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Journal of Henan University of Technology

DISCUSSION ON QUANTUM COMPUTER

GU Guo-tai

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

This paper first introduces the concept of quantum computer and some basic applications,then looks back the general research situation of quantum computer theory,explaining the basic quantum computer theory,the differences between quantum computer and classic computer,and at last points out the situations to realize quantum computer and the present difficulties.

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This paper deals with alternative cryptosystems which resist the attacks of quantum computers. The work is divided into 3 chapters. In the first chapter we give the motivation to observe such systems. We explain some basic concepts from cryptography and point out some key features that make a given cryptosystem good. Then we give a short introduction to quantum computing, explaining the difference between a classical and a quantum computer, in addition to showing how computation works in a quantum environment. For the end of the first chapter we briefly explain the most important quantum algorithm: Shor’s algorithm. Shor’s algorithm allows us to easily factorize numbers and thus break most of the cryptosystems used today. For this reason, there is a need for cryptosystems based on a different class of problems. In the second chapter we present the first class of such problems, the problems defined over lattices, and we explain an example of a cryptosystem based on these problems, the GGH cryptosystem with a public key. At the beginning this chapter, we define lattices and show some key features. Then we describe most of the major problems on lattices such as SVP and CVP. To conclude, we define the GGH cryptosystem, explain how it works and what are the drawbacks and advantages. In the last, third chapter, we present another class of problems that are currently resisting quantum attacks, code based problems. First we explain what the codes are and using an example code explain their essential properties. The most important of all these features is the ability to correct errors and precisely around this feature has Mceliece designed his cryptosystem. At the end of the chapter, we explain the idea of the Mceliece cryptosystem and comment on its quality for practical application.

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This paper first introduces the concept of quantum computer and some basic applications,then looks back the general research situation of quantum computer theory,explaining the basic quantum computer theory,the differences between quantum computer and classic computer,and at last points out the situations to realize quantum computer and the present difficulties.
A new paradigm of computation has appeared recently that is known as quantum computing and which is able to solve difficult problems that cannot be solved using classical computing.It provides a comprehensive overview of the basic concepts, computational models, architectures, tools, applications and implications of quantum computing.The paper is based on the latest research, and it's used to evaluate the state of quantum computing, from theory to practical, application-oriented implementations.Fundamental concepts such as qubits, superposition, entanglement and hybrid quantum-classical computation are explained, along with major models and frameworks of quantum computing, including Cirq, TensorFlow Quantum and ProjectQ.Furthermore, various significant application areas, such as cryptography, optimization, AI, drug discovery, and industrial computing, are explored, highlighting the applications' potential and their technological development.Although great strides have been made, scalability, noise, error correction, interoperability and hardware challenges are major problems in the NISQ era.It also examines new trends, future research directions and the societal, security and ethical considerations of the advancement of quantum technology.But the bigger picture indicates that quantum computing is progressing from theory to reality, and there are many technical and institutional challenges to be resolved along the way.Interdisciplinary studies and responsible innovation will be key to unlocking the potential of quantum computing as the next generation of computational technology.
This book belongs to a series of online books summarizing the recent state Topological Geometrodynamics (TGD) and its applications. TGD can be regarded as a unified theory of fundamental interactions but is not the kind of unified theory as so called GUTs constructed by graduate students at seventies and eighties using detailed recipes for how to reduce everything to group theory. Nowadays this activity has been completely computerized and it probably takes only a few hours to print out the predictions of this kind of unified theory as an article in the desired format. TGD is something different and I am not ashamed to confess that I have devoted the last 32 years of my life to this enterprise and am still unable to write The Rules. I got the basic idea of Topological Geometrodynamics (TGD) during autumn 1978, perhaps it was October. What I realized was that the representability of physical space-times as 4-dimensional surfaces of some higher-dimensional space-time obtained by replacing the points of Minkowski space with some very small compact internal space could resolve the conceptual difficulties of general relativity related to the definition of the notion of energy. This belief was too optimistic and only with the advent of what I call zero energy ontology the understanding of the notion of Poincare invariance has become satisfactory.
This paper deals with alternative cryptosystems which resist the attacks of quantum computers. The work is divided into 3 chapters. In the first chapter we give the motivation to observe such systems. We explain some basic concepts from cryptography and point out some key features that make a given cryptosystem good. Then we give a short introduction to quantum computing, explaining the difference between a classical and a quantum computer, in addition to showing how computation works in a quantum environment. For the end of the first chapter we briefly explain the most important quantum algorithm: Shor’s algorithm. Shor’s algorithm allows us to easily factorize numbers and thus break most of the cryptosystems used today. For this reason, there is a need for cryptosystems based on a different class of problems. In the second chapter we present the first class of such problems, the problems defined over lattices, and we explain an example of a cryptosystem based on these problems, the GGH cryptosystem with a public key. At the beginning this chapter, we define lattices and show some key features. Then we describe most of the major problems on lattices such as SVP and CVP. To conclude, we define the GGH cryptosystem, explain how it works and what are the drawbacks and advantages. In the last, third chapter, we present another class of problems that are currently resisting quantum attacks, code based problems. First we explain what the codes are and using an example code explain their essential properties. The most important of all these features is the ability to correct errors and precisely around this feature has Mceliece designed his cryptosystem. At the end of the chapter, we explain the idea of the Mceliece cryptosystem and comment on its quality for practical application.