Over the past 40 years there has been a dramatic miniaturization in computer technology. If current trends continue, by the year 2020 the basic memory components of a computer will be the size of individual atoms. At such scales, the current model of computation, based on a mathematical idealization known as the Universal Turing Machine, is simply invalid. A new field, called "quantum computing" is emerging that is re-inventing the foundations of computer science and information theory in a way that is consistent with quantum physics - the most accurate model of reality that is currently known. Remarkably this new theory predicts that quantum computers can perform tasks exponentially faster than any conventional computer. Moreover, quantum effects allow unprecedented tasks to be performed such as teleporting information, breaking supposedly "unbreakable" codes, generating true random numbers, and communicating with messages that betray the presence of eavesdropping. These capabilities are of significant practical importance to banks and government agencies. lndeed, a quantum scheme for sending and receiving ultra-secure messages has already been implemented over a distance of 30km-far enough to wire the financial district of any major city. Modem microprocessors have to be designed with quantum mechanics in mind in order to ensure that they function correctly. In essence they use quantum effects to ensure that their classical computations are upheld. What no current processor does is to fully exploit quantum effects Recently, it took 1,600 computers communicating over the Internet 8 months to solve the factorisation of a 129-digit number. Should it be possible to build a microprocessor which fully exploits quantum mechanics then it may be possible to carry out such factorisations in remarkably less time. The RSA algorithm, a widely used encryption system, is safe only if such factorisations cannot be performed quickly. Although modem computers already exploit some quantum phenomena they do not make use of the full repertoire of quantum phenomena that Nature provides. Harnessing these phenomena will take computing technology to the very brink of what is possible in this Universe.
Over the past 40 years there has been a dramatic miniaturization in computer technology. If current trends continue, by the year 2020 the basic memory components of a computer will be the size of individual atoms. At such scales, the current model of computation, based on a mathematical idealization known as the Universal Turing Machine, is simply invalid. A new field, called "quantum computing" is emerging that is re-inventing the foundations of computer science and information theory in a way that is consistent with quantum physics - the most accurate model of reality that is currently known. Remarkably this new theory predicts that quantum computers can perform tasks exponentially faster than any conventional computer. Moreover, quantum effects allow unprecedented tasks to be performed such as teleporting information, breaking supposedly "unbreakable" codes, generating true random numbers, and communicating with messages that betray the presence of eavesdropping. These capabilities are of significant practical importance to banks and government agencies. lndeed, a quantum scheme for sending and receiving ultra-secure messages has already been implemented over a distance of 30km-far enough to wire the financial district of any major city. Modem microprocessors have to be designed with quantum mechanics in mind in order to ensure that they function correctly. In essence they use quantum effects to ensure that their classical computations are upheld. What no current processor does is to fully exploit quantum effects Recently, it took 1,600 computers communicating over the Internet 8 months to solve the factorisation of a 129-digit number. Should it be possible to build a microprocessor which fully exploits quantum mechanics then it may be possible to carry out such factorisations in remarkably less time. The RSA algorithm, a widely used encryption system, is safe only if such factorisations cannot be performed quickly. Although modem computers already exploit some quantum phenomena they do not make use of the full repertoire of quantum phenomena that Nature provides. Harnessing these phenomena will take computing technology to the very brink of what is possible in this Universe.
In the preceding chapter we established that a suitable set of quantum gates, complemented by quantum error correction, allows us to produce a desired multiqubit unitary transformation. This transformation is one of the three steps in a quantum computation; the others, of course, are the preparation of the qubits in their initial state and the measurement of them after the transformation has been implemented. A quantum computation is designed to solve a problem or class of problems. The power of quantum computers is that they can do this, at least for some problems, very much more efficiently and quickly than any conventional computer based on classical logic operations. If we can build a quantum computer then a number of important problems which are currently intractable will become solvable. The potential for greatly enhanced computational power is, in itself, reason enough to study quantum computers, but there is another. Moore’s law is the observation that the number of transistors on a chip doubles roughly every eighteen months. A simple corollary is that computer performance also doubles on the same timescale. Associated with this exponential improvement is a dramatic reduction in the size of individual components. If the pace is to be kept up then it is inevitable that quantum effects will become increasingly important and ultimately will limit the operation of the computer. In these circumstances it is sensible to consider the possibility of harnessing quantum effects to realize quantum information processors and computers. We start with a brief introduction to the theory of computer science, the principles of which underlie the operation of what we shall refer to as classical computers. These include all existing machines and any based on the manipulation of classical bits. The development of computer science owes much to Turing, who devised a simple but powerful model of a computing device: the Turing machine. It its most elementary form, this consists of four elements. (i) A tape for data storage, which acts as a memory. This tape has a sequence of spaces, each of which has on it one of a finite set of symbols. (ii) A processor, which controls the operations of the machine.
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
In the Name of the Pasta, and of the Sauce, and of the Holy Meatballs … – Bobby Henderson, The Gospel of the Flying Spaghetti Monster, 2006 After the conceptual comes the practical. While the study of quantum foundations is as old as quantum theory itself, the field of quantum computing is relatively new. So new in fact that large-scale, practical quantum computing is still not a reality. A typical ‘quantum computer’ takes many months to set up before performing such astounding tasks as factoring 6 into 3 × 2. Nonetheless, if those machines would exist, we know that we would gain amazing speed-ups in solving some hard (classical) computational problems, such as those involved in breaking a huge portion of cryptographic systems in use today. Before we get into ‘quantum computing’, we should say a couple of things about ‘computing’. What is computing? Our answer by now probably won't come as such a shock: it's a process theory! Computation is indeed all about wiring the inputs and outputs of small processes together to make bigger processes. More specifically, a computation consists of a (finite) set of basic processes, which are wired together according to some (also finite) instructions, which we refer to as an algorithm or simply a program . The only essential difference between classical and quantum computation is the contents of the basic processes. For classical computation, these operations consist of things like logical operations (e.g. XOR) or reading/writing locations in memory. For quantum computation, we can extend this with quantum processes and classical-quantum interactions such as measurements. So quantum computing is all about figuring out how to write new kinds of programs that exploit these new building blocks to build faster algorithms or accomplish new kinds of tasks that aren't possible classically. The first quantum algorithms were ‘proofs of concept’, in the sense that they solved some problem much faster than a classical computer, but the kinds of problems they solved were not particularly interesting in their own right. However, this changed drastically with the advent of Grover's quantum search and Shor's factoring algorithms.
Computers today become faster by becoming smaller. By reducing the size of transistors, engineers are able to fit more of them on a given size microprocessor, thus increasing the processor's computational power. This process cannot continue forever. It has been estimated that sometime within the next two decades, at the current rate, engineers will be faced with the problem of building something that is smaller than an atom. This is as far as our current "classical" computing paradigm will take us. Quantum computing is a potential solution to this problem. This paradigm of computing seeks to directly exploit quantum mechanical phenomena to perform calculations or in some way boost computational efficiency. Some problems can theoretically be solved on a quantum computer exponentially faster than on a classical computer. An overview of the subject is provided here with emphasis on quantum information processing and physical realizations of a quantum computer. Included is a brief history of the subject, a discussion of quantum computing notions such as parallelism and entanglement and their use in quantum algorithms, and conjecture on the prospects and pitfalls of this theory.
Quantum Computation is an interdisciplinary field formed by the merge of quantum effect, information theory and algorithms. The future of computing lies with the quantum computers which may be a hypothetical paradigm but surely will be a reality very soon.This book describes about some quantum algorithms and programs which will prove as the foundation of quantum computers in the years to come.In quantum computers we exploit quantum effects to compute in ways that are faster or moreefficient than, or even impossible, on conventional computers. Quantum computers use aspecific physical implementation to gain a computational advantage over conventionalcomputers. Properties called superposition and entanglement may, in some cases, allow anexponential amount of parallelism. Also, special purpose machines like quantumcryptographic devices use entanglement and other peculiarities like quantum uncertainty.Quantum computing combines quantum mechanics, information theory, and aspects ofcomputer science. The field is a relatively new one that promises secure data transfer,dramatic computing speed increases, and may take component miniaturization to itsfundamental limit.
Quantum Computing The twenty-first century has witnessed remarkable advancements in computing technologies, transforming every aspect of modern society. As conventional computing systems approach their physical and computational limits, the search for new paradigms capable of solving increasingly complex problems has led to the emergence of Quantum Computing. By harnessing the principles of quantum mechanics, quantum computing represents a revolutionary approach that has the potential to redefine computation, communication, and information processing on an unprecedented scale. Quantum Computing is designed to provide readers with a comprehensive understanding of the concepts, principles, technologies, and applications that form the foundation of this rapidly evolving field. This book aims to bridge the gap between theoretical quantum mechanics and practical computational applications, enabling students, researchers, academicians, and professionals to explore the transformative potential of quantum technologies. The chapters in this book cover a broad spectrum of topics, including the fundamentals of quantum mechanics, quantum bits (qubits), quantum gates, superposition, entanglement, quantum circuits, quantum algorithms, quantum cryptography, quantum communication, and quantum error correction. The book also explores the architecture of quantum computers and examines the challenges involved in building scalable and fault-tolerant quantum systems. As industries increasingly seek innovative solutions to complex computational problems, quantum computing is emerging as a promising technology with applications in cryptography, artificial intelligence, machine learning, optimization, financial modeling, healthcare, pharmaceutical research, materials science, logistics, and climate modeling. The ability of quantum computers to process vast amounts of information simultaneously offers opportunities that were previously beyond the reach of classical computing systems. Special attention has been given to contemporary developments in quantum technologies, including quantum supremacy, hybrid quantum-classical computing, cloud-based quantum platforms, and the growing role of quantum computing in scientific discovery and industrial innovation. The book also discusses ethical, security, and societal implications associated with the advancement of quantum technologies. The primary objective of this book is to equip readers with both foundational knowledge and practical insights into the field of quantum computing. Through a balanced presentation of theory, applications, case studies, and emerging research trends, the book seeks to inspire curiosity, innovation, and further exploration in this transformative domain. We extend our sincere gratitude to the authors, reviewers, researchers, academicians, and industry experts whose valuable contributions have enriched the quality and relevance of this publication. Their dedication and expertise have helped create a resource that reflects the latest developments and future possibilities of quantum computing. We hope that Quantum Computing will serve as a valuable guide for students, educators, researchers, and technology professionals seeking to understand the next frontier of computational science. May this book inspire new ideas, foster innovation, and contribute to the advancement of knowledge in one of the most exciting technological revolutions of our time. Mr. M. Rajeshkumar Dr. R. Mariappan Mr. E.Janakiraman,