Universal gates from braiding and fusing anyons on quantum hardware.

Area of Science:

• Quantum Information Science
• Condensed Matter Physics
• Quantum Computing

Background:

• Quantum computers need global information manipulation for noise resilience.
• Topologically ordered phases offer encoding in ground states or anyonic excitations.
• Toric codes lack universal gates; braiding non-Abelian anyons is key for topological quantum computation.

Purpose of the Study:

• Demonstrate that anyon fusion can achieve universality in minimally non-Abelian topological states.
• Showcase the S3 topologically ordered state as a platform for universal quantum computation.
• Explore new pathways for quantum information manipulation using quantum matter properties.

Main Methods:

• Prepared a 54-qubit ground state of the quantum double of S3 on Quantinuum's H2 processor.
• Encoded logical information in the global fusion space of non-Abelian anyons.
• Combined braiding with anyon fusion to realize a universal topological gate set.

Main Results:

• Achieved universality in S3 topologically ordered states by incorporating anyon fusion.
• Successfully realized and read-out a universal topological gate set.
• Demonstrated topological preparation of a magic state using the S3 system.

Conclusions:

• The S3 topologically ordered state is scalable and sufficient for universal quantum computation.
• Anyon fusion is a viable computational primitive for topological quantum computers.
• This work advances the use of quantum matter for robust quantum information processing.