Anyons
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Fractional Statistics and Anyon Superconductivity
Part I: Concepts in fractional statistics, part II: States of anyon matter, part III: Reprinted papers
The Diverse World of PDEs
Author: I. S. Krasil′shchik
language: en
Publisher: American Mathematical Society
Release Date: 2023-08-23
This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13–17, 2021, at Independent University of Moscow and Moscow State University, Moscow, Russia. The papers reflect the modern interplay between partial differential equations and various aspects of algebra and computer science. The topics discussed are: relations between integrability and differential rings, supermanifolds, differential calculus over graded algebras, noncommutative generalizations of PDEs, quantum vector fields, generalized Nijenhuis torsion, cohomological approach to the geometry of differential equations, the argument shift method, Frölicher structures in the formal Kadomtsev–Petviashvili hierarchy, and computer-based determination of optimal systems of Lie subalgebras. The companion volume (Contemporary Mathematics, Volume 788) is devoted to Geometry and Mathematical Physics.
Quantum Computing
Author: Richard Skiba
language: en
Publisher: After Midnight Publishing
Release Date: 2025-03-09
Quantum computing is revolutionizing the way we approach computation, unlocking unprecedented capabilities that challenge the limits of classical computers. This book is a guide for anyone seeking to understand the complexities of this emerging field. Whether you are a student, researcher, or technology enthusiast, this book provides a comprehensive exploration of the core concepts, algorithms, hardware, and real-world applications of quantum computing. The book begins with a solid introduction to quantum mechanics, the foundational science that makes quantum computing possible. Readers will gain an understanding of key principles such as superposition, entanglement, and quantum interference—phenomena that enable quantum computers to process vast amounts of data in parallel. The discussion then shifts to qubits, the fundamental building blocks of quantum computation, explaining their physical implementations using superconducting circuits, trapped ions, photonic systems, and other technologies. As the book progresses, it delves into the architecture of quantum computing, covering quantum logic gates, circuit design, and universal gate sets that define how quantum computers perform calculations. It explores groundbreaking quantum algorithms such as Shor’s algorithm for factoring large numbers and Grover’s algorithm for quantum search, demonstrating how quantum computing achieves exponential speedup over classical methods. A key challenge in quantum computing is error correction and noise mitigation. This book provides an in-depth analysis of quantum error correction techniques, fault-tolerant computing, and strategies for overcoming decoherence and environmental noise, making it accessible even to readers without a deep background in physics. The discussion extends beyond theory to practical implementations, examining quantum hardware developed by leading technology companies such as IBM, Google, Microsoft, IonQ, and Rigetti. It also explores the role of quantum computing in cybersecurity, highlighting quantum cryptography, post-quantum encryption, and quantum key distribution protocols that ensure secure communications. The latter sections of the book showcase real-world applications of quantum computing in fields such as artificial intelligence, drug discovery, climate modelling, financial modelling, and supply chain optimization. It also covers cloud-based quantum computing services like IBM Quantum Experience, Google Quantum AI, and Amazon Braket, providing insights into how organizations can leverage quantum computing without owning expensive quantum hardware. With an eye toward the future, Quantum Computing: Fundamental Principles of Quantum Computing Systems examines the ongoing challenges and expected advancements in the field, offering predictions on the evolution of quantum computing over the next two decades. This book is an indispensable resource for understanding one of the most exciting technological frontiers of our time.