Walshness: an intrinsic neural-network representability metric for quantum states

arXiv:2610.00505 · quant-ph, cond-mat.dis-nn · Submitted 2026-09-30 · Read on arXiv

quant-ph, cond-mat.dis-nn

Submitted: 2026-09-30

Updated: 2026-09-30

Code: https://github.com/rscortessa/basis-dependence-of-RBM-for-TFIM

Terminology

• Adam — 26× in this paper · explained in 2 episodes
• Entanglement — 23× in this paper · explained in 3 episodes
• Stabilizer States — 21× in this paper · explained in 2 episodes
• Entanglement Entropy — 7× in this paper · explained in 2 episodes
• Accuracy — 6× in this paper · explained in 1 episode
• Topological Order — 6× in this paper · explained in 2 episodes
• Fidelity — 5× in this paper · explained in 2 episodes
• Hilbert Space — 4× in this paper · explained in 2 episodes
• Generalization — 3× in this paper · explained in 13 episodes
• Loss Function — 3× in this paper · explained in 2 episodes
• Ab Initio — 2× in this paper · explained in 1 episode
• Additivity — 2× in this paper · explained in 1 episode
• Anyons — 2× in this paper · explained in 2 episodes
• Core — 2× in this paper · explained in 2 episodes
• Frustration — 2× in this paper · explained in 2 episodes
• Phase Transitions — 2× in this paper · explained in 2 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Activation Function — 1× in this paper · explained in 1 episode
• Anisotropy — 1× in this paper · explained in 3 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Curse of Dimensionality — 1× in this paper · explained in 6 episodes
• Interpretability — 1× in this paper · explained in 15 episodes
• Kavli Institute for Theoretical Physics — 1× in this paper
• Neural Network Approximation — 1× in this paper · explained in 2 episodes
• Quantum Circuits — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes

Sources

• Basis dependence of Neural Quantum States for the Transverse Field Ising Model
• Exploring the Effect of Basis Rotation on NQS Performance
• Towards Interpretability of Neural Quantum States
• When can classical neural networks represent quantum states?
• Learning complexity of many-body quantum sign structures through the lens of Boolean Fourier analysis
• Expressibility of neural quantum states: a Walsh-complexity perspective
• Hardness of Learning Fixed Parities with Neural Networks
• Qubit stabilizer states are complex projective 3-designs
• Bootstrapping ground state properties of classical frustrated magnets

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