The goal of this pedagogical article is to describe for IT engineering researchers and master course students main mathematical operations with matrices and linear operators used in quantum computing and quantum information theory. These operations are defined in the framework of linear algebra and therefore for their understanding there is no need to introduce physical background of quantum mechanics.
The goal of this pedagogical article is to describe for IT engineering researchers and master course students main mathematical operations with matrices and linear operators used in quantum computing and quantum information theory. These operations are defined in the framework of linear algebra and therefore for their understanding there is no need to introduce physical background of quantum mechanics.
В статье представлен краткий обзор современных достижений в квантовой информатике, проблем и перспектив развития квантовых вычислений. Обсуждаются элементарная математическая модель квантовых вычислений и понятие квантового превосходства. Рассматривается применение ультрахолодных атомов для реализации квантовых процессоров. The article provides a brief overview of modern achievements in quantum information science, problems and prospects for the development of quantum computing. The elementary mathematical model of quantum computing and the concept of quantum supremacy are discussed. The use of ultracold atoms for the implementation of quantum processors is considered.
This book is intended as an introductory textbook at graduate or advanced undergraduate level. Students with diverse backgrounds, in mathematics, physics and computer science, can use it to become acquainted with the quantum theory of information. Its scope is deliberately chosen to be not too broad, while being self-consistent and usable for a semester-long course for beginners. The subject is presented using a balanced mix of intuitive arguments and rigorous formalism. The emphasis is not on the physical interpretation, but rather on the formal and mathematical features of quantum information theory, in order to be accessible from different backgrounds, the only requirement being a basic knowledge of linear algebra. In particular, a background in quantum mechanics is not needed, since quantum theory is used as a mere mathematical framework without entering into physical interpretations. The book introduces all necessary concepts from quantum theory and classical information theory, to cover the elements of quantum Shannon theory: quantum states and channels, data compression and entropy, error correcting codes and channel capacities, as well as the basics of entanglement theory and quantum cryptography. Examples are provided to help the reader in understanding the different concepts, together with exercises at the end of each chapter.
Abstract Quantum Computing and Quantum Physics: A Linear Algebra Approach provides a distinctive and accessible introduction to the rapidly growing fields of quantum information science and quantum computing. The book is designed for undergraduate students with little or no background in physics but with some familiarity with linear algebra. Higher education faculty members and secondary school mathematics, physics, and computer science educators who want to learn about quantum computing and perhaps teach a course accessible to students with wide ranging backgrounds will also find the book useful and enjoyable. While broadly accessible, the book does not dodge providing a solid conceptual and formal understanding of quantum states and entanglement—the key ingredients in quantum computing. The authors dish up a hearty meal for the readers, disentangling and explaining many of the classic quantum algorithms that demonstrate how and when quantum computing has an advantage over classical computers. The book is spiced with Try Its, brief exercises that engage the readers and help them digest the many counterintuitive quantum information science and quantum computing concepts. Self-contained chapters on time dependence in quantum mechanics, magnetic resonance, density matrices, simple harmonic oscillator, quantum perturbation theory, and number operators provide a basis for further reading and work in quantum information science and quantum computing.
Important concepts from the diverse fields of physics, mathematics, engineering and computer science coalesce in this foundational text on the cutting-edge field of quantum information. Designed for undergraduate and graduate students with any STEM background, and written by a highly experienced author team, this textbook draws on quantum mechanics, number theory, computer science technologies, and more, to delve deeply into learning about qubits, the building blocks of quantum information, and how they are used in quantum computing and quantum algorithms. The pedagogical structure of the chapters features exercises after each section as well as focus boxes, giving students the benefit of additional background and applications without losing sight of the big picture. Recommended further reading and answers to select exercises further support learning. Written in approachable and conversational prose, this text offers a comprehensive treatment of the exciting field of quantum information while remaining accessible to students and researchers within all STEM disciplines.
Abstract With this chapter, we begin to transit from digital information processing to quantum information processing. However, to be able to master this transition, we first need to familiarize ourselves with quantum mechanical principles and the mathematics used to describe them. Since we already know about abstract state spaces, tensor products, and Hamiltonian operators and their eigenvectors and eigenvalues, this should not be too difficult or too alien. And yet, there remain a few challenges: Mathematical descriptions of quantum states usually involve the Dirac notation, require complex linear algebra in high dimensional spaces, and encode unintuitive probabilistic interpretations. Rising to these challenges, we briefly study the notion of Hilbert spaces, introduce the Dirac notation, and discuss the axioms of quantum mechanics and some of their consequences. All this will admittedly be dense and abstract but prepare us for everything that is still to follow. Our main goal is to emphasize that quantum mechanics and therefore quantum computing is just complex linear algebra in very high dimensional spaces so that quantum computing needs a different kind of thinking than we are used to in digital computing.
Important concepts from the diverse fields of physics, mathematics, engineering and computer science coalesce in this foundational text on the cutting-edge field of quantum information. Designed for undergraduate and graduate students with any STEM background, and written by a highly experienced author team, this textbook draws on quantum mechanics, number theory, computer science technologies, and more, to delve deeply into learning about qubits, the building blocks of quantum information, and how they are used in quantum computing and quantum algorithms. The pedagogical structure of the chapters features exercises after each section as well as focus boxes, giving students the benefit of additional background and applications without losing sight of the big picture. Recommended further reading and answers to select exercises further support learning. Written in approachable and conversational prose, this text offers a comprehensive treatment of the exciting field of quantum information while remaining accessible to students and researchers within all STEM disciplines.