Introduction Quantum information and quantum foundations Quantum information science is about the processing of information by the exploitation of some distinguishing features of quantum systems, such as electrons, photons, ions. In recent years a lot has been promised in the domain of quantum information. In quantum computing it was promised that NP-problems would be solved in polynomial time. In quantum cryptography there were claims that protocols would have practically 100% security. At the moment it is too early to say anything definitive regarding the final results of this great project. In quantum computing a few quantum algorithms and developed devices, “quantum pre-computers” with a few quantum registers, were created. However, difficulties could no longer be ignored. For some reason it was impossible to create numerous quantum algorithms that could be applied to various problems. Up to now the whole project is based on two or three types of algorithm, and among them one, namely, the algorithms for prime factorization, might be interesting for real-world application. There is a general tendency to consider this situation with quantum algorithms as an occasional difficulty. But, as the years pass, one might start to think that there is something fundamentally wrong. The same feelings are induced by developments in quantum hardware. It seems that the complexity of the problem of creation of a device with a large number N of quantum registers increases extremely non-linearly with increasing N . In quantum cryptography the situation is opposite to that of quantum computing. There were tremendous successes in the development of technologies for production and transmission of quantum information, especially pairs of entangled photons.
Introduction Quantum information and quantum foundations Quantum information science is about the processing of information by the exploitation of some distinguishing features of quantum systems, such as electrons, photons, ions. In recent years a lot has been promised in the domain of quantum information. In quantum computing it was promised that NP-problems would be solved in polynomial time. In quantum cryptography there were claims that protocols would have practically 100% security. At the moment it is too early to say anything definitive regarding the final results of this great project. In quantum computing a few quantum algorithms and developed devices, “quantum pre-computers” with a few quantum registers, were created. However, difficulties could no longer be ignored. For some reason it was impossible to create numerous quantum algorithms that could be applied to various problems. Up to now the whole project is based on two or three types of algorithm, and among them one, namely, the algorithms for prime factorization, might be interesting for real-world application. There is a general tendency to consider this situation with quantum algorithms as an occasional difficulty. But, as the years pass, one might start to think that there is something fundamentally wrong. The same feelings are induced by developments in quantum hardware. It seems that the complexity of the problem of creation of a device with a large number N of quantum registers increases extremely non-linearly with increasing N . In quantum cryptography the situation is opposite to that of quantum computing. There were tremendous successes in the development of technologies for production and transmission of quantum information, especially pairs of entangled photons.
Nowadays quantum information science is in a state of theoretic completeness; much is invested to research quality physical solution for quantum computer and applications, so the field is led by physicists and information science and technology professionals. This field proved its potential and many (including us) believe it is in the right direction to go. In this paper we'll try to present and analyze the philosophy and nature of quantum information science and discuss hot topics around them. Although there is plenty of space for discussion around this field, we will concentrate on some important issues, such as quantum communication, algorithms and cryptography. Communication promises to be one of the directions where huge breakthroughs will be observed (entanglement as communication), algorithms have already shown exponential advantage (Shor's factoring) over classical counterparts and different paradigm of information processing. Cryptography seems to utilize general achievements in quantum information science and make encryption protocols very secure. Quantum computation can be understood as a generalization of classical computation: The possible states of a quantum computer are superpositions of bit strings, where the tensor factor is called a quantum bit or qubit. To evaluate the computational complexity of an algorithm, either classical or quantum, it is necessary to specify a set of elementary operations, the number of which used during the computation quantities the complexity. If we allow arbitrary permutations classically, or arbitrary unitary transformations quantum mechanically, any state can be reached from any other state in a single step. The general kind of quantum computer should be programmed to perform distinctively quantum operations such as generating two bits in a superposition state. An appropriate measurement on the final superposed state of the computer produces a probabilistic behavior of the output, and because of this quantum parallelization does not reduce the average time required for parallelizable computation completion. The development of quantum computing science and technology as well as quantum computers as thinking machines is very dependent on different achievements of modern research in fundamental and applied physics as well as novel mathematical methods and tools.
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.
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.
In order to provide novel techniques for processing, storing, and transmitting information, the multidisciplinary field of quantum information science (QIS) integrates ideas from quantum physics [ 4 ] with information science. However, due to a number of events, including Peter Shor’s invention of quantum algorithms and the rise in interest in quantum computing, the history of QIS started to expand quickly in the early to middle 1990s. Peter Shor, a physicist and mathematician, developed the first quantum algorithm that could factor big numbers exponentially more rapidly than any classical algorithm in 1994. This finding triggered strong interest in quantum computing’s potential to tackle issues that are currently unsolvable for classical computers. Since then, QIS has advanced due to the development of novel quantum algorithms and enhancements in the hardware used for quantum computing. Understanding complex quantum phenomena like entanglement and superposition and developing novel strategies for utilizing them for information processing and communication are the core goals of QIS. Quantum bits (qubits) can exist in superpositions of 0 and 1 simultaneously, which enables far more efficient computation than classical bits, which can only be in one state or the other at a given time. Superposition is a key concept in quantum computing. In addition to superposition, entanglement, coherence, and quantum algorithms are other important QIS concepts. Entanglement is a key feature of quantum mechanics and has been observed experimentally in a wide range of physical systems, including photons, atoms, and superconducting qubits. Two particles can get entangled with one another through a phenomenon called entanglement in which their quantum states exhibit a high correlation. This indicates that even if two particles are separated by a considerable distance, modifying the state of one can change the state of the other. No matter how far away two separate particles are from one another when they are entangled, measuring the state of one particle immediately gives the state of another particle. It plays a central role in many quantum technologies, including quantum computing for solving complex problems that take classical computers a long time to solve, quantum cryptography for secure communications, quantum sensing for quantum properties of particles to enable more precise measurements, and quantum networking to improve communication and processing speed over both short and long distances. Quantum metrology methods use the principles of quantum mechanics to improve the accuracy of measurements in fields like gravity sensors, timekeeping, and frequency standards. Some of the benefits of QIS are enhanced computing power, improved communication, advanced cryptography, more precise scientific measurements, and better logistics optimization.
Introduction In an ordinary computer, information is stored in a collection of tiny circuits each of which is designed to have two stable and easily distinguishable configurations: each represents a bit . In our study of quantum cryptography, we have seen how it can be useful to express information not in ordinary bits but in qubits . Whereas a bit can have only two values, say 0 and 1, a qubit can be in any quantum superposition of ∣0〉 and ∣1〉. Moreover, a qubit can be entangled with other qubits. Thus one might wonder whether a quantum computer, in which the basic elements for storing and processing information are qubits, can outperform an ordinary (classical) computer in certain ways. This question was addressed by researchers starting in the 1980s. In terms of practical consequences, perhaps the most dramatic answer has been given by Peter Shor in his 1994 factoring algorithm for a quantum computer, an algorithm that is exponentially faster than any known classical algorithm. As we have seen in Chapter 1, the difficulty of factoring a product of two large primes is the basis of the security of the RSA cryptosystem. So if one could build a large enough quantum computer – and there is no reason in principle why this could not be done – the RSA system would be rendered ineffective. In this chapter we present the basics of quantum computation and then focus on Shor's factoring algorithm.
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