Neural Quantum States in Non-Stabilizer Regimes: Benchmarks with Atomic Nuclei

TL;DR

This paper investigates the ability of neural quantum states, specifically RBMs, to represent complex, entangled nuclear ground states, revealing non-stabilizerness as a key factor affecting learnability.

Contribution

It demonstrates how non-stabilizerness impacts the representational efficiency of RBMs in modeling entangled nuclear states, using a second-quantized formulation.

Findings

States with higher non-stabilizerness are harder to learn with RBMs.

Non-stabilizerness influences the compression efficiency of neural quantum states.

The study motivates exploring more advanced neural network architectures.

Abstract

As neural networks are known to efficiently represent classes of tensor-network states as well as volume-law-entangled states, identifying which properties determine the representational capabilities of neural quantum states (NQS) remains an open question. We construct NQS representations of ground states of medium-mass atomic nuclei, which typically exhibit significant entanglement and non-stabilizerness, to study their performance in relation to the quantum complexity of the target state. Leveraging a second-quantized formulation of NQS tailored for nuclear-physics applications, we perform calculations in active orbital spaces using a restricted Boltzmann machine (RBM), a prototypical NQS ansatz. For a fixed number of configurations, we find that states with larger non-stabilizerness are systematically harder to learn, as evidenced by reduced accuracy. This finding suggests that non-stabilizerness is a primary factor governing the compression and representational efficiency of RBMs in entangled regimes, and motivates extending these studies to more sophisticated network architectures.