Phases of matrix-product states with symmetries and measurements: Finite nilpotent groups

• URL: http://arxiv.org/abs/2602.15168v1
• Date: Mon, 16 Feb 2026 20:13:03 GMT
• Title: Phases of matrix-product states with symmetries and measurements: Finite nilpotent groups
• Authors: David Gunn, Georgios Styliaris, Barbara Kraus, Tristan Kraft,
• Abstract summary: We classify phases of one-dimensional matrix-product states under symmetric circuits augmented with symmetric measurements and feedforward.<n>We show that symmetric measurements lead to a complete collapse of both symmetry-protected and non-normal MPS phases for all finite nilpotent symmetry groups.
• Score: 0.057270606438162557
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We classify phases of one-dimensional matrix-product states (MPS) under symmetric circuits augmented with symmetric measurements and feedforward. Building on the framework introduced in Gunn et al., Phys. Rev. B 111, 115110 (2025), we extend the analysis from abelian and class-2 nilpotent groups to all finite nilpotent groups. For any such symmetry group $G$, we construct explicit protocols composed of $G$-symmetric circuits and measurements with feedforward that transform symmetry-protected topological (SPT) states into the trivial phase and vice versa using a finite number of measurement rounds determined by the nilpotency class of $G$. Although these transformations are approximate, we prove that their success probability converges to unity in the thermodynamic limit, establishing asymptotically deterministic equivalence. Consequently, all SPT phases protected by finite nilpotent groups collapse to a single phase once symmetric measurements and feedforward are allowed. We further show that the same holds for non-normal MPS with long-range correlations, including GHZ-type states. The central technical ingredient is a hierarchical structure of irreducible representations of nilpotent groups, which enables a recursive reduction of non-abelian components to abelian ones. Our results demonstrate that symmetric measurements lead to a complete collapse of both symmetry-protected and non-normal MPS phases for all finite nilpotent symmetry groups.

Related papers

• Matrix product state classification of 1D multipole symmetry protected topological phases [21.762451041359906]
  We classify one dimensional bosonic symmetry protected topological phases protected respecting multipole symmetries by employing matrix product state formalism.<n>The symmetry action induces projective representations at the ends of an open chain, which we identify via group cohomology.
  arXiv  Detail & Related papers  (2025-09-11T08:26:51Z)
• Trading Mathematical for Physical Simplicity: Bialgebraic Structures in Matrix Product Operator Symmetries [20.76275069383104]
  We show that simple quantum spin chains of physical interest are not included in the rigid framework of fusion categories and weak Hopf algebras.<n>We show that our work provides a bridge between well-understood topological defect symmetries and those that arise in more realistic models.
  arXiv  Detail & Related papers  (2025-09-03T18:01:22Z)
• Sequential Circuit as Generalized Symmetry on Lattice [19.75535599298441]
  Generalized symmetry extends the usual notion of symmetry to ones that are of higher-form, acting on subsystems, non-invertible, etc.<n>In this paper, we ask how to obtain the full, potentially non-invertible symmetry action from the unitary sequential circuit.<n>We find that for symmetries that contain the trivial symmetry operator as a fusion outcome, the sequential circuit fully determines the symmetry action and puts various constraints on their fusion.<n>In contrast, for unannihilable symmetries, like that whose corresponding twist is the Cheshire string, a further 1D sequential circuit is needed
  arXiv  Detail & Related papers  (2025-07-30T05:28:27Z)
• Predicting symmetries of quantum dynamics with optimal samples [41.42817348756889]
  Identifying symmetries in quantum dynamics is a crucial challenge with profound implications for quantum technologies.<n>We introduce a unified framework combining group representation theory and subgroup hypothesis testing to predict these symmetries with optimal efficiency.<n>We prove that parallel strategies achieve the same performance as adaptive or indefinite-causal-order protocols.
  arXiv  Detail & Related papers  (2025-02-03T15:57:50Z)
• Topological nature of edge states for one-dimensional systems without symmetry protection [46.87902365052209]
  We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells)<n>Our winding number is invariant under unitary or similarity transforms.
  arXiv  Detail & Related papers  (2024-12-13T19:44:54Z)
• Symmetries from outer automorphisms and unorthodox group extensions [0.0]
  Symmetries play an essential role in the construction and phenomenology of quantum field theories (QFTs) We discuss how to construct symmetries of QFTs by extending minimal "seed" symmetry groups to larger groups that contain the seed as subgroup(s) We show that all symmetry groups, including the different possible classes of CP and continuous symmetry groups, can be obtained from extensions of the smallest possible symmetry CP1 by consecutive outer automorphisms.
  arXiv  Detail & Related papers  (2024-10-14T19:59:22Z)
• Classifying symmetric and symmetry-broken spin chain phases with anomalous group actions [0.0]
  We consider the classification problem of quantum spin chains invariant under local decomposable group actions. We derive invariants for our classification that naturally cover one-dimensional symmetry protected topological phases.
  arXiv  Detail & Related papers  (2024-03-27T13:54:45Z)
• Symmetry-restricted quantum circuits are still well-behaved [45.89137831674385]
  We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2n)$. It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space.
  arXiv  Detail & Related papers  (2024-02-26T06:23:39Z)
• Phases of Matrix Product States with Symmetric Quantum Circuits and Symmetric Measurements with Feedforward [0.2010986461330016]
  Two matrix product states (MPS) are in the same phase in the presence of symmetries. We consider how symmetry-preserving measurements with feedforward alter the phase classification of MPS in the presence of global on-site symmetries.
  arXiv  Detail & Related papers  (2023-12-21T13:38:46Z)
• Identifying the Group-Theoretic Structure of Machine-Learned Symmetries [41.56233403862961]
  We propose methods for examining and identifying the group-theoretic structure of such machine-learned symmetries. As an application to particle physics, we demonstrate the identification of the residual symmetries after the spontaneous breaking of non-Abelian gauge symmetries.
  arXiv  Detail & Related papers  (2023-09-14T17:03:50Z)
• Classifying phases protected by matrix product operator symmetries using matrix product states [0.0]
  We classify the different ways in which matrix product states (MPSs) can stay invariant under the action of matrix product operator (MPO) symmetries. This is achieved through a local characterization of how the MPSs, that generate a ground space, remain invariant under a global MPO symmetry.
  arXiv  Detail & Related papers  (2022-03-23T17:25:30Z)
• One-dimensional symmetric phases protected by frieze symmetries [0.0]
  We make a systematic study of symmetry-protected topological gapped phases of quantum spin chains in the presence of the frieze space groups in one dimension using matrix product states. We identify seventeen distinct non-trivial phases, define canonical forms, and compare the topological indices obtained from the MPS analysis with the group cohomological predictions.
  arXiv  Detail & Related papers  (2022-02-25T18:41:26Z)
• The classification of symmetry protected topological phases of one-dimensional fermion systems [0.0]
  We introduce an index for symmetry protected topological (SPT) phases of infinite fermionic chains with an on-site symmetry given by a finite group $G$. This index takes values in $mathbbZ times H1(G,mathbbZ_2) times H2(G, U(1)_mathfrakp)$ with a generalized Wall group law under stacking.
  arXiv  Detail & Related papers  (2020-06-26T22:32:34Z)

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.