Quantum conservative many-valued computing

doi:10.1016/j.fss.2007.09.014

2008-05-01

PRE

Gianpiero Cattaneo

Alberto Leporati

Roberto Leporini *

DOI：10.1016/j.fss.2007.09.014

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摘要

En 中文

We extend the basic principles and results of conservative logic to include the main features of many-valued logics with a finite number of truth values. Different approaches to many-valued logics are examined in order to determine some possible functionally complete sets of logic connectives. As a result, we describe some possible finite-valued gates which realize a functionally complete set of fundamental connectives. One of the purposes of this work is to show that the framework of reversible and conservative computation can be extended toward some non-classical reasoning environments, originally proposed to deal with propositions which embed imprecise and/or uncertain information, that are Usually based upon many-valued and modal logics. We also describe a possible quantum realization of the proposed gates, using creation and annihilation operators. In such realization the gates are expressed as formulas that are obtained using three techniques: a brute force technique, an extension of the Conditional Quantum Control method introduced by Barenco, Deutsch, Ekert and Jozsa [Conditional quantum control and logic gates, Phys. Rev. Lett. 74 (1995) 4083], and a new technique that we call the Constants method. We show the Constants method allows one to reduce the number of local operators in the formulas which cot-respond to the proposed gates. (c) 2007 Elsevier B.V. All rights reserved.

Keyword:

quantum computing

conservative logic

many-valued logics