The important problems that is quantum superposition and en ta ngled state in the quantum computation, quantum communication and quantum comput er have been discussed. From these, it is pointed out that the problems which ar e concern with quantum information can be handled by the quantum mechanics theor ies: quantum computing and transformation of the quantum information follows the Schrdinger Equation and U transformation in quantum system, respectively.
The important problems that is quantum superposition and en ta ngled state in the quantum computation, quantum communication and quantum comput er have been discussed. From these, it is pointed out that the problems which ar e concern with quantum information can be handled by the quantum mechanics theor ies: quantum computing and transformation of the quantum information follows the Schrdinger Equation and U transformation in quantum system, respectively.
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.
This chapter discusses quantum mechanics and certain quantum computing elements are initially. Errors are introduced in quantum computation because a quantum system cannot be completely isolated from its environment. The chapter explores certain quantum algorithms. It aims to develop a formal model of quantum computation via quantum Turing machine. The chapter outlines preliminaries for stating the laws of quantum mechanics. It aanlyses the strengths and drawbacks of the quantum computing paradigm. Quantum communication channels, encoders, and decoders are some of the examples of superoperators. One of the important concepts in quantum computation and communication is that of quantum entanglement. Analogously quantum information theory addresses the problem of optimal communication over a quantum channel. Information theory is the study of communication systems from a probabilistic point of view. Analogous to classical communication theory, quantum communication theory studies the limits of efficient data storage and transmission of quantum information. Quantum cryptography uses the principles of quantum mechanics.
In this presentation, an overview of Quantum Information Systems is given. Therefore, the postulates of quantum mechanics are given based on one interpretation that is called the Copenhagen interpretation. The main pillars of quantum mechanics are: Superposition, Interference, and Entanglement. Quantum Information Systems comprise three disciplines: Quantum Computation, Quantum Communication, and Quantum Control. Each one of them has a number of topics with some implementations that have reached the commercial level. Quantum Computation has three models: the circuit model that is using different techniques like superconducting elements and special Silicon-based elements. The Adiabatic quantum model has reached the commercial stage through a start-up company using superconducting chips. The categorical quantum model is based on category theory and one of its main applications is the study and verification of network and cryptographic protocols. Quantum communication started with defining the basic unit of information, the qubit. Then the quantum compression theorem was proved. The quantum channel capacity problem was divided into two problems: transmitting classical information over a quantum channel, and transmitting quantum information over a quantum channel. The first problem was partially resolved. However, the second problem is being researched upon. Two applications will be briefly presented: quantum teleportation and superdense coding. Both of them employs quantum entanglement. Quantum Key Distribution (QKD) using cryptographic protocols has received much attention due its importance in network security. A number of protocols have been proposed and some of them have been implemented, and now a number of commercial products have been announced. Also, some experimental networks have been implemented. QKD using space links have been proposed and experimented with. In few years quantum satellites will be launched. Quantum cryptographic protocols are being proposed to protect infrastructure networks like the electric power grid. Also, it is being used as a countermeasure against global spying networks like ECHELON that are detrimental for national economies. The Quantum Internet is also being considered using quantum teleportation together with Cavity Quantum Electrodynamics with some experimental work going on. Quantum Control is essential for both Quantum Computation and Quantum Communication. Intensive research is going on in: State estimation (called Quantum State Tomography), system identification (called Quantum Process Tomography), and Quantum Feedback Control. The basic concepts will be briefly considered in this presentation. University education has witnessed major changes to support the above developments. At the postgraduate level many universities offer many courses related to the above disciplines. Recently, a number of institutions started to offer undergraduate courses and some of them have even started to introduce Quantum Engineering 4 years undergraduate programs. A brief account will be given to such developments.
Quantum computing and quantum information are two of the fastest-growing and most exciting research areas in physics. The possibilities of using non-local behaviour of quantum mechanics to factorize integers in random polynomial time have added to this new interest. This invaluable book provides a collection of problems in quantum computing and quantum information together with detailed solutions. It consists of two parts: in the first part finite-dimensional systems are considered, while the second part deals with finite-dimensional systems. All the important concepts and topics are included, such as quantum gates and quantum circuits, entanglement, teleportation, Bell states, Bell inequality, Schmidt decomposition, quantum Fourier transform, magic gates, von Neumann entropy quantum cryptography, quantum error correction, coherent states, squeezed states, POVM measurement, beam splitter and Kerr-Hamilton operator. The topics range in difficulty from elementary o advanced. Almost all of the problems are solved in detail and most of them are self-contained. All relevant definitions are given. Students can learn from this book important principles and strategies required for problem solving. Teachers will find it useful as a supplement, since important concepts and techniques are developed through the problems. It can also be used as a text or a supplement for linear and multilinear algebra or matrix theory.
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.
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.