19,017 research outputs found
Atomic-scale representation and statistical learning of tensorial properties
This chapter discusses the importance of incorporating three-dimensional
symmetries in the context of statistical learning models geared towards the
interpolation of the tensorial properties of atomic-scale structures. We focus
on Gaussian process regression, and in particular on the construction of
structural representations, and the associated kernel functions, that are
endowed with the geometric covariance properties compatible with those of the
learning targets. We summarize the general formulation of such a
symmetry-adapted Gaussian process regression model, and how it can be
implemented based on a scheme that generalizes the popular smooth overlap of
atomic positions representation. We give examples of the performance of this
framework when learning the polarizability and the ground-state electron
density of a molecule
Tools for Quantum Algorithms
We present efficient implementations of a number of operations for quantum
computers. These include controlled phase adjustments of the amplitudes in a
superposition, permutations, approximations of transformations and
generalizations of the phase adjustments to block matrix transformations. These
operations generalize those used in proposed quantum search algorithms.Comment: LATEX, 15 pages, Minor changes: one author's e-mail and one reference
numbe
- …