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This article gives an elementary introduction to quantum computing. It is a draft for a book chapter of the "Handbook of Nature-Inspired and Innovative Computing", Eds. A. Zomaya, G.J. Milburn, J. Dongarra, D. Bader, R. Brent, M.…
The history of computer science and brain sciences are intertwined. In his unfinished manuscript "The Computer and the Brain," von Neumann debates whether or not the brain can be thought of as a computing machine and identifies some of the…
We develop in detail most of the theory of the Picard scheme that Grothendieck sketched in two Bourbaki talks and in commentaries on them. Also, we review in brief much of the rest of the theory developed by Grothendieck and by others. But…
Computational mechanics is a method for discovering, describing and quantifying patterns, using tools from statistical physics. It constructs optimal, minimal models of stochastic processes and their underlying causal structures. These…
Drawing independent samples from a probability distribution is an important computational problem with applications in Monte Carlo algorithms, machine learning, and statistical physics. The problem can in principle be solved on a quantum…
The purpose of this report is to show that computer and allied technologies can be used to increase energy efficiency. The report is divided into transport, industrial, commercial and domestic sections, which correspond to the major energy…
The recent development in analog computation is reviewed in this paper. Analog computation was used in many applications where power and energy efficiency is of paramount importance. It is shown that by using innovative architecture and…
Despite rapid progress in the field, it is still challenging to discover new ways to take advantage of quantum computation: all quantum algorithms need to be designed by hand, and quantum mechanics is notoriously counterintuitive. In this…
Gibbs sampling is fundamental to a wide range of computer algorithms. Such algorithms are set to be replaced by physics based processors$-$be it quantum or stochastic annealing devices$-$which embed problem instances and evolve a physical…
A computer model of "a sense of humour" suggested previously [arXiv:0711.2058,0711.2061], relating the humorous effect with a specific malfunction in information processing, is given in somewhat different exposition. Psychological aspects…
Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction…
This is a set of lecture notes suitable for a Master's course on quantum computation and information from the perspective of theoretical computer science. The first version was written in 2011, with many extensions and improvements in…
In the last few years, theoretical study of quantum systems serving as computational devices has achieved tremendous progress. We now have strong theoretical evidence that quantum computers, if built, might be used as a dramatically…
Quantum computers have the potential to expand the utility of lattice gauge theory to investigate non-perturbative particle physics phenomena that cannot be accessed using a standard Monte Carlo method due to the sign problem. Thanks to the…
It's hard to imagine human life in the digital and AI age without polynomials because they are everywhere but mostly invisible to ordinary people: in data trends, on computer screens, in the shapes around us, and in the very fabric of…
In the words of the esteemed mathematician Paul Erd\"os, the mathematician's task is to \emph{prove and conjecture}. These two processes form the bedrock of all mathematical endeavours, and in the recent years, the mathematical community…
Many aspects of Schubert calculus are easily modeled on a computer. This enables large-scale experimentation to investigate subtle and ill-understood phenomena in the Schubert calculus. A well-known web of conjectures and results in the…
We study how the paradigm of Newton's science, based on the organization of scientific knowledge as a series of mathematical laws, was definitively accepted in science courses - in the last decades of the XVIII century, in England as well…
With traditional computing technologies reaching their limit, a new field has emerged seeking to follow the example of the human brain into a new era: neuromorphic computing. This paper provides an introduction to neuromorphic computing,…
This essay examines how what is considered to be artificial intelligence (AI) has changed over time and come to intersect with the expertise of the author. Initially, AI developed on a separate trajectory, both topically and…