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The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues and eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such as quantum phase estimation because fully quantum algorithms require quantum hardware that will not be accessible in the near future. VQE has been successfully applied to solve the electronic Schr{o}dinger equation for a variety of small molecules. However, the scalability of this method is limited by two factors: the complexity of the quantum circuits and the complexity of the classical optimization problem. Both of these factors are affected by choice of the variational ansatz used to represent the trial wave function. Hence, the construction of efficacious ansatz is an active area of research. Put another way, modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatze for problems that map onto more than several qubits. In this review, we present recent developments in the field of designing effective ansatzes that fall into two categories -- chemistry inspired and hardware efficient -- that produce quantum circuits that are easier to run on modern hardware. We discuss the shortfalls of ansatzes originally formulated for VQE simulations, how they are addressed in more sophisticated methods, and the potential ways for further improvements.
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This short survey contains some recent developments of the algebraic theory of racks and quandles. We report on some elements of representation theory of quandles and ring theoretic approach to quandles.
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A review of the present status, recent enhancements, and applicability of the SIESTA program is presented. Since its debut in the mid-nineties, SIESTAs flexibility, efficiency and free distribution has given advanced materials simulation capabilities to many groups worldwide. The core methodological scheme of SIESTA combines finite-support pseudo-atomic orbitals as basis sets, norm-conserving pseudopotentials, and a real-space grid for the representation of charge density and potentials and the computation of their associated matrix elements. Here we describe the more recent implementations on top of that core scheme, which include: full spin-orbit interaction, non-repeated and multiple-contact ballistic electron transport, DFT+U and hybrid functionals, time-dependent DFT, novel reduced-scaling solvers, density-functional perturbation theory, efficient Van der Waals non-local density functionals, and enhanced molecular-dynamics options. In addition, a substantial effort has been made in enhancing interoperability and interfacing with other codes and utilities, such as Wannier90 and the second-principles modelling it can be used for, an AiiDA plugin for workflow automatization, interface to Lua for steering SIESTA runs, and various postprocessing utilities. SIESTA has also been engaged in the Electronic Structure Library effort from its inception, which has allowed the sharing of various low level libraries, as well as data standards and support for them, in particular the PSML definition and library for transferable pseudopotentials, and the interface to the ELSI library of solvers. Code sharing is made easier by the new open-source licensing model of the program. This review also presents examples of application of the capabilities of the code, as well as a view of on-going and future developments.
Radiogenic heating is a key component of the energy balance and thermal evolution of the Earth. It contributes to mantle convection, plate tectonics, volcanoes, and mountain building. Geo-neutrino observations estimate the present radiogenic power of our planet. This estimate depends on the quantity and distribution of heat-producing elements in various Earth reservoirs. Of particular geological importance is radiogenic heating in the mantle. This quantity informs the origin and thermal evolution of our planet. Here we present: currently reported geo-neutrino observations; estimates of the mantle geo-neutrino signal, mantle radiogenic heating, and mantle cooling; a comparison of chemical Earth model predictions of the mantle geo-neutrino signal and mantle radiogenic heating; a brief discussion of radiogenic heating in the core, including calculations of geo-neutrino signals per pW/kg; and finally a discussion of observational strategy.
Recent years have seen rapid developments in our knowledge and understanding of meson spectroscopy, especially in the charm quark sectors. In my invited overview I discussed some of these recent new developments, including theoretical developments, new production mechanisms such as B decays and double charmonium production, and the discovery of several of the many new candidates for excited charmonia, charm meson molecules, and hybrid (excited glue) mesons, in both charmonium and light quark sectors. In this writeup, due to length constraints I will restrict my discussion to a few examples of these new states, some of their broader theoretical implications, and future prospects.
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