Gauging Modulated Symmetries via Multiple Gauge Symmetry Operators and Adaptive Quantum Circuits

Abstract

We introduce an extended framework for the simultaneous gauging of modulated symmetries in $(d+1)$ dimensions, employing {\it multiple} gauge symmetry operators whose corresponding gauging procedures must be carried out simultaneously. Simultaneous gauging can capture a broader class of dualities than sequential gauging, the latter corresponding to the conventional gauging applied in successive steps. In general, performing simultaneous gauging and conventional gauging in sequence constitutes the most general framework for gauging modulated symmetries. We further show that the associated duality transformations can be implemented via adaptive state preparation protocols. As a concrete example, we consider a dipole symmetry in $(2+1)$D and illustrate both the simultaneous gauging procedure and the adaptive preparation protocol. Interestingly, we find that the intermediate state of the simultaneous gauging/adaptive circuit corresponds to a symmetry-protected topological phase protected by the dipole bundle symmetry. Finally, we utilize the duality to analyze the phase diagram of the rank-2 toric code under transverse fields.

arXiv comment18 pages, 7 figures

References in corpus (68)

• Persistent entanglement in arrays of interacting particles
• Demonstration of the trapped-ion quantum-CCD computer architecture
• Fractons
• Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians
• Generalized Symmetries in Condensed Matter
• Fracton Phases of Matter
• Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains
• Fracton hydrodynamics
• Mott insulators in strong electric fields
• Long-range quantum entanglement in noisy cluster states
• Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory
• Exotic $U(1)$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
• Anomalous Diffusion in Dipole- and Higher-Moment Conserving Systems
• Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor
• Subdiffusion and heat transport in a tilted 2D Fermi-Hubbard system
• Dynamically Generated Logical Qubits
• Foliated fracton order from gauging subsystem symmetries
• The Higgs Mechanism in Higher-Rank Symmetric $U(1)$ Gauge Theories
• Fracton topological order from Higgs and partial confinement mechanisms of rank-two gauge theory
• Kinetically constrained freezing transition in a dipole-conserving system
• Measurement as a shortcut to long-range entangled quantum matter
• Quantum Circuits assisted by LOCC: Transformations and Phases of Matter
• Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• Long-range entanglement from measuring symmetry-protected topological phases
• Higher order symmetry-protected topological states for interacting bosons and fermions
• The dipolar Bose-Hubbard model
• Shortest Route to Non-Abelian Topological Order on a Quantum Processor
• Cluster state as a non-invertible symmetry protected topological phase
• An Introduction to Higher-Form Symmetries
• Gauging fractons: immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies
• Fractonic Luttinger Liquids and Supersolids in a Constrained Bose-Hubbard Model
• Dipole condensates in tilted Bose-Hubbard chains
• Position-Dependent Excitations and UV/IR Mixing in the ${\mathbb{Z}}_N$ Rank-2 Toric Code and its Low-Energy Effective Field Theory
• Gauging permutation symmetries as a route to non-Abelian fractons
• Rank-2 Toric Code in Two Dimensions
• Ground state degeneracy on torus in a family of ${\mathbb{Z}}_N$ toric code
• 2+1d Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• Non-invertible and higher-form symmetries in 2+1d lattice gauge theories
• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• Exact solution for the filling-induced thermalization transition in a 1D fracton system
• Searching for Fracton Orders via Symmetry Defect Condensation
• Lattice Gauge Theories and Spin Models
• Effective Fractonic Behavior in a Two-Dimensional Exactly Solvable Spin Liquid
• Generating Lattice Non-invertible Symmetries
• Foliated BF theories and Multipole symmetries
• Formation of spontaneous density-wave patterns in DC driven lattices
• A Chern-Simons theory for dipole symmetry
• Aspects of ${\mathbb{Z}}_N$ rank-2 gauge theory in $(2+1)$ dimensions: construction schemes, holonomies, and sublattice one-form symmetries
• Symmetry-enriched topological order from partially gauging symmetry-protected topologically ordered states assisted by measurements
• Effective Field Theory of Dipolar Braiding Statistics in Two Dimensions
• Gapped Lineon and Fracton Models on Graphs
• Multipole and fracton topological order via gauging foliated SPT phases
• Symmetric higher rank topological phases on generic graphs
• Gauging non-invertible symmetries on the lattice
• Entanglement Properties of Gauge Theories from Higher-Form Symmetries
• Tensor networks for non-invertible symmetries in 3+1d and beyond
• Topological order and Fractons from Gauging Exponential Symmetries
• Gauging U(1) symmetry in (2+1)d topological phases
• Noninvertible operators in one, two, and three dimensions via gauging spatially modulated symmetry
• Efficient Preparation of Solvable Anyons with Adaptive Quantum Circuits
• Protocols for Creating Anyons and Defects via Gauging
• Interplay between lattice gauge theory and subsystem codes
• Noninvertible symmetry and topological holography for modulated SPT in one dimension
• Unveiling UV/IR Mixing via Symmetry Defects: A View from Topological Entanglement Entropy
• A New Model for Fractons, Fluxons, and Freeons
• Generalized Modulated Symmetries in ${\mathbb{Z}}_2$ Topological Ordered Phases
• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
• Hybrid rank-1 and rank-2 U(1) lattice gauge theory, the F3 model, and its effective field theory

Cited by in corpus (2)

• Noninvertible symmetry and topological holography for modulated SPT in one dimension
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond