Qutrit toric code and parafermions in trapped ions.

Area of Science:

• Quantum Information Science
• Condensed Matter Physics
• Quantum Computing

Background:

• Topologically ordered states are crucial for robust quantum information storage and processing.
• While qudits (quantum digits) offer advantages for topological orders, experimental realizations have been limited to qubits.
• Previous experimental efforts focused on qubit-based lattice models for topological states.

Purpose of the Study:

• To experimentally realize and measure a complex topological state using qutrits.
• To explore novel defects and their manipulation beyond conventional qubit-based topological codes.
• To demonstrate control over topological qutrits through defect interactions and entanglement transfer.

Main Methods:

• Preparation and measurement of a Z_3 toric code ground state on 24 qutrits in a trapped ion quantum processor.
• Encoding one qutrit into two qubits for experimental implementation.
• Manipulation of parafermion defects and their bound states, going beyond standard qubit toric codes.

Main Results:

• Achieved high fidelity per qutrit exceeding 96.5(3)%.
• Successfully manipulated parafermion defects and their bound states.
• Demonstrated defect fusion and entanglement transfer between anyons and defects.

Conclusions:

• The study successfully implemented a topological code with qutrits, a significant step beyond qubit-based systems.
• The manipulation of novel defects and entanglement transfer provides new control mechanisms for topological qutrits.
• This work expands the possibilities for long-range entangled states with qudit degrees of freedom, relevant for quantum simulation and error correction.