Local Decoders for the 2D and 4D Toric Code

We analyze the performance of decoders for the 2D and 4D toric code which are local by construction. The 2D decoder is a cellular automaton decoder formulated by Harrington which explicitly has a finite speed of communication and computation. For a model of independent $X$ and $Z$ errors and faulty syndrome measurements with identical probability we report a threshold of $0.133\%$ for this Harrington decoder. We implement a decoder for the 4D toric code which is based on a decoder by Hastings arXiv:1312.2546 . Incorporating a method for handling faulty syndromes we estimate a threshold of $1.59\%$ for the same noise model as in the 2D case. We compare the performance of this decoder with a decoder based on a 4D version of Toom's cellular automaton rule as well as the decoding method suggested by Dennis et al. arXiv:quant-ph/0110143 .Comment: 22 pages, 21 figures; fixed typos, updated Figures 6,7,8,

Cellular automaton decoders of topological quantum memories in the fault tolerant setting

Active error decoding and correction of topological quantum codes—in particular the toric code—remains one of the most viable routes to large scale quantum information processing. In contrast, passive error correction relies on the natural physical dynamics of a system to protect encoded quantum information. However, the search is ongoing for a completely satisfactory passive scheme applicable to locally interacting two-dimensional systems. Here, we investigate dynamical decoders that provide passive error correction by embedding the decoding process into local dynamics. We propose a specific discrete time cellular-automaton decoder in the fault tolerant setting and provide numerical evidence showing that the logical qubit has a survival time extended by several orders of magnitude over that of a bare unencoded qubit. We stress that (asynchronous) dynamical decoding gives rise to a Markovian dissipative process. We hence equate cellular-automaton decoding to a fully dissipative topological quantum memory, which removes errors continuously. In this sense, uncontrolled and unwanted local noise can be corrected for by a controlled local dissipative process. We analyze the required resources, commenting on additional polylogarithmic factors beyond those incurred by an ideal constant resource dynamical decoder

Deep Learning with Photonic Neural Cellular Automata

Rapid advancements in deep learning over the past decade have fueled an insatiable demand for efficient and scalable hardware. Photonics offers a promising solution by leveraging the unique properties of light. However, conventional neural network architectures, which typically require dense programmable connections, pose several practical challenges for photonic realizations. To overcome these limitations, we propose and experimentally demonstrate Photonic Neural Cellular Automata (PNCA) for photonic deep learning with sparse connectivity. PNCA harnesses the speed and interconnectivity of photonics, as well as the self-organizing nature of cellular automata through local interactions to achieve robust, reliable, and efficient processing. We utilize linear light interference and parametric nonlinear optics for all-optical computations in a time-multiplexed photonic network to experimentally perform self-organized image classification. We demonstrate binary classification of images in the fashion-MNIST dataset using as few as 3 programmable photonic parameters, achieving an experimental accuracy of 98.0% with the ability to also recognize out-of-distribution data. The proposed PNCA approach can be adapted to a wide range of existing photonic hardware and provides a compelling alternative to conventional photonic neural networks by maximizing the advantages of light-based computing whilst mitigating their practical challenges. Our results showcase the potential of PNCA in advancing photonic deep learning and highlights a path for next-generation photonic computers

Fault tolerance issues in nanoelectronics

The astonishing success story of microelectronics cannot go on indefinitely. In fact, once devices reach the few-atom scale (nanoelectronics), transient quantum effects are expected to impair their behaviour. Fault tolerant techniques will then be required. The aim of this thesis is to investigate the problem of transient errors in nanoelectronic devices. Transient error rates for a selection of nanoelectronic gates, based upon quantum cellular automata and single electron devices, in which the electrostatic interaction between electrons is used to create Boolean circuits, are estimated. On the bases of such results, various fault tolerant solutions are proposed, for both logic and memory nanochips. As for logic chips, traditional techniques are found to be unsuitable. A new technique, in which the voting approach of triple modular redundancy (TMR) is extended by cascading TMR units composed of nanogate clusters, is proposed and generalised to other voting approaches. For memory chips, an error correcting code approach is found to be suitable. Various codes are considered and a lookup table approach is proposed for encoding and decoding. We are then able to give estimations for the redundancy level to be provided on nanochips, so as to make their mean time between failures acceptable. It is found that, for logic chips, space redundancies up to a few tens are required, if mean times between failures have to be of the order of a few years. Space redundancy can also be traded for time redundancy. As for memory chips, mean times between failures of the order of a few years are found to imply both space and time redundancies of the order of ten

Artificial life meets computational creativity?

I review the history of work in Artificial Life on the problem of the open-ended evolutionary growth of complexity in computational worlds. This is then put into the context of evolutionary epistemology and human creativity