Classification is an important task at which both biological and artificial neural networks excel 1,2 . In machine learning, nonlinear projection into a high-dimensional feature space can make data linearly separable 3,4 , simplifying the classification of complex features. Such nonlinear projections are computationally expensive in conventional computers. A promising approach is to exploit physical materials systems that perform this nonlinear projection intrinsically, because of their high computational density 5 , inherent parallelism and energy efficiency 6,7 . However, existing approaches either rely on the systems' time dynamics, which requires sequential data processing and therefore hinders parallel computation 5,6,8 , or employ large materials systems that are difficult to scale up 7 . Here we use a parallel, nanoscale approach inspired by filters in the brain 1 and artificial neural networks 2 to perform nonlinear classification and feature extraction. We exploit the nonlinearity of hopping conduction [9][10][11] through an electrically tunable network of boron dopant atoms in silicon, reconfiguring the network through artificial evolution to realize different computational functions. We first solve the canonical two-input binary classification problem, realizing all Boolean logic gates 12 up to room temperature, demonstrating nonlinear classification with the nanomaterial system. We then evolve our dopant network to realize feature filters 2 that can perform four-input binary classification on the Modified National Institute of Standards and Technology handwritten digit database. Implementation of our material-based filters substantially improves the classification accuracy over that of a linear classifier directly applied to the original data 13 . Our results establish a paradigm of silicon-based electronics for smallfootprint and energy-efficient computation 14 .Doping is a crucial process in semiconductor electronics, where impurity atoms are introduced to modulate the charge carrier concentration. Conventional semiconductor devices operate in the band regime of charge transport, where the delocalization of the charge carriers gives rise to high mobility and a linear response to an applied electric field. At sufficiently low doping concentration and temperature 9,15 , however, delocalization is lost, and carriers move sequentially from dopant atom to dopant atom. This is referred to as the hopping regime 10,11,16 , which exhibits higher resistivity and nonlinearity. Nonlinearity is often undesired, but it is a valuable asset for unconventional computing, that is, for systems that do not follow the Turing model of computation [6][7][8][17][18][19] . Rather than excluding nonlinearity, we can exploit it 12 and manipulate our physical system with artificial evolution to solve computational problems 17 . This evolution in materio has been used, for example, for frequency distinguishing by liquid crystals 18 and robot control with carbon nanotubes 19 . We recently showed that a disordered network of gold...

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We investigate the role played by large diffeomorphisms of quantum isolated horizons for the statistics of loop quantum gravity (LQG) black holes by means of their relation to the braid group. To this aim the symmetries of Chern-Simons theory are recapitulated with particular regard to the aforementioned type of diffeomorphisms. For the punctured spherical horizon, these are elements of the mapping class group of S 2 , which is almost isomorphic to a corresponding braid group on this particular manifold. The mutual exchange of quantum entities in two dimensions is achieved by the braid group, rendering the statistics anyonic. With this we argue that the quantum isolated horizon model of LQG based on SUð2Þ k -Chern-Simons theory exhibits non-Abelian anyonic statistics. In this way a connection to the theory behind the fractional quantum Hall effect and that of topological quantum computation is established, where non-Abelian anyons play a significant role.

In this work we investigate the role played by large diffeomorphisms of quantum isolated horizons for the statistics of Loop Quantum Gravity black holes by means of their relation to the braid group. The mutual exchange of quantum entities in two dimensions is achieved by the braid group, rendering the statistics anyonic. With this we argue that the quantum isolated horizon model of LQG based on SU(2) k -Chern-Simons theory explicitly exhibits non-abelian anyonic statistics, since the quantum gravitational degrees of freedom of the horizon can be seen as flux-charge composites. In this way a connection to the theory behind the fractional quantum Hall effect and that of topological quantum computation is established, where non-abelian anyons play a significant role.