Unveiling the Non-Abelian Statistics of D(S_{3}) Anyons Using a Classical Photonic Simulator

Area of Science:

• Quantum Information Science
• Condensed Matter Physics

Background:

• Simulators offer a way to study complex quantum phenomena without full physical implementation.
• Non-Abelian anyons exhibit exotic statistics crucial for topological quantum computation.

Purpose of the Study:

• To propose and demonstrate a resource-efficient scheme for simulating D(S3) non-Abelian anyons.
• To leverage classical photonic systems for high-fidelity simulation of anyonic properties.

Main Methods:

• Developed a qudit lattice representation of a planar code for local encoding of D(S3) anyons.
• Employed a classical photonic simulator to encode and manipulate a single qutrit.
• Performed fusion and braiding operations characteristic of non-Abelian D(S3) anyons.

Main Results:

• Successfully encoded and manipulated a single qutrit to exhibit D(S3) anyon statistics.
• Achieved high-fidelity nonunitary operations using photonic technology, surpassing current quantum computer capabilities.
• Demonstrated a proof-of-principle for simulating exotic anyonic behavior.

Conclusions:

• The proposed scheme provides a viable and resource-efficient method for simulating D(S3) non-Abelian anyons.
• Photonic simulators offer a promising platform for high-fidelity quantum simulations.
• This approach is generalizable to larger systems and other anyonic models, advancing quantum error correction and fundamental physics exploration.