Quantum Cellular Automata from Kramers-Wannier Dualities and Modular Relations

• URL: http://arxiv.org/abs/2607.21728v1
• Date: Thu, 23 Jul 2026 18:24:51 GMT
• Title: Quantum Cellular Automata from Kramers-Wannier Dualities and Modular Relations
• Abstract summary: We show that QCAs associated with gravitational topological responses arise in several related settings.<n>We derive new projective $mathrmSL (2,mathbbZ_N)$ relations whose projective phases are gravitational topological responses constructed from Stiefel-Whitney classes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Recent work has constructed higher-dimensional analogs of non-invertible symmetries similar to 1+1d Kramers-Wannier duality. Although their continuum descriptions often treat purely gravitational topological terms as inessential counterterms, these terms can have an essential lattice manifestation: they distinguish states prepared by finite-depth quantum circuits (FDQCs) from those entangled by nontrivial quantum cellular automata (QCAs). Motivated by this mismatch, we show that QCAs associated with gravitational topological responses arise in several related settings: (1) lattice realizations of projective $\mathrm{SL}(2,\mathbb{Z}_N)$ relations generated by topological operations on symmetries; (2) squares of dualities that generalize the relation between fermionization and Kramers-Wannier duality; (3) lattice implementations of QCAs through higher-form gauging; and (4) invertible phases protected by generalized time-reversal symmetries. We derive new projective $\mathrm{SL}(2,\mathbb{Z}_N)$ relations whose projective phases are gravitational topological responses constructed from Stiefel-Whitney classes. We furthermore give a general protocol for preparing the associated QCA-entangled states using finite-depth unitary circuits, measurements, and error correction. These results unify the study of gravitational topological responses in field theories, higher dimensional dualities, and quantum cellular automata.

Related papers

• Continuum field theory of matchgate tensor network ensembles [36.94429692322632]
  We develop a continuum description for random ensembles of two-dimensional fermionic matchgate tensor networks.<n>As a diagnostic of the resulting universal physics, we analyze disorder-averaged moments of fermionic two-point functions.<n>We show that disorder drives universal long-distance behavior governed by a nonlinear sigma-model of symmetry class D with a topological term.
  arXiv  Detail & Related papers  (2026-03-06T12:15:35Z)
• Hamiltonian Lattice QED$_3$ with One and Two Flavors of Wilson Fermions: Topological Structure and Response [5.803135196608668]
  We show that staggered-fermion discretizations in Hamiltonian gauge theories possesses an exact time-reversal symmetry.<n>In this work, we analyze fermion discretization effects in (2+1)D lattice Hamiltonians of fermions coupled to U(1) gauge fields that satisfy Gauss' law.
  arXiv  Detail & Related papers  (2026-03-05T19:18:46Z)
• Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors [40.72140849821964]
  We consider the massive Thirring and Gross-Neveu models with arbitrary number of fermion flavors, $N_f$, discretized on a spatial one-dimensional lattice of size $L$.<n>We prepare the ground states of both models with excellent fidelity for system sizes up to 20 qubits with $N_f = 1,2,3,4$.<n>Our work is a concrete step towards the quantum simulation of real-time dynamics of large $N_f$ fermionic quantum field theories models.
  arXiv  Detail & Related papers  (2026-02-25T19:00:01Z)
• Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls [0.0]
  We study conformal field theories (CFTs) and their classifications from a modern perspective.<n>We find a natural generalization of the quantum dimensions associated with (pseudo-)Hermitian systems and (non)-unitary CFTs.
  arXiv  Detail & Related papers  (2025-11-14T08:17:29Z)
• Anatomy of Non-Hermitian Dynamical Quantum Phase Transitions [0.0]
  We establish a unified framework for dynamical quantum phase transitions (DQPTs) in non-Hermitian systems.<n>We show that non-biorthogonal quenches from non-Hermitian to Hermitian Hamiltonians under chiral symmetry exhibit emergent topological characteristics of DQPTs.<n>This work establishes fundamental geometric and topological principles governing quantum criticality in open systems, with implications for quantum sensing and many-body physics in dissipative environments.
  arXiv  Detail & Related papers  (2025-07-21T08:40:46Z)
• Theory of the correlated quantum Zeno effect in a monitored qubit dimer [41.94295877935867]
  We show how the competition between two measurement processes give rise to two distinct Quantum Zeno (QZ) regimes.<n>We develop a theory based on a Gutzwiller ansatz for the wavefunction that is able to capture the structure of the Hilbert phase diagram.<n>We show how the two QZ regimes are intimately connected to the topology of the flow of the underlying non-Hermitian Hamiltonian governing the no-click evolution.
  arXiv  Detail & Related papers  (2025-03-28T19:44:48Z)
• 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)
• 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)
• Electric-magnetic duality and $\mathbb{Z}_2$ symmetry enriched Abelian lattice gauge theory [2.206623168926072]
  Kitaev's quantum double model is a lattice gauge theoretic realization of Dijkgraaf-Witten topological quantum field theory (TQFT) Topologically protected ground state space has broad applications for topological quantum computation and topological quantum memory.
  arXiv  Detail & Related papers  (2022-01-28T14:13:38Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)

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.