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

• URL: http://arxiv.org/abs/2603.28646v1
• Date: Mon, 30 Mar 2026 16:29:42 GMT
• Title: Neural Quantum States in Non-Stabilizer Regimes: Benchmarks with Atomic Nuclei
• Abstract summary: We study the performance of neural quantum states in relation to the quantum complexity of the target state.<n>For a fixed number of configurations, we find that states with larger non-stabilizerness are systematically harder to learn.<n>This finding suggests that non-stabilizerness is a primary factor governing the compression and representational efficiency of RBMs in entangled regimes.
• Score: 41.99844472131922
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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