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Introduction to Quantum Information, Quantum Computation, and Its Application to Cryptography

D.J. Guan

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

The development of quantum algorithms and quantum information theory, as well as the design and construction of experimental quantum computers, are the most exciting events in the scientific community in the last two decades. In this talk, I will briefly introduce quantum computation and quantum information. I will also discuss the influences of these developments on information security and our recent research results on the design of cryptographic protocol by using quantum information. Quantum Computers In 1982 Richard Feynman observed that certain quantum mechanical effects cannot be simulated efficiently on a traditional computer. It is speculated that computations may be done more efficiently by using these quantum effects.

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The development of quantum algorithms and quantum information theory, as well as the design and construction of experimental quantum computers, are the most exciting events in the scientific community in the last two decades. In this talk, I will briefly introduce quantum computation and quantum information. I will also discuss the influences of these developments on information security and our recent research results on the design of cryptographic protocol by using quantum information. Quantum Computers In 1982 Richard Feynman observed that certain quantum mechanical effects cannot be simulated efficiently on a traditional computer. It is speculated that computations may be done more efficiently by using these quantum effects.
In the last two decades, the interest in quantum computation has increased significantly among research communities. Quantum computing is the field that investigates the computational power and other properties of computers on the basis of the underlying quantum-mechanical principles. The main purpose is to find quantum algorithms that are significantly faster than any existing classical algorithms solving the same problem. While the quantum computers currently freely available to wider public count no more than two dozens of qubits, and most recently developed quantum devices offer some 50-60 qubits, quantum computer hardware is expected to grow in terms of qubit counts, fault tolerance, and resistance to decoherence. The main objective of this chapter is to present an introduction to the core quantum computing algorithms developed thus far for the field of cryptography.
Quantum Computing and Quantum Information Science seem very promising and developing rapidly since its inception in early 1980s by Paul Benioff with the proposal of quantum mechanical model of the Turing machine and later By Richard Feynman and Yuri Manin for the proposal of a quantum computers for simulating various problems that classical computer could not. Quantum computers have a computational advantage for some problems, over classical computers and most applications are trying to use an efficient combination of classical and quantum computers like Shor’s factoring algorithm. Other areas that are expected to be benefitted from quantum computing are Machine Learning and deep learning, molecular biology, genomics and cancer research, space exploration, atomic and nuclear research and macro-economic forecasting. This paper represents a brief overview of the state of art of quantum computing and quantum information science with discussions of various theoretical and experimental aspects adopted by the researchers.
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 main purpose of this paper is to examine some (potential) applications of quantum computation and to review the interplay between quantum theory. Quantum computation, a brief introduction to it is provided, and a famous but simple quantum algorithm is introduced so that they can appreciate the power of quantum computation. Also, a (quite personal) survey of quantum computation is presented in order to give the readers a (unbalanced) panorama of the field. Now a day’ quantum communication using quantum effects to send information without eavesdroppers listening undetected and quantum mechanics is a mathematical framework or set of rules for the construction of physical theories.. In this Literature survey, we introduce the motivation and the current and future circumstances of the art of research in quantum cryptography. In exacting we discuss the contemporary security model together with its assumptions, strengths and weaknesses. A syndrome measurement is planned to diagnose “which error corrupts in an encoded state “and to retrieve the true information. We survey the most recent developments in quantum model and counter measures against it. Quantum computing is a new trend in computation theory and a quantum mechanical system has several useful properties like Entanglement.
Richard Feynman's observation that certain quantum mechanical effects cannot be simulated efficiently on a computer led to speculation that computation in general could be done more efficiently if it used these quantum effects. This speculation proved justified when Peter Shor described a polynomial time quantum algorithm for factoring intergers. In quantum systems, the computational space increases exponentially with the size of the system, which enables exponential parallelism. This parallelism could lead to exponentially faster quantum algorithms than possible classically. The catch is that accessing the results, which requires measurement, proves tricky and requires new nontraditional programming techniques. The aim of this paper is to guide computer scientists through the barriers that separate quantum computing from conventional computing. We introduce basic principles of quantum mechanics to explain where the power of quantum computers comes from and why it is difficult to harness. We describe quantum cryptography, teleportation, and dense coding. Various approaches to exploiting the power of quantum parallelism are explained. We conclude with a discussion of quantum error correction.