In this book, we introduce quantum computation and its application to AI. We highlight problem solving and knowledge representation framework. Based on information theory, we cover two main principles of quantum computation - Quantum Fourier transform and Grover search. Then, we indicate how these two principles can be applied to problem solving and finally present a general model of a quantum computer that is based on production systems.

Highly topical and original monograph, introducing the author's work on the Riemann zeta function and its adelic interpretation of interest to a wide range of mathematicians and physicists.

Quantum physics has, on the one hand, drastically changed our theoretical description of the physical world and has, on the other hand, revolutionized everyday life, by allowing us to build lasers, atomic clocks used in GPS, and semiconductor-based devices such as laptop computers and smartphones. The object of this book is to give a self-contained introduction to both aspects. It contains a detailed account of the foundational principles: superposition, entanglement, quantum non-locality, decoherence and measurement theory, and of some selected applications: quantum cryptography and quantum computers, cold atoms, light emitting and laser diodes, and atomic clocks. The book is aimed at a general audience and the only prerequisite is a high-school background in mathematics.

Quantum physics has, on the one hand, drastically changed our theoretical description of the physical world and has, on the other hand, revolutionized everyday life, by allowing us to build lasers, atomic clocks used in GPS, and semiconductor-based devices such as laptop computers and smartphones. The object of this book is to give a self-contained introduction to both aspects. It contains a detailed account of the foundational principles: superposition, entanglement, quantum non-locality, decoherence and measurement theory, and of some selected applications: quantum cryptography and quantum computers, cold atoms, light emitting and laser diodes, and atomic clocks. The book is aimed at a general audience and the only prerequisite is a high-school background in mathematics.

Dimensional and order-of-magnitude estimates are practiced by almost everybody but taught almost nowhere. When physics students engage in their first theoretical research project, they soon learn that exactly solvable problems belong only to textbooks, that numerical models are long and resource consuming, and that "something else" is needed to quickly gain insight into the system they are going to study. Qualitative methods are this "something else", but typically, students have never heard of them before.The aim of this book is to teach the craft of qualitative analysis using a set of problems, some with solutions and some without, in advanced undergraduate and beginning graduate Quantum Mechanics. Examples include a dimensional analysis solution for the spectrum of a quartic oscillator, simple WKB formulas for the matrix elements of a coordinate in a gravitational well, and a three-line-long estimate for the ionization energy of atoms uniformly valid across the whole periodic table. The piece de resistance in the collection is a series of dimensional analysis questions in Integrable Nonlinear Partial Differential Equations with no dimensions existing a priori. Solved problems include the relationship between the size and the speed of solitons of the Korteweg-de Vries equation and an expression for the oscillation period of a Nonlinear Schroedinger breather as a function of its width.

This volume, written by a highly cited author, presents the history of quantum theory together with open questions and remaining problems in terms of the plausibility of quantum chemistry and physics. It also provides insights into the theory of matter-wave mechanics. The content is aimed at students and lecturers in chemistry, physics and the philosophy of science.

In this work, the interaction between the Higgs boson and the top quark is studied with the proton-proton collisions at 13 TeV provided by the LHC at the CMS detector at CERN (Geneva). At the LHC, these particles are produced simultaneously via the associate production of the Higgs boson with one top quark (tH process) or two top quarks (ttH process). Compared to many other possible outcomes of the proton-proton interactions, these processes are very rare, as the top quark and the Higgs boson are the heaviest elementary particles known. Hence, identifying them constitutes a significant experimental challenge. A high particle selection efficiency in the CMS detector is therefore crucial. At the core of this selection stands the Level-1 (L1) trigger system, a system that filters collision events to retain only those with potential interest for physics analysis. The selection of hadronically decaying leptons, expected from the Higgs boson decays, is especially demanding due to the large background arising from the QCD interactions. The first part of this thesis presents the optimization of the L1 algorithm in Run 2 (2016-2018) and Run 3 (2022-2024) of the LHC. It includes the development of a novel trigger concept for the High-Luminosity LHC, foreseen to start in 2027 and to deliver 5 times the current instantaneous luminosity. To this end, sophisticated algorithms based on machine learning approaches are used, facilitated by the increasingly modern technology and powerful computation of the trigger system. The second part of the work presents the search of the tH and ttH processes with the subsequent decays of the Higgs boson to pairs of lepton, W bosons or Z bosons, making use of the data recorded during Run 2. The presence of multiple particles in the final state, along with the low cross section of the processes, makes the search an ideal use case for multivariant discriminants that enhance the selectivity of the signals and reject the overwhelming background contributions. The discriminants presented are built using state-of-the-art machine learning techniques, able to capture the correlations amongst the processes involved, as well as the so-called Matrix Element Method (MEM), which combines the theoretical description of the processes with the detector resolution effects. The level of sophistication of the methods used, along with the unprecedented amount of collision data analyzed, result in the most stringent measurements of the tH and ttH cross sections up to date.

The functional formulation of quantum mechanics and relativistic quantum field theories are widely studied subjects. Nevertheless, certain aspects of this formulation are frequently overlooked, in spite of their relevance from a structural point of view. This book aims to fill up this gap. The non-relativistic regime has been found particularly appropriate for these purposes.

Yang-Mills gravity is a new theory, consistent with experiments, that brings gravity back to the arena of gauge field theory and quantum mechanics in flat space-time. It provides solutions to long-standing difficulties in physics, such as the incompatibility between Einstein's principle of general coordinate invariance and modern schemes for a quantum mechanical description of nature, and Noether's 'Theorem II' which showed that the principle of general coordinate invariance in general relativity leads to the failure of the law of conservation of energy. Yang-Mills gravity in flat space-time appears to be more physically coherent than conventional gravity in curved space-time. The problems of quantization of the gravitational field, the operational meaning of space-time coordinates and momenta, and the conservation of energy-momentum are all resolved in Yang-Mills gravity.The aim of this book is to provide a treatment of quantum Yang-Mills gravity, with an emphasis on the ideas and evidence that the gravitational field is the manifestation of space-time translational symmetry in flat space-time, and that there exists a fundamental space-time symmetry framework that can encompass all of physics, including gravity, for all inertial and non-inertial frames of reference.

This volume is based on lectures given during the program "Complex Quantum Systems" held at the National University of Singapore's Institute for Mathematical Sciences from 17 February to 27 March 2010. It guides the reader through two introductory expositions on large Coulomb systems to five of the most important developments in the field: derivation of mean field equations, derivation of effective Hamiltonians, alternative high precision methods in quantum chemistry, modern many-body methods originating from quantum information, and - the most complex - semirelativistic quantum electrodynamics. These introductions are written by leaders in their fields; amongst them are Volker Bach, Rafael Benguria, Thomas Chen, and Jan Philip Solovej. Together, they fill a gap between current textbooks and the vast modern literature on complex quantum systems.

This book focuses on AdS3/CFT2, addressing different aspects of this correspondence in field theory and in gravity, including entanglement entropy, higher genus partition function, and conformal block. Holographic entanglement entropy is an important area in holographic and quantum information, which implies a deep relation between geometry and quantum entanglement. In this book, the authors use holographic entanglement entropy as a tool to investigate AdS3/CFT2. They study the entanglement entropy at high temperature in field theory and in holographics, and show that the results match each other in classical and one-loop order. In the AdS3/CFT2 system, they examine in detail the correspondence, exploring the higher genus partition function, entanglement entropy in a general system and conformal block, and they find good correspondence in field theory and gravity. The result strongly supports AdS3/CFT2 correspondence. In addition, they develop several important techniques in 2d CFT and 3d gravity, which also offer inspiration for other fields.

If there is a central conceptual framework that has reliably borne the weight of modern physics as it ascends into the twenty-first century, it is the framework of quantum mechanics. Because of its enduring stability in experimental application, physics has today reached heights that not only inspire wonder, but arguably exceed the limits of intuitive vision, if not intuitive comprehension. For many physicists and philosophers, however, the currently fashionable tendency toward exotic interpretation of the theoretical formalism is recognized not as a mark of ascent for the tower of physics, but rather an indicator of sway-one that must be dampened rather than encouraged if practical progress is to continue. In this unique two-part volume, designed to be comprehensible to both specialists and non-specialists, the authors chart out a pathway forward by identifying the central deficiency in most interpretations of quantum mechanics: That in its conventional, metrical depiction of extension, inherited from the Enlightenment, objects are characterized as fundamental to relations-i.e., such that relations presuppose objects but objects do not presuppose relations. The authors, by contrast, argue that quantum mechanics exemplifies the fact that physical extensiveness is fundamentally topological rather than metrical, with its proper logico-mathematical framework being category theoretic rather than set theoretic. By this thesis, extensiveness fundamentally entails not only relations of objects, but also relations of relations. Thus, the fundamental quanta of quantum physics are properly defined as units of logico-physical relation rather than merely units of physical relata as is the current convention. Objects are always understood as relata, and likewise relations are always understood objectively. In this way, objects and relations are coherently defined as mutually implicative. The conventional notion of a history as "a story about fundamental objects" is thereby reversed, such that the classical "objects" become the story by which we understand physical systems that are fundamentally histories of quantum events. These are just a few of the novel critical claims explored in this volume-claims whose exemplification in quantum mechanics will, the authors argue, serve more broadly as foundational principles for the philosophy of nature as it evolves through the twenty-first century and beyond.

Quantum Chromodynamics (QCD) is the most up-to-date theory of the strong interaction. Its predictions have been verified experimentally, and it is a cornerstone of the Standard Model of particle physics. However, standard perturbative procedures fail if applied to low-energy QCD. Even the discovery of the Higgs Boson will not solve the problem of masses originating from the non-perturbative behavior of QCD. This book presents a new method, the introduction of the mass gap', first suggested by Arthur Jaffe and Edward Witten at the turn of the millennium. It attempts to show that, to explain the mass-spectrum of QCD, one needs the mass scale parameter (the mass gap) instead of other massive particles. The energy difference between the lowest order and the vacuum state in Yang-Mills quantum field theory, the mass gap is in principle responsible for the large-scale structure of the QCD ground state, and thus also for its non-perturbative phenomena at low energies. This book not only presents the mass gap, but also details the applications and outlook of the mass gap method. A detailed summary of references and problems are included as well. This book is best for scientists and highly advanced students interested in non-perturbative effects and methods in QCD.

This is a collection of articles on fundamental physical principles and methods, the topics ranging from matrix models, random surfaces, quantum dots and rings, to black holes, cosmology and testing of the tiny effects predicted by General Relativity. Among the authors are Sir Roger Penrose and other well-known experts and the articles are addressed to graduate students and researchers. The volume is a Festschrift to a noted physicist and mentor Sergei Matinyan.

This volume is based on the fifth international conference of quantum bio-informatics held at the QBI Center of Tokyo University of Science.This volume provides a platform to connect mathematics, physics, information and life sciences, and in particular, research for new paradigm for information science and life science on the basis of quantum theory.The following topics are discussed:

Following the emergence of quantum computing, the subsequent quantum revolution will be that of interconnecting individual quantum computers at the global level. In the same way that classical computers only realised their full potential with the emergence of the internet, a fully-realised quantum internet is the next stage of evolution for quantum computation. This cutting-edge book examines in detail how the quantum internet would evolve in practise, focusing not only on the technology itself, but also the implications it will have economically and politically, with numerous non-technical sections throughout the text providing broader context to the discussion. The book begins with a description of classical networks before introducing the key concepts behind quantum networks, such as quantum internet protocols, quantum cryptography, and cloud quantum computing. Written in an engaging style and accessible to graduate students in physics, engineering, computer science and mathematics.

The aim of the book is to give a coherent and comprehensive account of quantum scattering theory with applications to atomic, molecular and nuclear systems. The motivation for this is to supply the necessary theoretical tools to calculate scattering observables of these many-body systems. Concepts which are seemingly different for atomic/molecular scattering from those of nuclear systems, are shown to be the same once physical units such as energy and length are diligently clarified. Many-body resonances excited in nuclear systems are the same as those in atomic systems and come under the name of Feshbach resonances. We also lean heavily on semi-classical methods to explain the physics of quantum scattering -- especially the interference seen in the angle dependence of the cross section. Having in mind a wide readership, the book includes sections on scattering in two dimensions which is of use in surface physics. Several problems are also included at the end of each of the chapters.

Time decays form the basis of a multitude of important and interesting phenomena in quantum physics that range from spectral properties, resonances, return and approach to equilibrium, to quantum mixing, dynamical stability properties and irreversibility and the "arrow of time".This monograph is devoted to a clear and precise, yet pedagogical account of the associated concepts and methods.

This book contains exclusively invited contributions from collaborators of Maximilian Kreuzer, giving accounts of his scientific legacy and original articles from renowned theoretical physicists and mathematicians, including Victor Batyrev, Philip Candelas, Michael Douglas, Alexei Morozov, Joseph Polchinski, Peter van Nieuwenhuizen, and Peter West.Besides a collection of review and research articles from high-profile researchers in string theory and related fields of mathematics (in particular, algebraic geometry) which discuss recent progress in the exploration of string theory vacua and corresponding mathematical developments, this book contains a pedagogical account of the important work of Brandt, Dragon, and Kreuzer on classification of anomalies in gauge theories. This highly cited work, which is also quoted in the textbook of Steven Weinberg on quantum field theory, has not yet been presented in full detail except in private lecture notes by Norbert Dragon.Similarly, the software package PALP (Package for Analyzing Lattice Polytopes with applications to toric geometry), which has been incorporated in the SAGE (Software for Algebra and Geometry Experimentation) project, has not yet been documented in full detail. This book contains a user manual for a new thoroughly revised version of PALP.By including these two very useful original contributions, researchers in quantum field theory, string theory, and mathematics will find added value in a pedagogical presentation of the classification of quantum gauge field anomalies, and the accompanying comprehensive manual and tutorial for the powerful software package PALP.

As the twenty-first century progresses, plasma technology will play an increasing role in our lives, providing new sources of energy, ion-plasma processing of materials, wave electromagnetic radiation sources, space plasma thrusters, and more. Studies of the plasma state of matter not only accelerate technological developments but also improve the understanding of natural phenomena. Beginning with an introduction to the characteristics and types of plasmas, Introduction to Plasma Dynamics covers the basic models of classical diffuse plasmas used to describe such phenomena as linear and shock waves, stationary flows, elements of plasma chemistry, and principles of plasma lasers. The author presents specific examples to demonstrate how to use the models and to familiarize readers with modern plasma technologies. The book describes structures of magnetic fields-one- and zero-dimensional plasma models. It considers single-, two-, and multi-component simulation models, kinetics and ionization processes, radiation transport, and plasma interaction with solid surfaces. The text also examines self-organization and general problems associated with instabilities in plasma systems. In addition, it discusses cosmic plasma dynamic systems, such as Earth's magnetosphere, spiral nebulas, and plasma associated with the Sun. This text provides wide-range coverage of issues related to plasma dynamics, with a final chapter addressing advanced plasma technologies, including plasma generators, plasma in the home, space propulsion engines, and controlled thermonuclear fusion. It demonstrates how to approach the analysis of complex plasma systems, taking into account the diversity of plasma environments. Presenting a well-rounded introduction to plasma dynamics, the book takes into consideration the models of plasma phenomena and their relationships to one another as well as their applications.

The principal goal of this book is to provide state-of-the-art coverage of the non-relativistic three- and four-body theories at intermediate and high energy ion-atom and ion-molecule collisions. The focus is on the most frequently studied processes: electron capture, ionization, transfer excitation and transfer ionization. The content is suitable both for graduate students and experienced researchers. For these collisions, the literature has seen enormous renewal of activity in the development and applications of quantum-mechanical theories. This subject is of relevance in several branches of science and technology, like accelerator-based physics, the search for new sources of energy and high temperature fusion of light ions. Other important applications are in life sciences via medicine, where high-energy ion beams are used in radiotherapy for which a number of storage ring accelerators are in full operation, under construction or planned to be built worldwide. Therefore, it is necessary to review this field for its most recent advances with an emphasis on the prospects for multidisciplinary applications.

This book is a collection of lecture notes from the Symposium on Quantum Computing, Thermodynamics, and Statistical Physics, held at Kinki University in March 2012. Quantum information theory has a deep connection with statistical physics and thermodynamics. This volume introduces some of the topics on interface among the mentioned fields. Subjects included in the lecture notes include quantum annealing method, nonequilibrium thermodynamics and spin glass theory, among others. These subjects were presented with much emphasis put in its relevance in quantum information theory. These lecture notes are prepared in a self-contained manner so that a reader with modest background may understand the subjects.

This book is a collection of lecture notes and contributions in "Summer School on Diversities in Quantum Computation/Information" held on 1-5 August, 2010 at U-Community Hotel, Higashi-Osaka, Japan. Lecturers are world class authorities in respective areas in quantum information and quantum computing including physics, mathematics, chemistry and information science. They lectured on cutting-edge research frontiers where they are currently working, including quantum error correction, relativistic quantum information, quantum computing of link polynomials, quantum algorithms, etc. Each lecture note is written in a self-contained manner so that it may be used as a textbook for one semester graduate course or advanced undergraduate course. Contributions report current research subjects also in a self-contained manner. We believe that these articles are accessible to the readers form various disciplines.

This book contains advanced subjects in solid state physics with emphasis on the theoretical exposition of various physical phenomena in solids using quantum theory, hence entitled "A modern course in the quantum theory of solids". The use of the adjective "modern" in the title is to reflect the fact that some of the new developments in condensed matter physics have been included in the book. The new developments contained in the book are mainly in experimental methods (inelastic neutron scattering and photoemission spectroscopy), in magnetic properties of solids (the itinerant magnetism, the superexchange, the Hubbard model, and giant and colossal magnetoresistance), and in optical properties of solids (Raman scattering). Besides the new developments, the Green's function method used in many-body physics and the strong-coupling theory of superconductivity are also expounded in great detail.

This book is a collection of contributions to the Symposium on Interface between Quantum Information and Statistical Physics held at Kinki University in November 2011. Subjects of the symposium include quantum adiabatic computing, quantum simulator using bosons, classical statistical physics, among others. Contributions to this book are prepared in a self-contained manner so that a reader with a modest background may understand the subjects.