Isometric Tensor Network representation of string-net liquids

Abstract

Recently, a class of tensor networks called isometric tensor network states (isoTNS) was proposed which generalizes the canonical form of matrix product states to tensor networks in higher dimensions. While this ansatz allows for efficient numerical computations, it remained unclear which phases admit an isoTNS representation. In this work, we show that two-dimensional string-net liquids, which represent a wide variety of topological phases including discrete gauge theories, admit an exact isoTNS representation. We further show that the isometric form can be preserved after applying a finite depth local quantum circuit. Taken together, these results show that long-range entanglement by itself is not an obstruction to isoTNS representation and suggest that all two-dimensional gapped phases with gappable edges admit an isoTNS representation.

20 pages, 22 figures

References in corpus (34)

• Fault-tolerant quantum computation by anyons
• The density-matrix renormalization group in the age of matrix product states
• Efficient classical simulation of slightly entangled quantum computations
• Detecting topological order in a ground state wave function
• Efficient simulation of one-dimensional quantum many-body systems
• String-net condensation: A physical mechanism for topological phases
• An Area Law for One Dimensional Quantum Systems
• Time-dependent variational principle for quantum lattices
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Tensor renormalization group approach to 2D classical lattice models
• Spectral Gap and Exponential Decay of Correlations
• Corner Transfer Matrix Renormalization Group Method
• Models for gapped boundaries and domain walls
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
• Simulation of two dimensional quantum systems on an infinite lattice revisited: corner transfer matrix for tensor contraction
• Tensor Network Renormalization
• The computational complexity of PEPS
• Second Renormalization of Tensor-Network States
• Protected edge modes without symmetry
• Variational optimization with infinite projected entangled-pair states
• Gradient methods for variational optimization of projected entangled-pair states
• Loop optimization for tensor network renormalization
• Explicit tensor network representation for the ground states of string-net models
• Interferometry of non-Abelian Anyons
• Topological quasiparticles and the holographic bulk-edge relation in 2+1D string-net models
• Generalizations and limitations of string-net models
• Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension
• Projected entangled-pair states can describe chiral topological states
• An improved 1D area law for frustration-free systems
• Rigorous RG algorithms and area laws for low energy eigenstates in 1D
• Tensor product representation of topological ordered phase: necessary symmetry conditions
• Conversion of projected entangled pair states into a canonical form
• Tensor-product representations for string-net condensed states

Cited by in corpus (36)

• Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements
• Holographic quantum algorithms for simulating correlated spin systems
• Generalized string-nets for unitary fusion categories without tetrahedral symmetry
• Riemannian optimization of isometric tensor networks
• Methods for simulating string-net states and anyons on a digital quantum computer
• Sequential generation of projected entangled-pair states
• Absence of barren plateaus in finite local-depth circuits with long-range entanglement
• Efficient Simulation of Dynamics in Two-Dimensional Quantum Spin Systems with Isometric Tensor Networks
• Gauging tensor networks with belief propagation
• Holographic quantum simulation of entanglement renormalization circuits
• Three-dimensional isometric tensor networks
• Typical Correlation Length of Sequentially Generated Tensor Network States
• Quantum State Tomography with Locally Purified Density Operators and Local Measurements
• Observation of a non-Hermitian supersonic mode on a trapped-ion quantum computer
• Isometric tensor network representations of two-dimensional thermal states
• Probing phases of quantum matter with an ion-trap tensor-network quantum eigensolver
• Simulating 2D topological quantum phase transitions on a digital quantum computer
• Many-body-localization protection of eigenstate topological order in two dimensions
• Fermionic Isometric Tensor Network States in Two Dimensions
• Dual-isometric Projected Entangled Pair States
• Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits
• Generation of photonic tensor network states with Circuit QED
• Quantum Phase Transitions between Symmetry-Enriched Fracton Phases
• Sequential quantum simulation of spin chains with a single circuit QED device
• TensorKrowch: Smooth integration of tensor networks in machine learning
• Two Dimensional Isometric Tensor Networks on an Infinite Strip
• Quantum Gauge Networks: A New Kind of Tensor Network
• Adiabatic ground state preparation in an expanding lattice
• Diagonal Isometric Form for Tensor Network States in Two Dimensions
• Scalable projected entangled-pair state representation of random quantum circuit states
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model
• Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits
• Pseudoentanglement from tensor networks
• Skeleton of isometric Tensor Network States for Abelian String-Net Models
• Holographic duality between bulk topological order and boundary mixed-state order
• Sampling two-dimensional isometric tensor network states