String operators for Cheshire strings in topological phases

Abstract

Elementary point charge excitations in 3+1D topological phases can condense along a line and form a descendant excitation called the Cheshire string. Unlike the elementary flux loop excitations in the system, Cheshire strings do not have to appear as the boundary of a 2d disc and can exist on open line segments. On the other hand, Cheshire strings are different from trivial excitations that can be created with local unitaries in 0d and finite depth quantum circuits in 1d and higher. In this paper, we show that to create a Cheshire string, one needs a linear depth circuit that acts sequentially along the length of the string. Once a Cheshire string is created, its deformation, movement and fusion can be realized by finite depths circuits. This circuit depth requirement applies to all nontrivial descendant excitations including symmetry-protected topological chains and the Majorana chain.

5+5 pages. 11 figures. v2 Published version with minor clarifications added

References in corpus (29)

• Topological quantum memory
• Models for gapped boundaries and domain walls
• Sequential generation of entangled multi-qubit states
• Higher Gauging and Non-invertible Condensation Defects
• On the classification of topological orders
• Entanglement renormalization and topological order
• Sequential Generation of Matrix-Product States in Cavity QED
• Non-Abelian String and Particle Braiding in Topological Order: Modular SL(3,Z) Representation and 3+1D Twisted Gauge Theory
• A classification of 3+1D bosonic topological orders (I): the case when point-like excitations are all bosons
• Topological invariants for gauge theories and symmetry-protected topological phases
• Generalized modular transformations in 3+1D topologically ordered phases and triple linking invariant of loop braiding
• Topological color code and symmetry-protected topological phases
• Boundary-bulk relation in topological orders
• Layer construction of 3D topological states and string braiding statistics
• Bulk-boundary correspondence in (3+1)-dimensional topological phases
• Cheshire charge in (3+1)-D topological phases
• Gapped boundaries, group cohomology and fault-tolerant logical gates
• Classification of topological phases with finite internal symmetries in all dimensions
• Methods for simulating string-net states and anyons on a digital quantum computer
• The center of monoidal 2-categories in 3+1D Dijkgraaf-Witten Theory
• Codimension-2 defects and higher symmetries in (3+1)D topological phases
• Sequentially generated states for the study of two dimensional systems
• Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions
• Sequential Quantum Circuits as Maps between Gapped Phases
• Categories of quantum liquids I
• Defects in the 3-dimensional toric code model form a braided fusion 2-category
• Anyon and Loop Braiding Statistics in Field Theories with a Topological $\Theta -$term
• Graph gauge theory of mobile non-Abelian anyons in a qubit stabilizer code
• Quantum circuits for toric code and X-cube fracton model

Cited by in corpus (6)

• Non-invertible and higher-form symmetries in 2+1d lattice gauge theories
• Non-invertible symmetry-protected topological order in a group-based cluster state
• Non-invertible symmetries in finite-group gauge theory
• Transition between 2D Symmetry Protected Topological Phases on a Klein Bottle
• Fusion of Low-Entanglement Excitations in 2D Toric Code
• Preparing Code States via Seed-Entangler-Enriched Sequential Quantum Circuits: Application to Tetra-Digit Topological Error-Correcting Codes