Non-Abelian topological order and anyons on a trapped-ion processor

Area of Science:

• Condensed Matter Physics
• Quantum Information Science
• Quantum Computing

Background:

• Non-Abelian topological order is a complex state of matter featuring exotic quasiparticles (anyons) with potential applications in quantum computing.
• Realizing and controlling these non-Abelian anyons has been a significant challenge in physics.

Purpose of the Study:

• To experimentally realize and demonstrate control over non-Abelian topological order and its anyonic excitations.
• To explore the unique properties of non-Abelian braiding and its implications for quantum information.

Main Methods:

• Utilized an adaptive quantum circuit on a 27-qubit trapped-ion quantum processor (Quantinuum's H2).
• Prepared the ground-state wavefunction of D4 topological order on a kagome lattice.
• Employed anyon interferometry and spacetime braiding techniques to probe non-Abelian properties.

Main Results:

• Achieved high-fidelity realization of non-Abelian topological order (fidelity per site > 98.4%).
• Demonstrated intrinsically non-Abelian braiding by moving anyons along Borromean rings.
• Observed the creation of all 22 ground states and a unique excited state by tunnelling anyons around a torus.

Conclusions:

• This work provides the first experimental realization and control of non-Abelian topological order and its excitations.
• Highlights the counterintuitive behaviors of non-Abelions, crucial for advancing fault-tolerant quantum computing.
• Enables further study of these exotic states of matter in controllable quantum devices.