Uniquely identifying topological order based on boundary-bulk duality and anyon condensation

Area of Science:

• Quantum physics
• Condensed matter physics

Background:

• Topological order represents a quantum phase beyond Landau's symmetry-breaking paradigm.
• Key features include degenerate ground states, long-range entanglement, and anyons.
• R and F matrices characterize anyon fusion-braiding properties and uniquely identify topological order.

Purpose of the Study:

• To experimentally measure R and F matrices for topological order identification.
• To develop a model-independent experimental protocol for characterizing topological phases.

Main Methods:

• Utilized boundary-bulk duality and anyon condensation to determine R matrices from half braidings of boundary excitations.
• Measured F matrices by comparing quantum states from different fusion orders of three anyons.
• Employed quantum simulations of a toric code model with boundaries on a three- and four-qubit system.

Main Results:

• Successfully determined R matrices through half braiding measurements.
• Successfully determined F matrices by analyzing fusion processes.
• Achieved the first experimental measurement of R and F matrices using an NMR quantum computer at room temperature.

Conclusions:

• A model-independent experimental protocol for uniquely identifying topological order has been established.
• The findings pave the way for experimental verification and characterization of novel quantum phases.
• Demonstrated the feasibility of measuring topological properties using accessible quantum computing platforms.