The marriage of quantum physics and information technology has the potential to generate radically new information processing devices. Examples are quantum cryptosystems, which provide guaranteed secure communication, and quantum computers, which manipulate data quantum mechanically and could thus solve some problems currently intractable to conventional (classical) computation. This introductory chapter serves two purposes. Firstly, I discuss some of the basic aspects of quantum physics which underpin quantum information technology (QIT). These will be used (and in somes cases further expanded upon) in subsequent chapters. Secondly, and as a lead into the whole book, I outline some of the ideas of QIT and its possible uses. To appear as Chapter 1 of Introduction to Quantum Computation and Information, eds. H.-K. Lo, S. Popescu and T. P. Spiller, (World Scientific Press 1998), http://www.wspc.com.sg/. 1 1 Introduction Information technology (IT) can feed off quantum physic...
The marriage of quantum physics and information technology has the potential to generate radically new information processing devices. Examples are quantum cryptosystems, which provide guaranteed secure communication, and quantum computers, which manipulate data quantum mechanically and could thus solve some problems currently intractable to conventional (classical) computation. This introductory chapter serves two purposes. Firstly, I discuss some of the basic aspects of quantum physics which underpin quantum information technology (QIT). These will be used (and in somes cases further expanded upon) in subsequent chapters. Secondly, and as a lead into the whole book, I outline some of the ideas of QIT and its possible uses. To appear as Chapter 1 of Introduction to Quantum Computation and Information, eds. H.-K. Lo, S. Popescu and T. P. Spiller, (World Scientific Press 1998), http://www.wspc.com.sg/. 1 1 Introduction Information technology (IT) can feed off quantum physic...
Present information technology is based on the laws of classical physics. However, advances in quantum physics have stimulated interest in its potential impact on such technology. This article is an introductory review of three aspects of quantum information processing, cryptography, computation, and teleportation. The author serves up hors d'oeuvres on the relevant parts of quantum physics and the sorts of quantum systems which might form the building blocks for quantum processors. Quantum cryptography utilizes states of individual quantum systems for the transfer of conventional classical bits of information. The impossibility of measuring quantum systems without disturbing them guarantees the detection of eavesdropping and hence secure information transfer is possible. In a sense, teleportation is the inverse of cryptography, using more robust classical bits to faithfully transfer a quantum state through a noisy environment. Quantum computation utilizes the evolving quantum state of a complex system, which consists of many interacting individuals. If such a machine could be built, it would be capable of solving some problems which are intractable on any conventional computer; he illustrates this with Shor's (see Proc. 35th IEEE Symposium on Foundations of Computer Science, p.124, 1994) quantum factoring algorithm. Details are given of the current experimental achievements, proposals, and prospects for the future and of the patents granted to date.
The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarize not just quantum computing, but the whole subject of quantum information theory. Information can be identified as the most general thing which must propagate from a cause to an effect. It therefore has a fundamentally important role in the science of physics. However, the mathematical treatment of information, especially information processing, is quite recent, dating from the mid-20th century. This has meant that the full significance of information as a basic concept in physics is only now being discovered. This is especially true in quantum mechanics. The theory of quantum information and computing puts this significance on a firm footing, and has led to some profound and exciting new insights into the natural world. Among these are the use of quantum states to permit the secure transmission of classical information (quantum cryptography), the use of quantum entanglement to permit reliable transmission of quantum states (teleportation), the possibility of preserving quantum coherence in the presence of irreversible noise processes (quantum error correction), and the use of controlled quantum evolution for efficient computation (quantum computation). The common theme of all these insights is the use of quantum entanglement as a computational resource. It turns out that information theory and quantum mechanics fit together very well. In order to explain their relationship, this review begins with an introduction to classical information theory and computer science, including Shannon's theorem, error correcting codes, Turing machines and computational complexity. The principles of quantum mechanics are then outlined, and the Einstein, Podolsky and Rosen (EPR) experiment described. The EPR-Bell correlations, and quantum entanglement in general, form the essential new ingredient which distinguishes quantum from classical information theory and, arguably, quantum from classical physics. Basic quantum information ideas are next outlined, including qubits and data compression, quantum gates, the `no cloning' property and teleportation. Quantum cryptography is briefly sketched. The universal quantum computer (QC) is described, based on the Church-Turing principle and a network model of computation. Algorithms for such a computer are discussed, especially those for finding the period of a function, and searching a random list. Such algorithms prove that a QC of sufficiently precise construction is not only fundamentally different from any computer which can only manipulate classical information, but can compute a small class of functions with greater efficiency. This implies that some important computational tasks are impossible for any device apart from a QC. To build a universal QC is well beyond the abilities of current technology. However, the principles of quantum information physics can be tested on smaller devices. The current experimental situation is reviewed, with emphasis on the linear ion trap, high- Q optical cavities, and nuclear magnetic resonance methods. These allow coherent control in a Hilbert space of eight dimensions (three qubits) and should be extendable up to a thousand or more dimensions (10 qubits). Among other things, these systems will allow the feasibility of quantum computing to be assessed. In fact such experiments are so difficult that it seemed likely until recently that a practically useful QC (requiring, say, 1000 qubits) was actually ruled out by considerations of experimental imprecision and the unavoidable coupling between any system and its environment. However, a further fundamental part of quantum information physics provides a solution to this impasse. This is quantum error correction (QEC). An introduction to QEC is provided. The evolution of the QC is restricted to a carefully chosen subspace of its Hilbert space. Errors are almost certain to cause a departure from this subspace. QEC provides a means to detect and undo such departures without upsetting the quantum computation. This achieves the apparently impossible, since the computation preserves quantum coherence even though during its course all the qubits in the computer will have relaxed spontaneously many times. The review concludes with an outline of the main features of quantum information physics and avenues for future research.
A new quantum information technology (QIT) could emerge in the future, based on current research in the fields of quantum information processing and communication1, 2, 3 (QIPC). In contrast to conventional IT, where quantum mechanics plays a support role in improving the building blocks, fundamental quantum phenomena play a central role in QIPC — information is stored, processed, and communicated according to the laws of quantum physics. This additional freedom could enable future QIT to perform tasks we will never achieve with ordinary IT. Today many people are familiar with at least the consequences of Moore’s Law — the fastest computer in the shops doubles in speed about every 18 months to two years. This exponential progress, first noted4 by Gordon Moore — cofounder and former CEO of Intel — in 1965, has continued ever since. But it cannot go on forever. Hurdles exist, for example: silicon will hit problems, with oxide thinness or track width5; new materials or even new paradigms, such as self-assembled nano-devices or molecular electronics, will be needed; lots of dollars will be required as Moore’s second law tells us that fabrication costs are also growing exponentially. However, even if the hurdles can be overcome, we will eventually run into nature.
We may be on the brink of a quantum transfor -mation driven by our increasing ability to realize, detect, control, and manipulate high-purity quantum states. For decades the quantum world has crept into our lives through modern information technology, the most visible side of science that permeates almost every aspect of our daily conduct. Yet quantumness in its full glory remains a promise for the future, as existing mainstream technologies are essentially based on properties of mixed quantum states realized in, e.g., metal–oxide–semiconductor heterostructures. The scientific backbone of current technologies combines quantum theory with information theory and the theory of computation, everything being sprinkled with a healthy dose of mathematics and brought into reality by remarkable engineering achievements. This multidisciplinary approach has enabled us to understand key physical phenomena and material properties, to communicate and process information efficiently, and, ultimately, to build functional devices that provide us with unprecedented convenience and mastery over nature, possibly with the price of being in danger to become the slaves of our computers and gadgets. However, our technological success is built on a combination of essentially distinct and largely independent scientific fields. Harnessing high-purity quantum states, on the other hand, sets these previously separated “continents of knowledge” on a collision path. The main goal of the last three chapters of this book is to provide a bird's eye view of the “collision zone” and prepare the reader to explore, enjoy, and perhaps exploit the newly raising mountains. We start with a brief introduction to basic concepts in quantum information, which also includes a summary of the operational formulation of quantum mechanics (the “natural” language of quantum information theory) and a synopsis of classical information theory ( Chapter 10 ). For a thorough treatment of concepts, problems, and techniques in quantum information theory the reader is referred to the books by Nielsen and Chuang [ 389 ] and Wilde [ 548 ]. The book by Watrous [ 530 ] focuses on the mathematical theory of quantum information. An undergraduate level introduction to this subject can be found, for example, in Schumacher and Westmoreland [ 458 ]. Some of the philosophical implications of the relationship between quantum mechanics and information theory are discussed in Timpson [ 505 ]. Our survey continues with Chapter 11 , where we discuss a few key aspects pertaining to quantum computation, which can be viewed as the quintessential quantum technology involving the controlled realization and manipulation of high-purity quantum states within a large Hilbert space. Finally, Chapter 12 focuses on topological quantum computation, a promising approach to overcoming the fundamental challenge associated with quantum decoherence based on harnessing the underlying robustness of topological quantum states. This also marks our final return to the realm of topological quantum matter.
"Introduction to Quantum Mechanics And Quantum Computing" is a comprehensive book chapter that provides an in-depth exploration of the groundbreaking field of quantum computing. Beginning with an introduction to the fundamental principles of quantum mechanics, the chapter navigates through the evolution of quantum computing, from its conceptual origins to the challenges faced in its development. The core concepts of quantum bits (qubits) and their unique properties, such as entanglement and superposition, are explained, laying the foundation for understanding quantum information processing. The chapter further delves into the building blocks of quantum computing—qubits—detailing their diverse physical implementations. Quantum gates and circuits, analogous to classical computing, are explored, shedding light on the mechanisms enabling quantum algorithms to perform complex tasks efficiently. Highlighting renowned algorithms like Shor's and Grover's, the chapter emphasizes the potential computational supremacy of quantum computers over classical counterparts. Recognizing the sensitivity of quantum systems to noise and decoherence, the chapter introduces quantum error correction as a crucial aspect of ensuring reliable quantum computation. The exploration concludes with an examination of the current state of quantum computing, outlining progress in industry and academia while addressing the challenges in building large-scale, fault-tolerant quantum computers. The potential applications of quantum computing in cryptography, drug discovery, optimization problems, and beyond are discussed, offering a glimpse into the transformative impact this emerging technology may have on various industries. "Introduction to Quantum Mechanics And Quantum Computing" serves as a comprehensive guide for readers seeking a nuanced understanding of the theoretical foundations and practical applications of quantum computing.
T HE FUNDAMENTAL KNOWLEDGE BEHIND MODERN INformation technology, the most visible side of science which permeates almost every aspect of our daily lives, rests on two pillars: information science and quantum mechanics. Knowing how to efficiently communicate and process information and understanding the physical phenomena and material properties that are essential to building functional devices have provided us with unprecedented convenience and mastery over nature, possibly with the price of becoming the slaves of our computers and gadgets. Nevertheless, information science and quantum mechanics enter the backbone of current technologies as distinct and independent fields. Therefore, one is naturally tempted to ask several questions. Is there land between these two realms? If yes, what can grow out of that land? In particular, can information theory tell us something relevant about the foundations of quantum mechanics? On the other hand, can one formulate a quantum information science and in what sense would this be different from the classical version? In this chapter we introduce several basic concepts that will allow us to better understand the implications of these questions and grasp the essential ideas behind the answers formulated so far. Discussing these fundamental concepts will also shed light on the role of topological quantum matter in the economy of quantum computation. Here we focus on the key ideas that were launched into the arena by classical information theory and classical computation science. The metamorphosis of these ideas after the encounter with quantum mechanics will be discussed in the final three chapters of this book.