Mannucci Mirco A. - Quantum Computing for Computer Scientists

Noson S. Yanofsky

Brooklyn College, City University of New York

and

Mirco A. Mannucci

HoloMathics, LLC

Quantum computing is a fascinating new field at the intersection of computer science, mathematics, and physics, which strives to harness some of the uncanny aspects of quantum mechanics to broaden our computational horizons. This book presents some of the most exciting and interesting topics in quantum computing. Along the way, there will be some amazing facts about the universe in which we live and about the very notions of information and computation.

The text you hold in your hands has a distinct flavor from most of the other currently available books on quantum computing. First and foremost, we do not assume that our reader has much of a mathematics or physics background. This book should be readable by anyone who is in or beyond their second year in a computer science program. We have written this book specifically with computer scientists in mind, and tailored it accordingly: we assume a bare minimum of mathematical sophistication, a first course in discrete structures, and a healthy level of curiosity. Because this text was written specifically for computer people, in addition to the many exercises throughout the text, we added many programming drills. These are a hands-on, fun way of learning the material presented and getting a real feel for the subject.

The calculus-phobic reader will be happy to learn that derivatives and integrals are virtually absent from our text. Quite simply, we avoid differentiation, integration, and all higher mathematics by carefully selecting only those topics that are critical to a basic introduction to quantum computing. Because we are focusing on the fundamentals of quantum computing, we can restrict ourselves to the finite-dimensional mathematics that is required. This turns out to be not much more than manipulating vectors and matrices with complex entries. Surprisingly enough, the lions share of quantum computing can be done without the intricacies of advanced mathematics.

Nevertheless, we hasten to stress that this is a technical textbook. We are not writing a popular science book, nor do we substitute hand waving for rigor or mathematical precision.

Most other texts in the field present a primer on quantum mechanics in all its glory. Many assume some knowledge of classical mechanics. We do not make these assumptions. We only discuss what is needed for a basic understanding of quantum computing as a field of research in its own right, although we cite sources for learning more about advanced topics.

There are some who consider quantum computing to be solely within the domain of physics. Others think of the subject as purely mathematical. We stress the computer science aspect of quantum computing.

It is not our intention for this book to be the definitive treatment of quantum computing. There are a few topics that we do not even touch, and there are several others that we approach briefly, not exhaustively. As of this writing, the bible of quantum computing is Nielsen and Chuangs magnificent Quantum Computing and Quantum Information (2000). Their book contains almost everything known about quantum computing at the time of its publication. We would like to think of our book as a useful first step that can prepare the reader for that text.