Quantum logic as a basis for computations
type: Item
instance of: scholarly article
title: Quantum logic as a basis for computations
zbMATH Open document ID: 0962.03058
DOI: 10.1023/A:1003678913718
author: Jarosław Pykacz
published in: International Journal of Theoretical Physics
publication date: 2001-02-25T00:00:00Z
review text: Lately, several algorithms have been proposed which use quantum mechanical phenomena to speed up computations. These initial successes make researchers believe that there is a great potential in using quantum effects in computing. To analyze these future potential possibilities, the author starts analyzing the problem of quantum computation from the foundational viewpoint. Traditional (non-classical) computations are based on binary logic; adders and other elements of modern computers are formed from logical ``gates'' which implement basic logical operations. Similarly, quantum mechanics can be described in terms of quantum logic. It is therefore reasonable to analyze what we would be able to compute if we had quantum ``gates'' which implement operations of quantum logic. In particular, an interesting result is related to the implementation of an approximately known number like ``nearly 3''. At first glance, since 3 is usually represented, in a computer, as \(011_2\), it makes sense to implement ``nearly 3'' by using three bits, one ``almost 0'' and two ``almost 1'' 's. The drawback of this approach is that while the intuitive meaning of ``nearly 3'' includes 4 (\(=100_2\)), the probability of changing all three bits to get 4 is extremely small. The author therefore proposes to use, instead of a normal binary representation, special codes (called Gray codes) in which the code for \(n+1\) differs from a code for \(n\) in only one bit. It is worth mentioning that, in contrast to the known algorithms of quantum computing, which are based on -- really or potentially -- physically possible schemes, we do not know neither how to implement quantum logic operations nor whether it is physically possible to implement them. Thus, the author's research is, at present, more foundational than practical.
Mathematics Subject Classification ID: 03G12
Mathematics Subject Classification ID: 68Q05
Mathematics Subject Classification ID: 81P10
Mathematics Subject Classification ID: 03D05
zbMATH DE Number: 1529166
zbMATH Keywords: quantum logic
zbMATH Keywords: computations using quantum logics
zbMATH Keywords: quantum computation
zbMATH Keywords: Gray codes
reviewed by: Vladik Kreinovich
MaRDI profile type: Publication
full work available at URL: a:1003678913718
OpenAlex ID: W122853693
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description: scientific article; zbMATH DE number 1529166