Topologically robust programmable logic arrays using light and matter skyrmions

Photonic computing offers a low-power, high-bandwidth paradigm for information processing; however, the analogue nature of conventional architectures means that intrinsic noise and fabrication imperfections greatly impact performance, thereby severely limiting scalability. Recent work on optical skyrmions offers a route to overcoming these limitations by exploiting perturbation-resilient topological invariants assigned to the optical field for computation. Crucially, owing to its relative novelty, an architectural perspective on integrating individual components that manipulate topological charge into a functional system remains an important open goal. In this paper, we take concrete steps toward system-level design by introducing a platform-independent architecture for skyrmion-based logic, built around a modular library of topologically robust optical primitives, including generators, converters, registers, and adders. This framework enables the synthesis and arithmetic manipulation of topological numbers within a unified programmable architecture. We then experimentally validate this approach using multichannel arrays, demonstrating accurate charge readout and high robustness against alignment errors and environmental noise. These results provide a scalable foundation for topologically robust programmable logic arrays, paving the way for compact and integrated photonic processing circuits.

💡 Research Summary

This paper introduces a platform‑independent architectural framework for performing logic operations with topologically protected optical skyrmions and merons. The authors argue that the quantized topological charge associated with these polarization textures—an integer‑valued skyrmion number for skyrmions and a fractional charge for merons—provides a discrete, noise‑resilient information carrier. By exploiting the fact that the charge is invariant under continuous deformations of the field as long as the boundary conditions are preserved, the proposed system gains robustness against fabrication imperfections, alignment errors, and environmental perturbations that typically cripple analogue photonic processors.

The core of the framework is the concept of an “arbitrary retarder”: a spatially varying, tunable elliptical retarder that can be realized on a variety of matter platforms (liquid‑crystal spatial light modulators, metasurfaces, gradient‑index optics, etc.). The design methodology focuses exclusively on the transformation of the field’s boundary curve; the internal distribution of fast‑axis orientation and retardance can be freely deformed without affecting functionality. This boundary‑centric approach yields strong topological protection and enables seamless cascading of multiple devices, because each primitive’s operation depends only on the exiting field’s boundary, not on the detailed interior of the preceding element.

Four elementary optical primitives are defined, forming a minimal toolkit:

1. Generator – converts a uniform input beam into a skyrmion or meron of arbitrary order by imposing a radial retardance profile together with a prescribed fast‑axis distribution.

2. Converter (Skyrmion‑Meron Interconverter) – swaps a skyrmion for a meron (or vice‑versa) while preserving the topological charge, achieved by altering only the fast‑axis pattern while keeping the boundary unchanged.

3. Register (Meron‑to‑Meron Transport) – transports and stores a meron without modifying its boundary state or charge, effectively acting as a memory element.

4. Adder (Skyrmion‑to‑Skyrmion Arithmetic) – adds the topological charges of two skyrmions, realized by superimposing retardance profiles so that the resulting field carries the summed integer charge.

The authors experimentally implement these primitives using a cascade of three liquid‑crystal spatial light modulators (LC‑SLMs). Mueller‑matrix polarimetry and Lu‑Chipman decomposition are employed to retrieve the actual fast‑axis and retardance maps, confirming that the fabricated devices match the theoretical designs. Stokes‑field measurements show that generated skyrmions and merons possess the intended topological numbers, with deviations well within experimental uncertainty.

To demonstrate scalability, a dual‑stage multichannel array is built: a reconfigurable preparation layer followed by a fixed processing layer. By programming the same retarder array with different input beam patterns, the authors realize simultaneous execution of multiple logical functions—skyrmion generation (GS), meron generation (GM), registration (R), conversion (C), and addition (A)—across independent channels. The experimental results reveal negligible crosstalk, accurate charge readout, and sustained performance even when complex aberrations and random noise are deliberately introduced. Notably, only a single reconfigurable stage is required, reducing system complexity, cost, and footprint compared with prior demonstrations that needed multiple programmable layers.

A key insight is the combined use of skyrmions (integer charge) and merons (fractional charge) as distinct computational units. Because merons occupy a smaller portion of the available charge spectrum, the same maximum charge budget can encode roughly three times as many logical states, lowering the required spatial resolution of the underlying matter field and easing pixel‑size constraints. This dual‑unit strategy also cleanly separates processing (skyrmions) from storage (merons), simplifying logic synthesis and enabling modular reuse of primitives.

The discussion emphasizes that the boundary‑driven design confers intrinsic topological robustness: any perturbation that does not alter the field’s boundary curve leaves the logical operation unchanged. This property is validated experimentally by adding high‑order aberrations and stochastic noise, yet the measured skyrmion numbers remain correct. The modular library of primitives supports systematic composition, allowing more complex operations (e.g., cascaded adders, conditional logic) to be built from the same building blocks.

In summary, the paper delivers a comprehensive, experimentally validated blueprint for topologically robust, programmable photonic logic arrays based on optical skyrmions. By abstracting logic into a small set of retarder‑based primitives, demonstrating platform independence, and proving multichannel parallelism with high tolerance to imperfections, the work paves the way toward scalable, low‑power, high‑bandwidth photonic processors that can compete with electronic and other emerging neuromorphic platforms.