دانلود کتاب محاسبات کوانتومی از هاپفیلد نتس -کتاب درسی با مثال‌های کد پایتون

This book is intended for students of computer science who are looking for a gentle introduction to the world of quantum computing. More specifically, it is written for readers who have basic knowledge of Artificial Intelligence (AI) and Machine Learning (ML) and are passingly familiar with search algorithms, optimization techniques, and neural networks. This is not because we are interested in quantum AI or quantum ML but because our basic premise is that there exists a conceptual bridge between certain AI/ML models and certain quantum computing models. Our purpose in this book is therefore (1) to revisit these AI/ML models and their applications and (2) to build on this familiar foundation to segue into the study of quantum computing and its possible use cases. Our presentation is technical but pragmatic and practice oriented. We cover theory to the necessary extent but largely proceed in an example-driven manner. Most of our examples are concerned with combinatorial optimization and consider prob-lems that can be cast as quadratic unconstrained binary optimization problems. Numerous Python/NumPy/SciPy codes will support our mathematical discussion and demonstrate how to put theory into practice. Quantum computers harness quantum mechanical effects such as superposition, entanglement, or quantum tunneling for information processing. When used cleverly, this allows for levels of computational efficiency which are unreachable with digital computers. Indeed, quantum computing algorithms can generally be expected to be at least quadratically faster than their classical counterparts. For certain problems, there can be even up to exponential speedup. This is of course of interest in a world with ever growing demand for efficient number crunching. The theoretical foundations of quantum computing were first established in the 1980s and substantial theoretical progress happened in the 1990s. Technical progress, on the other hand, was a longer time coming and only became noteworthy in the 2010s. But by now we are living in a world where there exist working quantum computers. Granted, at the time of writing this book, these are of still limited capabil-ities but they demonstrate that quantum computing is feasible and progress is evident. It therefore comes as little surprise that more and more researchers and industrial players are excited about quantum algorithms and their potential applications. The above then begs the questions of why quantum computing has not yet received widespread attention in mainstream computer science and why it is not yet widely taught at computer science departments. Well, while quantum computing offers great computational power, it also requires a different kind of thinking than digital computing. Indeed, experience shows that there are at least three major obstacles for a broader engagement with the topic: 1. Quantum mechanical phenomena appear to be weird, abstract, and hard to accept for they mainly manifest on sub-atomic scales and cannot be observed in our daily environments. 2. The mathematical tools used for modeling these phenomena are complex (no pun intended) and again rather abstract. 3. To the uninitiated, the mathematical notation used in the quantum computing literature appears even more abstract and needs getting used to. With this book, we try to rise to the challenge and go on an extended journey towards understating core concepts of quantum computing. Our journey starts in territory far away from quantum mechanics but first (re)visits areas more familiar to computer scientists before it ends in the realm of applied quantum physics. Along the way, we are going to encounter familiar ideas and models as well as rather abstract mathematical concepts and physical principles. The latter are only rarely considered in mainstream computer science but will turn out to be fundamental to theory and practice of quantum computing. Put less prosaically, we structure the material in this book into three major parts: Preliminaries, Hopfield Nets, and Quantum Computing. Hopfield nets are a venerable family of rather simple recurrent neural networks which allow for combinatorial problem solving. Their underlying principles have close ties to models and concepts used in physics but are all in all fairly easy to understand. This motivates our basic idea for this book: By studying Hopfield nets from a variety of uncommon angles, we can familiarize ourselves with mathematical tools and techniques which play a central role in quantum mechanics and thus in quantum computing. To be able to consider these uncommon angles, we need a few preliminaries. Once we have studied those and their connections to Hopfield nets, we should be well prepared to venture into the abstract and at first sight unintuitive worlds of quantum mechanics and quantum computing.