Related papers: A generic tool to evaluate second quantization
Quantifier elimination (QE) is an important problem that has numerous applications. Unfortunately, QE is computationally very hard. Earlier we introduced a generalization of QE called $\mathit{partial}$ QE (or PQE for short). PQE allows to…
Conventional AI evaluation approaches concentrated within the AI stack exhibit systemic limitations for exploring, navigating and resolving the human and societal factors that play out in real world deployment such as in education, finance,…
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…
Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced,…
Quantum theory provides an extremely accurate description of fundamental processes in physics. It thus seems likely that the theory is applicable beyond the, mostly microscopic, domain in which it has been tested experimentally. Here we…
In this introductory review, we focus on applications of quantum computation to problems of interest in physics and chemistry. We describe quantum simulation algorithms that have been developed for electronic-structure problems,…
General method is suggested to find non-relativistic and relativistic matrix elements of one- and two-electron operators for any number of open shells in atom, requiring neither coefficients of fractional parentage nor unit tensors. It is…
These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…
We firstly show that the standard interpretation of natural quantification in mathematical logic does not provide a satisfying account of its original richness. In particular, it ignores the difference between generic and distributive…
Increasingly sophisticated programmable quantum simulators and quantum computers are opening unprecedented opportunities for exploring and exploiting the properties of highly entangled complex quantum systems. The complexity of large…
Harmonic inversion techniques have been shown to be a powerful tool for the semiclassical quantization and analysis of quantum spectra of both classically integrable and chaotic dynamical systems. Various computational procedures have been…
Quantum mechanics is a challenging subject, even for advanced undergraduate and graduate students. Here, we discuss the development and evaluation of research-based concept tests for peer instruction as a formative assessment tool in…
Most continuous mathematical formulations arising in science and engineering can only be solved numerically and therefore approximately. We shall always assume that we're dealing with a numerical approximation to the solution. There are two…
Refined Algebraic Quantization and Group Averaging are powerful methods for quantizing constrained systems. They give constructive algorithms for generating observables and the physical inner product. This work outlines the current status…
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent…
Accurate models for open quantum systems -- quantum states that have non-trivial interactions with their environment -- may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction…
Second-order quantifier-elimination is the problem of finding, given a formula with second-order quantifiers, a logically equivalent first-order formula. While such formulas are not computable in general, there are practical algorithms and…
By quantum calibration we name an experimental procedure apt to completely characterize an unknown measurement apparatus by comparing it with other calibrated apparatuses. Here we show how to achieve the calibration of an arbitrary…
The idea to use quantum mechanical devices to simulate other quantum systems is commonly ascribed to Feynman. Since the original suggestion, concrete proposals have appeared for simulating molecular and materials chemistry through quantum…
Quantum mechanical methods have been devised for the elucidation and clarification of reaction paths of chemical processes over decades. While they are typically deployed in routine calculations on systems for which some insights have…