Counting gauge-invariant states with matter fields and finite gauge groups

• URL: http://arxiv.org/abs/2509.02173v1
• Date: Tue, 02 Sep 2025 10:29:28 GMT
• Title: Counting gauge-invariant states with matter fields and finite gauge groups
• Authors: Alessandro Mariani,
• Abstract summary: We generalize the exact number of gauge-invariant states to include the case of scalar and fermionic matter.<n>Results are relevant for resource estimation and also as a crosscheck when working in a gauge-invariant basis.
• Score: 51.56484100374058
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Gauge theories with finite gauge groups have applications to quantum simulation and quantum gravity. Recently, the exact number of gauge-invariant states was computed for pure gauge theories on arbitrary lattices. In this work, we generalize this counting to include the case of scalar and fermionic matter, as well as various kinds of boundary conditions. As a byproduct, we consider several related questions, such as the implementation of charge conjugation for a generic finite group. These results are relevant for resource estimation and also as a crosscheck when working in a gauge-invariant basis.

Related papers

• Symmetry Packaging II: A Group-Theoretic Framework for Packaging Under Finite, Compact, Higher-Form, and Hybrid Symmetries [0.0]
  We develop a group-theoretic framework to describe the symmetry packaging for a variety of concrete symmetries.<n>We show how Bell-type packaged entangled states, color confinement, and hybrid gauge-invariant configurations all arise naturally.<n>Our approach unifies tools from group theory, gauge theory, and topological classification.
  arXiv  Detail & Related papers  (2025-03-26T07:35:58Z)
• Packaged Quantum States for Quantum Simulation of Lattice Gauge Theories [0.0]
  In this formalism, every single excitation transforms as a complete textbfirreducible representation (irrep) of the local gauge group.<n>All IQNs of such packaged entangled states remain inseparably entangled.<n>We illustrate this approach for $mathrmU(1)$, $mathrmSU(2)$, and $mathrmSU(3)$ lattice gauge theories.
  arXiv  Detail & Related papers  (2025-02-20T15:44:44Z)
• Fine-Grained Uncertainty Relations for Quantum Testers [0.0]
  Fine-grained uncertainty relations (FGURs) are a contemporary interpretation of the uncertainty principle. In this study, we develop FGURs in terms of quantum testers. Specifically, we explore quantum testers involving maximally entangled states in detail.
  arXiv  Detail & Related papers  (2024-09-13T05:30:36Z)
• Gaussian Entanglement Measure: Applications to Multipartite Entanglement of Graph States and Bosonic Field Theory [50.24983453990065]
  An entanglement measure based on the Fubini-Study metric has been recently introduced by Cocchiarella and co-workers. We present the Gaussian Entanglement Measure (GEM), a generalization of geometric entanglement measure for multimode Gaussian states. By providing a computable multipartite entanglement measure for systems with a large number of degrees of freedom, we show that our definition can be used to obtain insights into a free bosonic field theory.
  arXiv  Detail & Related papers  (2024-01-31T15:50:50Z)
• Quantum Computation of Thermal Averages for a Non-Abelian $D_4$ Lattice Gauge Theory via Quantum Metropolis Sampling [0.0]
  We show the application of the Quantum Metropolis Sampling (QMS) algorithm to a toy gauge theory with discrete non-Abelian gauge group $D_4$ in (2+1)-dimensions.
  arXiv  Detail & Related papers  (2023-09-13T17:05:03Z)
• Convergence of Dynamics on Inductive Systems of Banach Spaces [68.8204255655161]
  Examples are phase transitions in the thermodynamic limit, the emergence of classical mechanics from quantum theory at large action, and continuum quantum field theory arising from renormalization group fixed points. We present a flexible modeling tool for the limit of theories: soft inductive limits constituting a generalization of inductive limits of Banach spaces.
  arXiv  Detail & Related papers  (2023-06-28T09:52:20Z)
• Fermionic anyons: entanglement and quantum computation from a resource-theoretic perspective [39.58317527488534]
  We develop a framework to characterize the separability of a specific type of one-dimensional quasiparticle known as a fermionic anyon. We map this notion of fermionic-anyon separability to the free resources of matchgate circuits. We also identify how entanglement between two qubits encoded in a dual-rail manner, as standard for matchgate circuits, corresponds to the notion of entanglement between fermionic anyons.
  arXiv  Detail & Related papers  (2023-06-01T15:25:19Z)
• Hamiltonians and gauge-invariant Hilbert space for lattice Yang-Mills-like theories with finite gauge group [0.0]
  We show that the electric Hamiltonian admits an interpretation as a certain natural, non-unique Laplacian operator on the finite Abelian or non-Abelian group. We illustrate the use of the gauge-invariant basis to diagonalize a dihedral gauge theory on a small periodic lattice.
  arXiv  Detail & Related papers  (2023-01-28T15:16:33Z)
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory [44.99833362998488]
  We introduce quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple quantum numbers. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories.
  arXiv  Detail & Related papers  (2022-12-28T18:56:25Z)
• Error bounds for Lie Group representations in quantum mechanics [44.99833362998488]
  We provide state-dependent error bounds for strongly continuous unitary representations of Lie groups. Our method works for any connected Lie group and the metric is independent of the chosen representation.
  arXiv  Detail & Related papers  (2022-11-15T23:55:53Z)
• Conformal field theory from lattice fermions [77.34726150561087]
  We provide a rigorous lattice approximation of conformal field theories given in terms of lattice fermions in 1+1-dimensions. We show how these results lead to explicit error estimates pertaining to the quantum simulation of conformal field theories.
  arXiv  Detail & Related papers  (2021-07-29T08:54:07Z)
• Scaling limits of lattice quantum fields by wavelets [62.997667081978825]
  The renormalization group is considered as an inductive system of scaling maps between lattice field algebras. We show that the inductive limit of free lattice ground states exists and the limit state extends to the familiar massive continuum free field.
  arXiv  Detail & Related papers  (2020-10-21T16:30:06Z)
• Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories [0.0]
  Hamiltonian formulation of lattice gauge theories (LGTs) is the most natural framework for the purpose of quantum simulation. It remains an important task to identify the most accurate, while computationally economic, Hamiltonian formulation(s) in such theories. This paper is a first step toward addressing this question in the case of non-Abelian LGTs.
  arXiv  Detail & Related papers  (2020-09-24T16:44:39Z)

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.