This is an advanced graduate course on quantum computation and quantum information, for which prior knowledge of quantum mechanics is required. Topics include quantum computation, advanced quantum error correction codes, fault tolerance, quantum algorithms beyond factoring, properties of quantum entanglement, and quantum protocols and communication complexity.
This is an advanced graduate course on quantum computation and quantum information, for which prior knowledge of quantum mechanics is required. Topics include quantum computation, advanced quantum error correction codes, fault tolerance, quantum algorithms beyond factoring, properties of quantum entanglement, and quantum protocols and communication complexity.
From the Publisher:
This book aims to provide a pedagogical introduction to the subjects of quantum information and computation. Topics include non-locality of quantum mechanics, quantum computation, quantum cryptography, quantum error correction, fault-tolerant quantum computation as well as some experimental aspects of quantum computation and quantum cryptography. Only knowledge of basic quantum mechanics is assumed. Whenever more advanced concepts and techniques are used, they are introduced carefully. This book is meant to be a self-contained overview. While basic concepts are discussed in detail, unnecessary technical details are excluded. It is well-suited for a wide audience ranging from physics graduate students to advanced researchers.
Quantum computation and information is one of the most exciting developments in science and technology of the last twenty years. To achieve large scale quantum computers and communication networks it is essential not only to overcome noise in stored quantum information, but also in general faulty quantum operations. Scalable quantum computers require a far-reaching theory of fault-tolerant quantum computation. This comprehensive text, written by leading experts in the field, focuses on quantum error correction and thoroughly covers the theory as well as experimental and practical issues. The book is not limited to a single approach, but reviews many different methods to control quantum errors, including topological codes, dynamical decoupling and decoherence-free subspaces. Basic subjects as well as advanced theory and a survey of topics from cutting-edge research make this book invaluable both as a pedagogical introduction at the graduate level and as a reference for experts in quantum information science.
Quantum computing exists at the intersection of mathematics, physics, chemistry, and engineering; the main goal of quantum computing is the creation of devices and algorithms which use the properties of quantum mechanics to store, manipulate and measure information. There exist many families of algorithms, which, using non-classical logical operations, can outperform traditional, classical algorithms in terms of memory and processing requirements. In addition, quantum computing devices are fundamentally smaller than classical processors and memory elements; since the physical models governing their performance are applicable on all scales, as opposed to classical logic elements, whose underlying principles rely on the macroscopic nature of the device in question. \n \nQuantum algorithms, for the most part, are predicated on a theory of resources. It is often assumed that quantum computers can be placed in a precise fiducial state prior to computation, and that logical operations are perfect, inducing no error on the system which they affect. These assumptions greatly simplify algorithmic design, but are fundamentally unrealistic. In order to justify their use, it is necessary to develop a framework for using a large number of imperfect devices to simulate the action of a perfect device, with some acceptable probability of failure. This is the study of fault-tolerant quantum computing. In order to pursue this study effectively, it is necessary to understand the fundamental nature of generic quantum states and operations, as well as the means by which one can correct quantum errors. Additionally, it is important to attempt to minimize the use of computational resources in achieving error reduction and fault-tolerant computing. \n \nThis thesis is concerned with three projects related to the use of error-prone quantum systems to transmit and manipulate information. The first of these is concerned with the use of imperfectly-prepared states in error-correction routines. Using optimal quantum error correction, we are able to deduce a method of partially protecting encoded quantum information against preparation errors prior to encoding, using no additional qubits. The second of these projects details the search for entangled states which can be used to transmit classical information over quantum channels at a rate superior to classical states. The third of these projects concerns the transcoding of data from one quantum code into another using few ancillary resources. The descriptions of these projects are preceded by a brief introduction to representations of quantum states and channels, for completeness. \n \nThree techniques of general interest are presented in appendices. The first is an introduction to, and a minor advance in the development of optimal error correction codes. The second is a more efficient means of calculating the action of a quantum channel on a given state, given that the channel acts non-trivially only on a subsystem, rather than the entire system. Finally, we include documentation on a software package developed to aid the search for quantum transcoding operations.
Abstract This comprehensive and self-consistent textbook presents quantum information science, a rapidly evolving interdisciplinary scientific field that will change modern computer science. The book is divided into four parts. The first part starts with a gentle introduction to some important mathematical concepts, followed by a discussion of computational models, linear algebra, and quantum mechanics. The second part explains more advanced topics of quantum mechanics, which are necessary to describe the decoherence of quantum states. The third part includes a presentation of entanglement, early quantum algorithms and quantum simulation, focussing on computational problems that quantum computers can solve faster than classical machines. The last part presents superconducting devices, a promising architecture for the implementation of quantum computers. With more than 200 figures and 100 exercises (with solutions), this book is ideal for a master’s course on quantum information processing. Readers starting a master’s program or a graduate course in physics, computer science, mathematics or quantum engineering will develop a good understanding of the fundamental concepts of the field.
This is a course on the theory of quantum computing. It consists of 16 lessons, each with a video and written component, covering the basics of quantum information, quantum algorithms (including query algorithms, Shor's algorithm for integer factorization, and Grover's algorithm), the general formulation of quantum information (including density matrices, quantum channels, and general measurements), and quantum error correction (including the basics, the stabilizer formalism, CSS codes, the toric code, and fault-tolerant quantum computation).
Aimed at advanced undergraduate and graduate-level students, this textbook covers the core topics of quantum computing in a format designed for a single-semester course. It will be accessible to learners from a range of disciplines, with an understanding of linear algebra being the primary prerequisite. The textbook introduces central concepts such as quantum mechanics, the quantum circuit model, and quantum algorithms, and covers advanced subjects such as the surface code and topological quantum computation. These topics are essential for understanding the role of symmetries in error correction and the stability of quantum architectures, which situate quantum computation within the wider realm of theoretical physics. Graphical representations and exercises are included throughout the book and optional expanded materials are summarized within boxed 'Remarks'. Lecture notes have been made freely available for download from the textbook's webpage, with instructors having additional online access to selected exercise solutions.