Building a Silicon Photonic Universal Cellular Automaton

Introduction

Cellular automata (CA) are mathematical models that consist of a grid of cells, each in one of a finite number of states. The state of each cell is updated in discrete time steps according to a set of rules that depend on the states of the cell and its neighbors. CAs have found applications in modeling various systems, from biological processes to computational systems

In a recent breakthrough, researchers at Hewlett Packard Labs have demonstrated the first silicon photonic cellular automaton. This system uses silicon photonic devices to implement the rules of cellular automata, opening up new possibilities for optical computing. In this tutorial, we'll explore the key concepts behind this work and guide you through building your own silicon photonic CA.

Background

The idea of cellular automata was first introduced by John von Neumann and Stanislaw Ulam in the 1940s. However, it was John Conway's Game of Life in 1970 that popularized the use of CAs to demonstrate life-like behaviors. One significant milestone was achieved in 2004 when Matthew Cook proved that the Rule 110 CA is Turing complete, meaning it can perform any computation that a Turing machine can.

Silicon photonics has emerged as a promising platform for computing due to its potential for high-speed, low-power operations. The work by the researchers at Hewlett Packard Labs demonstrates the first implementation of a universal cellular automaton using a silicon photonic platform.

Experimental Setup

The experimental setup used by the researchers is shown in Figure 1. It consists of two cascaded microring modulators (MRMs) fabricated by CEA-LETI.

Figure 1: Two cascaded silicon MRMs, manufactured by CEA-LETI.

The setup also includes two external tunable lasers, optical amplifiers (PDFAs), optical bandpass filters, optical power meters, and photodetectors. The optical signal is manipulated electro-optically using the p-n junction microring modulators, which are biased between 0 and 1 V.

Implementing Cellular Automaton Rules

The researchers demonstrated the implementation of three cellular automaton rules: Rule 90, Rule 250, and Rule 110. These rules involve different logical operations between the states of a cell and its neighbors.

Figure 2: How Rule 110 is used to determine the next generation of cells.

Rule 90 is computed using an XOR operation between the left and right neighbor cells. The researchers used the two tunable lasers to represent the left neighbor and the two MRMs to represent the right neighbor.

Rule 250 is implemented by performing a simple optical OR operation between the left and right neighbor states. The truth tables for the OR and XOR operations are shown in Figures 3(b) and 3(c).

Fig. 3: (a) Experimental setup of silicon photonic cellular automata (CA). (b) The operating scheme used to calculate rule 250. (c) The operating scheme to calculate rule 90. Rule 110 is a combination of the schemes presented in (b) and (c). (d) Output photocurrent being read by the photodetector after the output grating coupler of the microring array after executing (d) Rule 90, (e) Rule 250, and (f) Rule 110. Below the photocurrent measurements are the decoded cell maps with black representing live cells and white representing dead cells.

Rule 110, which is Turing complete, is demonstrated through the logical operation [Ci AND (NOT Ci-1)] OR [Ci XOR Ci+1], where Ci represents the state of the current cell, Ci-1 represents the state of the left neighbor, and Ci+1 represents the state of the right neighbor. The researchers used a combination of OR, XOR, and NOT operations to implement this rule.

Results

The researchers successfully demonstrated the implementation of Rules 90, 250, and 110 using their silicon photonic setup. The output photocurrent measurements and the decoded cell maps for each rule are shown in Figures 3(d), 3(e), and 3(f).

Significance and Future Directions

The demonstration of a silicon photonic universal cellular automaton is a significant achievement, as it signifies that this computing system is Turing complete and can compute any program. The researchers envision using this technology in the future to program and execute Neural Cellular Automata (NCA), which can be used to simulate complex evolutionary morphologic tasks such as morphogenesis.

Recently, cellular automata have been observed to exhibit similar characteristics to Graph and Convolutional Neural Network models. By using the silicon photonic platform to implement NCAs, researchers can potentially develop new approaches to modeling and simulating complex systems.

Conclusion

The work by the researchers at Hewlett Packard Labs has demonstrated the first silicon photonic cellular automaton, capable of implementing various cellular automaton rules, including the Turing complete Rule 110. This achievement paves the way for optical computing systems based on cellular automata and opens up new possibilities for simulating and modeling complex systems using Neural Cellular Automata. As the field of silicon photonics continues to advance, we can expect to see more innovative applications of this technology in computing and simulation.

Reference

[1] B. Tossoun, Y. London, T. Van Vaerenbergh, and R. G. Beausoleil, "A Silicon Photonic Universal Cellular Automaton," Hewlett Packard Labs, Hewlett Packard Enterprise, Santa Barbara, CA, USA; Milpitas, CA, USA; Brussels, Belgium, 2024, pp. 1-6, doi: 979-8-3503-9404-7/24/$31.00 ©2024 IEEE.