Topology limits pure state models for quantum ground states
Topology Obstructs Pure Foundation Neural Quantum States
Artificial Intelligence
Summary
Foundation models help find quantum systems' lowest energy states, but the authors show a hidden problem: the shape of these states’ space prevents pure-state models from perfectly matching the true ground states everywhere. This means models can suddenly fail badly for certain conditions, giving false signals of phase changes. They prove that using more complex operator-based models solves this problem, keeping important topological information intact.
What this means in practice
- •For quantum computing engineers: Avoid pure-state models that fail across parameter spaces by adopting operator-valued models for reliable quantum ground state representations.
- •For materials simulation teams: Improve prediction of ground states in complex quantum materials by using operator-based neural models that handle topological effects absent in pure-state models.
A theory result. No direct application yet.
Authors
Timothy Heightman, Elena Orlova, Philip Mantrov, Aleksei Ustimenko
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, $Δ$, with an $O(Δ)$ 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.