Skeleton of Isometric Tensor Network States for Abelian String-Net Models

Area of Science:

• Quantum Information Science
• Condensed Matter Physics
• Topological Quantum Field Theory

Background:

• Topological order describes exotic phases of matter with long-range entanglement.
• String-net models are a key framework for realizing topological phases.
• Efficient simulation of topological phases on quantum hardware is a significant challenge.

Purpose of the Study:

• To develop a novel class of tensor network states, termed "skeletons," for studying Abelian topological order.
• To investigate stable deformations of string-net fixed points that exhibit finite correlation lengths.
• To establish a connection between topological phases and efficient computational methods.

Main Methods:

• Construction of parametrized isometric tensor network states (skeletons).
• Deformation of string-net fixed points using virtual symmetry conservation and local isometry constraints.
• Mapping 2D tensor networks to 1D stochastic automata for classical computation.

Main Results:

• Skeletons provide stable, finite correlation length deformations of topological phases.
• These states connect distinct topological phases through critical points, offering insights into phase transitions beyond anyon condensation.
• Expectation values of generalized Pauli strings can be computed efficiently using classical methods via the automata mapping.

Conclusions:

• Skeletons offer an organizing principle for Abelian topological order.
• They serve as a valuable test bed for quantum processors.
• The developed methods enable efficient classical computation of certain quantum properties.