Programmable lattices for non-Abelian topological photonics and braiding

TL;DR

This paper introduces programmable topological lattices in photonics that emulate non-Abelian phenomena, enabling reconfigurable quantum operations and braiding, with potential applications in quantum computing.

Contribution

It presents a novel design of topological spinor lattices for non-Abelian photonics, including reconfigurable unitary couplings and the demonstration of non-Abelian braiding.

Findings

Reconfigurable unitary coupling achieves universal rotation gates.

Emulation of extended quantum Hall family across eigenspinor bases.

Demonstration of non-Abelian braiding operations and Yang-Baxter relations.

Abstract

Non-Abelian physics, originating from noncommutative sequences of operations, unveils novel topological degrees of freedom for advancing band theory and quantum computation. In photonics, significant efforts have been devoted to developing reconfigurable non-Abelian platforms, serving both as classical testbeds for non-Abelian quantum phenomena and as programmable systems that harness topological complexities. Here we establish topological spinor lattices for non-Abelian programmable photonics. We design a building block for reconfigurable unitary coupling between pseudospin resonances, achieving a universal set of rotation gates through coupling along the unit cell boundary. The lattice assembly of our building blocks enables the emulation of the extended quantum Hall family across various eigenspinor bases. Particularly, we reveal the emergence of a non-Abelian interface even when the bulks are Abelian, which allows the topologically trivial engineering of topologically protected edge states. We also define the braid group for pseudospin observables, demonstrating non-Abelian braiding operations and the Yang-Baxter relations. Our results pave the way for realizing a reconfigurable testbed for a wide class of Abelian and non-Abelian topological phenomena and braiding operations.