Topology Obstructs Pure Foundation Neural Quantum States

• URL: http://arxiv.org/abs/2609.07591v1
• Date: Mon, 07 Sep 2026 15:04:10 GMT
• Title: Topology Obstructs Pure Foundation Neural Quantum States
• Abstract summary: We show that foundation models for ground states in spin-1/2 systems are topologically obstructed.<n>We show that operator-valued models canonically avoid these obstructions and preserve topological information.
• Score: 10.606940539062064
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Ground state preparation of random all-to-all Hamiltonians using ADAPT-VQE [36.587368823954584]
  We show thatADAPT-VQE can construct accurate ground states for dense and sparse SYK models containing up to $N$ fermions.<n>We find that while the preparation of ground states is efficient (in terms of operator pool size and circuit depth) for the SK model, it is not efficient for either dense or moderately sparse SYK models.
  arXiv  Detail & Related papers  (2026-06-16T18:00:00Z)
• Hysteretic squashed entanglement in many-body quantum systems [42.085941481155295]
  Entanglement in many-body quantum systems is distributed across spatial regions.<n>We propose hysteretic entanglement $T_sq$, a conditional entanglement that measures the genuine quantum correlations between two subregions.<n>We show that $T_sq$ can detect genuine quantum correlations across both adjacent and long-range subsystems.
  arXiv  Detail & Related papers  (2026-03-10T17:00:49Z)
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices [37.69303106863453]
  Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by unitary dynamics and dissipation.<n>We show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue.<n>We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model.
  arXiv  Detail & Related papers  (2025-04-11T14:06:05Z)
• Exactly solvable models for fermionic symmetry-enriched topological phases and fermionic 't Hooft anomaly [33.49184078479579]
  In the past decade, the concept of symmetry-enriched topological (SET) phases was proposed and their classifications have been systematically studied for bosonic systems.<n>How to realize all these fermionic SET (fSET) phases in lattice models remains to be a difficult open problem.
  arXiv  Detail & Related papers  (2024-10-24T19:52:27Z)
• Scattering Neutrinos, Spin Models, and Permutations [42.642008092347986]
  We consider a class of Heisenberg all-to-all coupled spin models inspired by neutrino interactions in a supernova with $N$ degrees of freedom. These models are characterized by a coupling matrix that is relatively simple in the sense that there are only a few, relative to $N$, non-trivial eigenvalues.
  arXiv  Detail & Related papers  (2024-06-26T18:27:15Z)
• $W$ state is not the unique ground state of any local Hamiltonian [0.0]
  characterization of ground states among all quantum states is an important problem in quantum many-body physics. We introduce a new class of simple states, including the $W$ state, that can only occur as a ground state alongside an exactly degenerate partner.
  arXiv  Detail & Related papers  (2023-10-16T18:00:01Z)
• Entanglement dynamics in the many-body Hatano-Nelson model [0.0]
  The entanglement dynamics in a non-Hermitian quantum system is studied numerically and analyzed from the viewpoint of quasiparticle picture. As opposed to an assertion of previous studies, the entanglement dynamics in this non-Hermitian quantum system is very different from the one in its Hermitian counterpart.
  arXiv  Detail & Related papers  (2023-08-06T10:12:41Z)
• Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors [7.371841894852217]
  Non-orthogonality in non-Hermitian quantum systems gives rise to tremendous exotic quantum phenomena. We introduce an interesting quantity (denoted as $eta$) as a new variant of the Petermann factor to measure non-unitarity.
  arXiv  Detail & Related papers  (2022-08-31T16:24:03Z)
• Estimating gate complexities for the site-by-site preparation of fermionic vacua [0.0]
  We study the ground state overlap as a function of the number of sites for a range of quadratic fermionic Hamiltonians. For one-dimensional systems, we find that two $N/2$-site ground states also share a large overlap with the $N$-site ground state everywhere except a region near the phase boundary.
  arXiv  Detail & Related papers  (2022-07-04T19:45:14Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Quasi-Locality Bounds for Quantum Lattice Systems. Part II. Perturbations of Frustration-Free Spin Models with Gapped Ground States [0.0]
  We study the stability with respect to a broad class of perturbations of gapped ground state phases of quantum spin systems. Under a condition of Local Topological Quantum Order, the bulk gap is stable under perturbations that decay at long distances faster than a stretched exponential.
  arXiv  Detail & Related papers  (2020-10-29T03:24:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.