The topic of these lectures lies in the new and rapidly growing field of quantum computing,which explores connections between physics and computing in general. Quantum informa-tion processing is a cross-disciplinary field and is of great importance from both a funda-mental, as well as technological perspective [27]. From the fundamental perspective we havedeepened our understanding of the relationship between physics, information and computa-tion in general, and have also gained a deeper understanding of the fundamental aspects ofquantum theory - non-locality and entanglement in particular [31]. From the technologicalperspective we have manipulated larger and larger quantum systems and obtained power-ful practical applications in the domain of communication and cryptography such as theunconditionally secure quantum cryptography (key exchange) and quantum teleportation[7, 14, 5].Historically, the greater potential of the quantum computer was first realised by Feyn-man, who noted that quantum systems appear to be exponentially hard to simulate withclassical computers [15]. He speculated that, therefore, quantum computers could poten-tially be much more powerful than their classical counterparts. This intuition has beenproven to be correct for some tasks, such as factoring large numbers and searching unstruc-tured databases. Every computer is fundamentally a physical system, and any computationis just a physical process undergone by this system. Quantum physics is the most accurateway of describing physical systems and their behaviour in general. Encoding informationinto quantum systems and processing it according to the laws of quantum physics results innew features which do not exist in the classical computation.Large scale quantum computation is still hypothetical. However, Moore’s law
The topic of these lectures lies in the new and rapidly growing field of quantum computing,which explores connections between physics and computing in general. Quantum informa-tion processing is a cross-disciplinary field and is of great importance from both a funda-mental, as well as technological perspective [27]. From the fundamental perspective we havedeepened our understanding of the relationship between physics, information and computa-tion in general, and have also gained a deeper understanding of the fundamental aspects ofquantum theory - non-locality and entanglement in particular [31]. From the technologicalperspective we have manipulated larger and larger quantum systems and obtained power-ful practical applications in the domain of communication and cryptography such as theunconditionally secure quantum cryptography (key exchange) and quantum teleportation[7, 14, 5].Historically, the greater potential of the quantum computer was first realised by Feyn-man, who noted that quantum systems appear to be exponentially hard to simulate withclassical computers [15]. He speculated that, therefore, quantum computers could poten-tially be much more powerful than their classical counterparts. This intuition has beenproven to be correct for some tasks, such as factoring large numbers and searching unstruc-tured databases. Every computer is fundamentally a physical system, and any computationis just a physical process undergone by this system. Quantum physics is the most accurateway of describing physical systems and their behaviour in general. Encoding informationinto quantum systems and processing it according to the laws of quantum physics results innew features which do not exist in the classical computation.Large scale quantum computation is still hypothetical. However, Moore’s law
Each computer is essentially an actual framework, and any calculation is only an actual cycle gone through by this framework. Quantum physics is the most dependable approach to depicting actual frameworks and their overall conduct. Encoding information into quantum frameworks and processing it as indicated by the laws of quantum physics brings about new elements which don’t exist in the old-style calculation. Quantum information processing is a cross-disciplinary field and is critical from, both, a crucial as well as an innovative viewpoint. According to the crucial viewpoint, we have developed how we might interpret the connection between physics, information, and calculation as a general rule, and have additionally acquired a more profound comprehension of the principal parts of the quantum hypothesis—non-area and entanglement specifically. According to the mechanical point of view, we have controlled increasingly large quantum frameworks and acquired strong down to earth applications in the area of correspondence and cryptography like the unequivocally solid quantum cryptography (key trade) and quantum instant transportation The more prominent capability of the quantum computer was first acknowledged by Feynman, who noticed that quantum frameworks give off an impression of being dramatically difficult to recreate with traditional computers and expressed that quantum computers might actually be significantly more remarkable than their old-style partners. The improvement of quantum information science (QIS) has been driven by hypothetical work of researchers dealing with the limit between Physics, Computer Science, Mathematics, and Information Theory. In the beginning phases of this turn of events, hypothetical work has regularly been a long way in front of test acknowledgement of these thoughts. Simultaneously, the hypothesis has given various propositions of how to execute fundamental thoughts and ideas from quantum information in explicit actual frameworks.
Quantum Information Science is a cross-disciplinary subject that has arisen in the last twenty years. It concerns itself with the consequences of our most complete description of the physical world (that is, quantum mechanics) for the reliable, secure, private, and rapid processing of information, both in communication and computation. While its invention is often ascribed to the famous theoretical physicist Richard Feynman in the 1980s, his contributions were only one of many that initiated the field around that time. While he perceived that new types of physical devices, in which the quantum laws of superposition and entanglement function at the logical level, could give new power in the simulation of quantum physics, it was others (Bennett, Brassard) who showed that the uncertainty principle led to fundamentally more secure ways of communicating secret messages. It was yet others (Deutsch, Vazirani) who understood that quantum theory defined a new kind of Turing machine, and that not only quantum physics simulations, but potentially many other computational problems, are sped up in this machine. And it was yet another (Shor) who found a simple, very fast algorithm for prime factorization. The word "qubit" was coined only in 1995. Its introduction is indicative of a new mindset that has developed in recent years for studying and using quantum systems. "Qubit" now stands for a durable paradigm that spans a very wide variety of fields. It thus has many sub-meanings: first, it is the basic abstract unit of information for workers ranging from optical communication engineers to NMR spectroscopists to black-hole theorists. Second, it is the name we now routinely give to physical two level systems, as they are realized by photons, atomic and ionic eigenlevels, electronic and nuclear spin, structural defects in solids, and circulating-current states of superconducting devices. Physics has long dealt with some of these two-level systems, but calling them qubits implies a whole suite of interrelated ideas and capabilities that we ascribe to these systems: the ability to precisely set, and to precisely measure, the quantum state of one unique specimen, to avoid its coupling with the environment while at the same time strongly and controllably coupling the qubits together, to exploit the resulting quantum entanglement as a resource for metrological, cryptographic, and computational tasks. Quantum Information is a very diverse subject pursued today in many different directions, by many hundreds of researchers internationally: In theoretical physics, it has enlivened and sharpened the understanding of efficient representations of entangled many-particle wavefunctions, and has provided the prospect of applications for new concepts such as anyons and majorana fermions. Information theorists has benefitted from having a rigorous extension of the basis of their field, in which classical information theory is subsumed into a greatly broader subject. Theoretical computer scientists continue the search for new quantum algorithms, and have used quantum concepts to prove new results about the classification of computational complexity. Coding theorists have had the new and subtle problem of quantum error correction to analyse and conquer. Most strikingly, the program of experimental physics has been influenced in many directions by Quantum Information Science. State-of-the-art optics experiments transmit quantum states over long distances and perform precision manipulations in single quanta (atomic ions, impurity spins, quantum dots) in the quest to have working quantum cyptography and quantum computing. Quantum Hall systems, and topological insulators, are being assiduously examined for new elementary excitations for use as qubits. In the course of ten years, superconducting devices have improved by over four orders of magnitude in their quantum coherence, a metric made precise by the ideas of quantum computing. [...] DiVincenzo, David
The success of the abstract model of computation, in terms of bits, logical operations, programming language constructs, and the like, makes it easy to forget that computation is a physical process. Our cherished notions of computation and information are grounded in classical mechanics, but the physics underlying our world is quantum. In the early 80s researchers began to ask how computation would change if we adopted a quantum mechanical, instead of a classical mechanical, view of computation. Slowly, a new picture of computation arose, one that gave rise to a variety of faster algorithms, novel cryptographic mechanisms, and alternative methods of communication. Small quantum information processing devices have been built, and efforts are underway to build larger ones. Even apart from the existence of these devices, the quantum view on information processing has provided significant insight into the nature of computation and information, and a deeper understanding of the physics of our universe and its connections with computation. We start by describing aspects of quantum mechanics that are at the heart of a quantum view of information processing. We give our own idiosyncratic view of a number of these topics in the hopes of correcting common misconceptions and highlighting aspects that are often overlooked. A number of the phenomena described were initially viewed as oddities of quantum mechanics. It was quantum information processing, first quantum cryptography and then, more dramatically, quantum computing, that turned the tables and showed that these oddities could be put to practical effect. It is these application we describe next. We conclude with a section describing some of the many questions left for future work, especially the mysteries surrounding where the power of quantum information ultimately comes from.
Information and computation theory have undergone a spurt of new growth, and a renewal of their historic connection to basic physics, as they have expanded to treat the intact transmission and processing of quantum states, and the interaction of such 'quantum information' with traditional forms of information. We may wonder why this did not happen earlier, as quantum principles have long been accepted as fundamental to all of physics. Perhaps the founders of information and computation theory, such as Shannon, Turing and von Neumann, were too accustomed to thinking of information processing in macroscopic terms, not yet having before them the powerful examples of the genetic code and ever-shrinking microelectronics. Be that as it may, information until recently has largely been thought of in classical terms, with quantum mechanics playing a supporting role in the design of the equipment to process it, and setting limits on the rate at which it could be sent through certain channels. Now we know that a fully quantum theory of information and information processing offers, among other benefits, a brand of cryptography whose security rests on fundamental physics, and a reasonable hope of constructing quan- tum computers that could dramatically speed up the solution of certain mathematical problems. These benefits depend on distinc- tively quantum properties such as uncertainty, interference and entanglement. At a more fundamental level, it has become clear that an information theory based on quantum principles extends and completes classical information theory, just as complex numbers extend and complete the reals. Besides quantum generalizations of classical notions such as sources, channels and codes, the new theory includes two complementary, quantifiable kinds of information— classical information and quantum entanglement. Classical infor- mation can be copied at will, but can only be transmitted forward in time, to a receiver in the sender's forward light cone. Entanglement in contrast, cannot be copied, but can connect any two points in space-time. Conventional data processing operations destroy entanglement, but quantum operations can create it and use it for various purposes, such as speeding up certain classical computa- tions and assisting in the transmission of classical information or intact quantum states. Part of the new quantum information theory is the qualitative and quantitative study of entanglement, and its interactions with classical information. Any means, such as an optical fibre, of delivering quantum systems more or less intact from one place to another, may be viewed as a quantum channel. Unlike classical channels, which are well characterized by a single capacity, quantum channels have several distinct capacities, depending on what one is trying to use them for, and what auxiliary resources are brought into play. New effects involving quantum information continue to be discovered, not only in the traditional areas of computation, channel capacity, and cryptography, but in areas such as commu- nication complexity and game theory.
Information is a physical. Physical systems register and process information. These facts generated enormus interest in the development of novel quantum tecnologies, especially because the construction of smaller electronic devices ultimately leads to a consideration of quantum mechanical effects in electronic and computer desingns. The notion of the classical bit of information theory was formally pushed into the realm of the quanta with the introduction of the quantum bit or qubit, in the seminal works of Deutsch (Deutsch, 1985) and Shor (Shor, 1994). They demostrated that, indeed, controlled multipartite qubit interference effects could provide the means for a radical new way of computing, allowing the computation of many intractable computational problems, such as the factoring of large number or exact simulation of large quantum systems. The field of experimental and theoretical research in quantum information and computation has emerged as very important player in the understanding of quantum phenomena the both the basic and technological levels. This has attracted the attention of numerous researchers with backgrounds ranging from computer science, mathematics and engineerin, to the physical sciences, and we now have an interdisciplinary field where great efforts are being made in order to build devices that allow the progressing of information at a quantum level. A concise introduction to the field of quantum information and quantum computation is presented. This stars with the bassic definitions of bits, quantum registers, through to the universal gate-set for building the universal quantum computer, from a quantum network model of computation. The work shows how two-qubit gates suffice for quantum computation, emphasing the power of the quantum circuit representation for entagling and disentagling quantum states. This leads to the “no-cloning theorem”, which leads us to many interesting applications, such as quantum cryptography. Two alternative approaches or performing quantum computation are also described i) the one-way or measurement based quantum computer method, and ii) holonomic or geometric quantum computation. Following this, quantum entaglement quantification is highlighted, particulary its usefulness as a communication resource, in order to describe some of its most celebrated practical applications to date: quantum teleportation, cryptography, dens coding, and data compression. Deutsch’s concept of quantum parallelism is enphasized in order to gain insight into the potential for efficiently solving certain classically intratable algorithms. A subject central to the field of QIP- quantum decoherence- is then introduced.. Possible ways to overcome it, in particular quantum error correction, are discussed. A descriptios of some of the currently available hardware of the practical implementation of quantum computation is provided with a discussion of the main physical quantum bits that are currently employed (or proposed) for a such a purpose.
Q uantum mechanics has had an enormous technological and societal impact.To grasp this point, it is sufficient to cite the invention of the transistor, perhaps the most remarkable among the countless other applications of quantum mechanics.It is also easy to see the enormous impact of computers on everyday life.The importance of computers is such that it is appropriate to say that we are now living in the information age.This information revolution became possible thanks to the invention of the tran sistor, that is, thanks to the synergy between computer science and quantum physics.Today this synergy offers completely new opportunities and promises exciting advances in both funda mental science and technological application.We are referring here to the fact that quantum mechanics can be used to process and transmit information [1,2].Miniaturization provides us with an intuitive way of under standing why, in the near future, quantum laws will become important for computation.The electronics industry for com puters grows hand-in-hand with the decrease in size of integrated circuits.This miniaturization is necessary to increase computa tional power, that is, the number of floating-point operations per second (flops) a computer can perform.In the 1950's, electronic computers based on vacuum-tube technology were capable of performing approximately 103 floating-point operations per second, while nowadays there exist supercomputers whose power is greater than lOteraflops (1013 flops).As we have remarked, this enormous growth of computational power has been made possi ble owing to progress in m in ia tu riz a tio n , w hich m ay be quantified empirically in Moore's law.This law is the result of a remarkable observation made by Gordon Moore in 1965: the number of transistors on a single integrated-circuit chip doubles approximately every 18 24 months.This exponential growth has not yet saturated and Moore's law is still valid.At the present time the limit is approximately 108 transistors per chip and the typical size of circuit components is of the order of 100 nanometres.Extrapolating Moore's law, one would estimate that around the year 2020 we shall reach the atomic size for storing a single bit of inform atio n .At th a t p o in t, q u a n tu m effects will becom e unavoidably dominant.One should be aware that, besides quantum effects, other fac tors could bring Moore's law to an end.In the first place, there are economic considerations.Indeed, the cost of building fabri cation facilities to m an u factu re chips has also increased exponentially with time.Nevertheless, it is important to under stand the ultimate limitations set by quantum mechanics.Even though we might overcome economic barriers by means of tech nological breakthroughs, quantum physics sets fundamental limitations on the size of the circuit components.The first ques tion under debate is whether it would be more convenient to push References