Editing DepartementKwantitatieweBestuur,Unisa, Posbus392,Uni sarand0003

Title: DepartementKwantitatieweBestuur,Unisa, Posbus392,Uni sarand0003

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Article Content:

The main ideas behind the development of quantum computation were formulated in the late 1970s and early 1980s by two physicists in the West and a mathematician in the former Soviet Union. It is not generally known in the West that the subject has roots in the Russian technical literature. The idea, as propagated by Benioff and (especially) Feynman, is reviewed along with the proposition of a foundation for this kind of computation by Manin in the Russian literature. The author hopes to present as impartial as possible a thesis on the early history of thought on this subject. The role of reversible and irreversible computational processes will be examined briefly as it relates to the origin of quantum computing and the so-called Information Paradox in physics. Information theory and physics, this paradox shows, have much to communicate to each other.

1. Introduction

Quantum computing is a rapidly developing field that holds great promise for various applications, such as cryptography, optimization, and machine learning. Over the past decade, several algorithms have been developed for prime factorization and database search using quantum computers. The author believes that a practical, efficient quantum algorithm for prime factorization would have significant implications for cryptography and secure communication.

2. Definitions of Computability

The strong need for a formal definition of an algorithm or computability arose due to two problems posed by Hilbert:

*The Decision Problem or the Turing Completeness Problem: Is there an algorithm that can determine if a given statement in first-order logic (like the Peano arithmetic) is true in all possible models?

*Hilbert's Tenth Problem: Is there an algorithm that can solve Diophantine equations, i.e., find all integer solutions to an equation given by a polynomial equation?

The Decision Problem was solved by Alan Turing and Alonzo Church independently in the mid-1930s. Church introduced the lambda calculus, a formal system that can define algorithms. Turing later defined an algorithm as a function that can be computed by a Turing machine, a hypothetical device that processes input and produces output according to a fixed set of rules. It was later proven that the class of recursive functions, functions that can be computed by a Turing machine, is the same as the class of functions that can be computed by a lambda calculus.

3. Quantum Computing

The author reviews the main ideas behind quantum computing, focusing on the development of quantum algorithms and the technology of quantum computation. Quantum algorithms have been developed for prime factorization and database search by Peter Shor at Bell Labs in 1994 and 1996, respectively. The author discusses the potential impact of efficient quantum algorithms on cryptography and secure communication.

4. Conclusion

In conclusion, the author believes that quantum computing has the potential to revolutionize various fields, particularly cryptography and secure communication. The development of efficient quantum algorithms could have significant implications for these areas. The author also emphasizes the importance of continued research and collaboration between information theory and physics to further advance the field of quantum computing.

Link to Article: https://arxiv.org/abs/0402037v2
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arXiv ID: 0402037v2

[[Category:Computer Science]]
[[Category:Quantum]]
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[[Category:Computing]]