Large-scale Sustainable Search on Unconventional Computing Hardware

Abstract

Since the advent of the Internet, quantifying the relative importance of web pages is at the core of search engine methods. According to one algorithm, PageRank, the worldwide web structure is represented by the Google matrix, whose principal eigenvector components assign a numerical value to web pages for their ranking. Finding such a dominant eigenvector on an ever-growing number of web pages becomes a computationally intensive task incompatible with Moore's Law. We demonstrate that special-purpose optical machines such as networks of optical parametric oscillators, lasers, and gain-dissipative condensates, may aid in accelerating the reliable reconstruction of principal eigenvectors of real-life web graphs. We discuss the feasibility of simulating the PageRank algorithm on large Google matrices using such unconventional hardware. We offer alternative rankings based on the minimisation of spin Hamiltonians. Our estimates show that special-purpose optical machines may provide dramatic improvements in power consumption over classical computing architectures.

Analog Photonics Computing for Information Processing, Inference, and Optimization

“…Calculating the principal eigenvector is also required in other fields such as social network analysis, bibliometrics, recommendation systems, DNA sequencing, bioinformatics, and distributed computing systems. [194][195][196] There are numerous applications of PageRank to chemistry and engineering sciences networks to investigate and analyse complex systems. As systems grow in size and complexity, the interactions between their networks and subnetworks can become increasingly complicated and difficult to track.…”

“…[198] Recent research has shown that optical systems can provide significant advantages for calculating the principal eigenvector. [196] By choosing appropriate control parameters for these optical systems, the steady state of optical networks can be used to solve an eigenvalue maximization problem. [199] This results in the identification of the energy state dictated by the signs of the eigenvector corresponding to the largest eigenvalue of the interaction matrix, that is, the principal eigenvector.…”

“…In particular, estimates presented in Ref. [196] suggest that specialpurpose optical machines for PageRank calculations may offer dramatic improvements in power consumption compared to classical computing architectures.…”

“…One can find several discussions of these devices in Refs. [196,247] with the corresponding comparison of the key metrics; see also Figure 12. In addition, we mention some of these electronic devices as reference points for comparison with optical devices.…”

“…One can use the ratio of the FLOPs to the power consumption in watts (W) to get the energy efficiency metrics. [196] The standard estimate of the modern CPU efficiency is 2 TFLOPs, while the power efficiency is about 10 GFLOPs W -1 . Therefore, we can use the Intel Xeon processor as one of the top devices in terms of efficiency for working with the doubleprecision format, which has 4.8 TFLOPs and 29 GFLOPs W -1 .…”