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This research identifies a fundamental topological obstruction preventing standard pure-state neural network models from accurately representing ground states in systems with non-trivial topology. The study demonstrates that continuous state-vector representations inevitably fail at specific parameter values, causing artificial energy spikes and false phase-transition signatures in quantum chemistry simulations. To overcome this limitation, the authors propose operator-valued models as a structurally necessary evolution for foundation neural quantum states to preserve topological information.
Topology Obstructs Pure Foundation Neural Quantum States
arXiv:2609.07591v1 Announce Type: new Abstract: Foundation models for ground states in spin-1/2 systems are a promising method for problems ranging from quantum chemistry to identifying new phase diagrams. Nearly all such models are currently pure-states that condition on the Hamiltonian's parameters, whose Monte Carlo samples give energy estimates according to the variational principle. In this contribution, we show that this representation is topologically obstructed. For any gapped Hamiltonian family whose ground-state bundle is non-trivial, every continuous normalized state-vector model has zero fidelity with the ground state at some parameter value in the Hamiltonian family. For that value, the energy is at least one spectral gap, $\Delta$, with an $O(\Delta)$ gap in an open-neighbourhood of that point. We show that this is a sufficient no-go also in the case of degenerate ground-state manifolds, time dynamics, and periodic systems with mixed space-time topology, demonstrating these obstructions on one- and two-qubit systems. We discuss how this causes a spike in the fidelity susceptibility, giving a numerical signature of a phase-transition where there is none. We then show that operator-valued models canonically avoid these obstructions and preserve topological information, implying a structural necessity in representation for foundation neural quantum states.
Abstract:Foundation models for ground states in spin-1/2 systems are a promising method for problems ranging from quantum chemistry to identifying new phase diagrams. Nearly all such models are currently pure-states that condition on the Hamiltonian's parameters, whose Monte Carlo samples give energy estimates according to the variational principle. In this contribution, we show that this representation is topologically obstructed. For any gapped Hamiltonian family whose ground-state bundle is non-trivial, every continuous normalized state-vector model has zero fidelity with the ground state at some parameter value in the Hamiltonian family. For that value, the energy is at least one spectral gap, $\Delta$, with an $O(\Delta)$ gap in an open-neighbourhood of that point. We show that this is a sufficient no-go also in the case of degenerate ground-state manifolds, time dynamics, and periodic systems with mixed space-time topology, demonstrating these obstructions on one- and two-qubit systems. We discuss how this causes a spike in the fidelity susceptibility, giving a numerical signature of a phase-transition where there is none. We then show that operator-valued models canonically avoid these obstructions and preserve topological information, implying a structural necessity in representation for foundation neural quantum states.
Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Strongly Correlated Electrons (cond-mat.str-el); Artificial Intelligence (cs.AI); Mathematical Physics (math-ph)
arXiv:2609.07591 [quant-ph]
(or arXiv:2609.07591v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.07591 arXiv-issued DOI via DataCite (pending registration)
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