptions that representability alone guarantees optimization success—geometric factors prove equally important. This has direct implications for near-term quantum applications relying on variational quantum eigensolvers (VQE) and other NQS-based methods, where basis selection currently receives minimal attention despite its demonstrated impact.

Developing landscape-aware architectural designs that account for geometric displacement becomes necessary for reliable quantum simulation. Researchers must now integrate information-geometric measures into architecture design rather than treating basis choice as a secondary consideration. This work potentially explains previously unexplained training failures across the NQS literature and opens pathways toward more robust quantum algorithms.

• →Basis rotations in Neural Quantum States relocate ground states through parameter space without changing physical content, creating optimization barriers
• →Shallow neural network architectures become trapped in saddle points created by geometric displacement, preventing convergence to correct solutions
• →Low energy optimization can coexist with fundamentally incorrect wavefunction structures, masking actual training failure
• →Representability of target states proves insufficient for successful NQS training without considering landscape geometry
• →Landscape-aware variational architecture design is necessary to overcome basis-dependent optimization challenges