Quantum information is physics' claim on computation: the argument, opened by Feynman in 1982, that quantum systems are efficiently simulated only by quantum machines, and the program—qubits, gates, algorithms, and error correction—that turned the argument into an engineering discipline. This article presents a narrative review of the primary literature that built the field, from Feynman's 1982 simulation proposal and Deutsch's 1985 universal quantum computer, through the Deutsch–Jozsa problem, which showed quantum algorithms' separation, Shor's 1994 factoring algorithm, whose period-finding broke public-key cryptography's assumptions, Grover's 1996 quadratic search speedup, Shor's 1995 and Steane's 1996 error-correcting codes, which answered decoherence—the field's standing objection—Cirac and Zoller's 1995 trapped-ion gates and Knill, Laflamme, and Milburn's 2001 linear-optical scheme, Bennett and Brassard's 1984 quantum cryptography, and Nielsen and Chuang's 2000 codifying textbook. The synthesis is organized around three themes: the computational settlement, in which quantum parallelism was formalized and weaponized into algorithms with provable speedups; the error-correction settlement, in which the no-cloning obstacle was circumvented and fragile states made correctable; and the physical settlement, in which implementations—ions, photons, and their successors—gave the theory its hardware. It is concluded that quantum information's history is the conversion of an objection—quantum states are too fragile to compute with—into the field's defining technology: error correction, the discipline that made the qubit a promise kept in principle.
Quantum information is physics' claim on computation: the argument, opened by Feynman in 1982, that quantum systems are efficiently simulated only by quantum machines, and the program—qubits, gates, algorithms, and error correction—that turned the argument into an engineering discipline. This article presents a narrative review of the primary literature that built the field, from Feynman's 1982 simulation proposal and Deutsch's 1985 universal quantum computer, through the Deutsch–Jozsa problem, which showed quantum algorithms' separation, Shor's 1994 factoring algorithm, whose period-finding broke public-key cryptography's assumptions, Grover's 1996 quadratic search speedup, Shor's 1995 and Steane's 1996 error-correcting codes, which answered decoherence—the field's standing objection—Cirac and Zoller's 1995 trapped-ion gates and Knill, Laflamme, and Milburn's 2001 linear-optical scheme, Bennett and Brassard's 1984 quantum cryptography, and Nielsen and Chuang's 2000 codifying textbook. The synthesis is organized around three themes: the computational settlement, in which quantum parallelism was formalized and weaponized into algorithms with provable speedups; the error-correction settlement, in which the no-cloning obstacle was circumvented and fragile states made correctable; and the physical settlement, in which implementations—ions, photons, and their successors—gave the theory its hardware. It is concluded that quantum information's history is the conversion of an objection—quantum states are too fragile to compute with—into the field's defining technology: error correction, the discipline that made the qubit a promise kept in principle.
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.
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
Quantum computation has teased scientific imagination ever since Richard Feynman dreamed in 1982 of quantum-mechanical computers, which could solve problems that are effectively out of reach of classical computation thanks to their ability to use superposition and entanglement. This critical survey recalls the field’s journey from theoretical advances to present-day engineering challenges, highlighting the yawning gulf between quantum computing’s lofty promises and its actual realizations. By examining three decades of developments, from Shor’s integer factorization and Grover’s search algorithms to recent demonstrations of quantum supremacy, this paper shows how idealized mathematical models interact with the noisy, resource-constrained realities of physical quantum systems. The author presents a literature review through critically analyzing key achievements in quantum computing research.. This paper concludes that quantum advantage will not arise from brute-force universality, but through application specific co-design, combining noise-adjusted algorithms to quantum hardware restrictions whilst mixing classical and quantum processing modes and fundamentally changing the way we think of error correction through the physics of qubits. This shift in paradigm from theoretical maximalism to engineering pragmatism embodies a realistic roadmap for practical quantum computation.
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.
In a ground breaking discovery in 1994, Shor has shown that quantum computers, if built, can factor numbers efficiently. Since then quantum computing has become a burgeoning field of research, attracting theoreticians and experimentalists alike, and regrouping researchers from fields like computer science, physics, mathematics and engineering. Quantum information is very fragile and prone to decoherence. Yet by the middle of 1996 it has been shown that fault-tolerant quantum computation is possible. We give a simple description of the elements of quantum error-correction and quantum fault-tolerance. After characterizing quantum errors we present several error correction schemes and outline the elements of a full fledged fault-tolerant computation, which works error-free even though all of its components can be faulty. We also mention alternative approaches to error-correction, so called error-avoiding or decoherence-free schemes. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Quantum computers operate on the principles of quantum logic, a fundamentally distinct paradigm from classical Boolean logic. This disparity leads to quantum computation's enhanced efficiency compared to classical computing. In this comprehensive review, we demystify the fundamental concepts of quantum computation, covering the creation of elementary gates and networks. We highlight the capabilities of quantum algorithms by examining the simple Deutsch problem and, in straightforward terms, dissect the renowned Shor algorithm for factoring large numbers into primes. Furthermore, we delve into the realm of physical quantum computer implementations, with a particular focus on tlo he linear ion trap approach. Here, we shed light on the primary challenge hindering the realization of practical quantum computers: the issue of decoherence. Nonetheless, we demonstrate that this hurdle can be overcome through the application of quantum error correction methods