Categorifying Clifford QCA

• URL: http://arxiv.org/abs/2504.14811v1
• Date: Mon, 21 Apr 2025 02:27:52 GMT
• Title: Categorifying Clifford QCA
• Authors: Bowen Yang,
• Abstract summary: We provide a complete classification of Clifford quantum cellular automata (QCAs) on arbitrary metric spaces.<n>We reinterpret QCAs as symmetric formations in a filtered additive category constructed from the geometry of the underlying space.
• Score: 8.115018475321948
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We provide a complete classification of Clifford quantum cellular automata (QCAs) on arbitrary metric spaces and any qudits (of prime or composite dimensions) in terms of algebraic L-theory. Building on the delooping formalism of Pedersen and Weibel, we reinterpret Clifford QCAs as symmetric formations in a filtered additive category constructed from the geometry of the underlying space. This perspective allows us to identify the group of stabilized Clifford QCAs, modulo circuits and separated automorphisms, with the Witt group of the corresponding Pedersen--Weibel category. For Euclidean lattices, the classification reproduces and expands upon known results, while for more general spaces -- including open cones over finite simplicial complexes -- we relate nontrivial QCAs to generalized homology theories with coefficients in the L-theory spectrum. We also outline extensions to QCAs with symmetry and mixed qudit dimensions, and discuss how these fit naturally into the L-theoretic framework.

Related papers

• On Multiquantum Bits, Segre Embeddings and Coxeter Chambers [0.0]
  We develop a systematic study of qubit moduli spaces, illustrating the geometric structure of entanglement through hypercube constructions and Coxeter chamber decompositions. This reveals a structure underlying the hierarchy of embeddings, with direct implications for quantum error correction schemes. The symmetry of the Segre variety under the Coxeter group of type $A$ allows us to analyze quantum states and errors through the lens of reflection groups.
  arXiv  Detail & Related papers  (2025-02-01T15:39:28Z)
• L-mosaics and orthomodular lattices [44.99833362998488]
  We introduce a class of hypercompositional structures called dualizable L-mosaics.<n>We prove that their category is equivalent to that formed by ortholattices.
  arXiv  Detail & Related papers  (2025-01-10T19:01:10Z)
• Hilbert space geometry and quantum chaos [39.58317527488534]
  We consider the symmetric part of the QGT for various multi-parametric random matrix Hamiltonians. We find for a two-dimensional parameter space that, while the ergodic phase corresponds to the smooth manifold, the integrable limit marks itself as a singular geometry with a conical defect.
  arXiv  Detail & Related papers  (2024-11-18T19:00:17Z)
• Hierarchical analytical approach to universal spectral correlations in Brownian Quantum Chaos [44.99833362998488]
  We develop an analytical approach to the spectral form factor and out-of-time ordered correlators in zero-dimensional Brownian models of quantum chaos.
  arXiv  Detail & Related papers  (2024-10-21T10:56:49Z)
• Galois Symmetries in the Classification and Quantification of Quantum Entanglement [0.0]
  We present a new interpretation of entanglement classification by revealing a profound connection to Galois groups. This work bridges the mathematical elegance of Galois theory with the complexities of quantum mechanics, opening pathways for advances in quantum computing and information theory.
  arXiv  Detail & Related papers  (2024-10-10T20:58:23Z)
• Clifford circuits over non-cyclic abelian groups [0.0]
  We show that every Clifford circuit can be efficiently classically simulated. We additionally provide circuits for a universal quantum computing scheme based on local two-qudit Clifford gates and magic states.
  arXiv  Detail & Related papers  (2024-02-21T18:26:25Z)
• Machine learning detects terminal singularities [49.1574468325115]
  Q-Fano varieties are positively curved shapes which have Q-factorial terminal singularities. Despite their importance, the classification of Q-Fano varieties remains unknown. In this paper we demonstrate that machine learning can be used to understand this classification.
  arXiv  Detail & Related papers  (2023-10-31T13:51:24Z)
• Entanglement of Sections: The pushout of entangled and parameterized quantum information [0.0]
  Recently Freedman & Hastings asked for a mathematical theory that would unify quantum entanglement/tensor-structure with parameterized/-structure. We make precise a form of the relevant pushout diagram in monoidal category theory. We show how this model category serves as categorical semantics for the linear-multiplicative fragment of Linear Homotopy Type Theory.
  arXiv  Detail & Related papers  (2023-09-13T18:28:43Z)
• Dagger linear logic and categorical quantum mechanics [0.0]
  This thesis develops the categorical proof theory for the non-compact multiplicative dagger linear logic. It investigates its applications to Categorical Quantum Mechanics (CQM)
  arXiv  Detail & Related papers  (2023-03-24T18:52:50Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Finite-Function-Encoding Quantum States [52.77024349608834]
  We introduce finite-function-encoding (FFE) states which encode arbitrary $d$-valued logic functions. We investigate some of their structural properties.
  arXiv  Detail & Related papers  (2020-12-01T13:53:23Z)
• Generalized string-nets for unitary fusion categories without tetrahedral symmetry [77.34726150561087]
  We present a general construction of the Levin-Wen model for arbitrary multiplicity-free unitary fusion categories. We explicitly calculate the matrix elements of the Hamiltonian and, furthermore, show that it has the same properties as the original one.
  arXiv  Detail & Related papers  (2020-04-15T12:21:28Z)
• Tensor network models of AdS/qCFT [69.6561021616688]
  We introduce the notion of a quasiperiodic conformal field theory (qCFT) We show that qCFT can be best understood as belonging to a paradigm of discrete holography.
  arXiv  Detail & Related papers  (2020-04-08T18:00:05Z)

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.