The speed of quantum and classical learning for performing the kth root of NOT

We consider quantum learning machines—quantum computers that modify themselves in order to improve their performance in some way—that are trained to perform certain classical task, i.e. to execute a function that takes classical bits as input and returns classical bits as output. This allows a fair comparison between learning efficiency of quantum and classical learning machines in terms of the number of iterations required for completion of learning. We find an explicit example of the task for which numerical simulations show that quantum learning is faster than its classical counterpart. The task is extraction of the kth root of NOT (NOT = logical negation), with k=2m and... The reason for this speed-up is that the classical machine requires memory of size log k=m to accomplish the learning, while the memory of a single qubit is sufficient for the quantum machine for any k.We acknowledge support from the EC Project QAP (no. 015848), the Austrian Science Foundation FWF within projects no. P19570-N16, SFB and CoQuS no. W1210-N16, the Ministerio de Ciencia e Innovación (Fellowship BES-2006-13234) and the Instituto Carlos I for the use of computational resources. The collaboration is a part of an ÖAD/MNiSW program

Reconsidering the Tribal-State Compact Process

This essay evaluates the tribal‐state compact process, as one of several alternative, nonadversarial processes, warranting attention. It argues that, because of its binding character and relatively low cost (in contrast to litigation), and because it is based in the idea of tribes and states exhibiting mutual respect, the compact process is an advanced version of negotiation and bargaining that tribes and states should consider where appropriate

Valuations on lattice polytopes

This survey is on classification results for valuations defined on lattice polytopes that intertwine the special linear group over the integers. The basic real valued valuations, the coefficients of the Ehrhart polynomial, are introduced and their characterization by Betke and Kneser is discussed. More recent results include classification theorems for vector and convex body valued valuations. © Springer International Publishing AG 2017

The geometry of quantum learning

Concept learning provides a natural framework in which to place the problems solved by the quantum algorithms of Bernstein-Vazirani and Grover. By combining the tools used in these algorithms-quantum fast transforms and amplitude amplification-with a novel (in this context) tool-a solution method for geometrical optimization problems-we derive a general technique for quantum concept learning. We name this technique "Amplified Impatient Learning" and apply it to construct quantum algorithms solving two new problems: Battleship and Majority, more efficiently than is possible classically.X1136sciescopu

CATION DIFFUSION AT THE POLYMER COATING/METAL INTERFACE

Theoretical and experimental studies were carried out on the transport of cations in the channel between a polymer coating and a metal substrate from a defect in the absence of an applied electrical potential. The model consists of two stages: an initial period during which ions diffuse in the coating/metal interfacial 'channel' and adsorb on the coating surface, and a propagation period during which ions also diffuse into the coating. The mathematical models were solved to predict the cation concentration and flux under the coating and the relative rate of diffusion between the initial and propagation periods. Model parameter values were derived from the results of an experiment conducted in a specially designed diffusion cell. The experiment measured the depletion of Naf ions in a cylindrical, central reservoir, which was placed within the perimeter of a defect through the coating of an epoxy-coated steel panel. Model predictions of concentration versus time agreed well with the experimental results, which showed that most of Naf ions were removed by lateral diffusion from the reservoir during the initial period. Further, the transport during the initial period was much faster than that during the propagation period. The results also indicated that during the propagation period, the rate-limiting step was the lateral diffusion along the coating/metal interface rather than diffusion through the coating