دانلود کتاب مقدمه‌ای بر پردازش اطلاعات کوانتومی

This book grew from lecture notes developed for the junior-level course Quantum Information Processing, which has been offered regularly to computer science, mathematics, physical sciences, and engineering ma- jors at the University of Central Florida since 2022. The course aims to introduce basis concepts, ideas, and methods in quantum information to undergraduates who had no previous exposition to quantum mechanics. Thus the prerequisites for the course are rather minimal: Physics I and II (calculus-based mechanics, electricity, magnetism, and optics), and Cal- culus with Analytic Geometry I, II, and III (derivatives, integrals, vectors fields, line and multiple integrals, simple ordinary differential equations, and matrices) or Matrix and Linear Algebra. At UCF, completing these courses marks the transition from sophomore to junior standing. The course is often taken by seniors as well. We follow the same approach of that course in this book and assume the reader knows no more than fundamental physics and mathematics at the junior level. The book attempts to be as self-contained as possi- ble and starts with a concise description of the historic and conceptual developments that led to quantum mechanics, from Planck’s black-body radiation to the Copenhagen interpretation. It then introduces vector spaces and operators utilizing Dirac’s notation to familiarize the reader with the mathematical formulation used in quantum mechanics. The last foundational step is a chapter with a formal presentation of quan- tum mechanics postulates. Chapters 5 to 9 cover key elements of quantum information with increasing level of complexity. After introducing qubits, gates and cir- cuits, Bloch sphere representation, and other basic concepts and tools, the book moves on to key results such as the non-cloning theorem, tele- portation, and quantum algorithms, from simple ones such as Deutsch’s to more complicated ones such as Shor’s and Grover’s. Those materials are the bulk of the course and the remaining chap- ters in the book are not always covered. The choice of which chapters to cover depends on the particular student cohort. For instance, when the majority of the students in the class is from computer science and en- gineering majors, chapters 10, 14, and 15 may be skipped. When the majority is from physics and optics & photonics, chapter 11 can be skipped and chapter 15 replaced by assigned term papers requiring a more detailed description of various physical realizations of qubits. It is also possible to skip certain sections in some chapters without compro- mising overall understanding. The book is organized in such a way that instructors adopting it in their courses may freely pick and choose what to cover according to the background and interests of their students. In the author’s own experience, it is actually quite difficult to cover all sections of all chapters in a 15-week term. All chapters but 12, 14, and 15 contain exercises to help students practice applying concepts and methods. These exercises were assigned as homework or featured in past mid-term and final exams. Solutions are provided only to instructors upon request. At several points in the course, Qiskit, a python library for simulat- ing and programming quantum computers, is used for practicing with quantum gates, quantum circuits, and for the graphical representation of Bloch spheres, circuits, quantum states and measurement outcomes. The book describes these activities; template codes are also available upon request. Python is such an accessible language that even students with very little familiarity with coding have been able to use the templates and complete the activities. An appendix explaining how to install and use Qiskit is included for convenience, but the reader should be aware that this package is constantly being updated, so the official online doc- umentation should be always checked first. Appendices are also included to help students with some linear alge- bra concepts and mathematical methods that are employed in the main text or are required for solving exercises. An appendix on the basics of computational complexity theory is also provided. This book does not attempt to be a comprehensive treatise of quan- tum information processing, which is now a vast and yet still rapidly evolving subject. Like in the course that inspired it, the goal of this book is to provide just enough information to prepare undergraduates for more specialized, higher-level courses, and for research and employment opportunities that require basic knowledge of the subject. The focus is primarily on quantum computation because it covers foundational mate- rial for both quantum communications and quantum sensing. Therefore, the latter two areas of quantum information processing are only sparsely touched in this first edition and will hopefully be enhanced in the future.