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Implementing an arbitrary reversible logic gate

Implementing an arbitrary reversible logic gate The (2w)! reversible logic gates of width w, i.e. reversible logic gates with w inputs and w outputs, together with the action of cascading, form a group R. We define a subgroup K, consisting of the SWITCHED gates. There are [(2w1)!]2 such gates. They partition the group R into 2w1 + 1 double cosets. This allows us to decompose an arbitrary reversible gate into the cascade of three gates: a SWITCHED gate, an upside-down simple control gate and a second SWITCHED gate. We present an algorithm to perform this factorization, and thus provide a method of implementing an arbitrary reversible gate into hardware. The algorithm can be used to automate the implementation of a reversible function in future (c-MOS) technologies, realizing low-cost computing. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Physics A: Mathematical and General IOP Publishing

Implementing an arbitrary reversible logic gate

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References (30)

Copyright
Copyright 2005 IOP Publishing Ltd
ISSN
0305-4470
eISSN
1361-6447
DOI
10.1088/0305-4470/38/16/007
Publisher site
See Article on Publisher Site

Abstract

The (2w)! reversible logic gates of width w, i.e. reversible logic gates with w inputs and w outputs, together with the action of cascading, form a group R. We define a subgroup K, consisting of the SWITCHED gates. There are [(2w1)!]2 such gates. They partition the group R into 2w1 + 1 double cosets. This allows us to decompose an arbitrary reversible gate into the cascade of three gates: a SWITCHED gate, an upside-down simple control gate and a second SWITCHED gate. We present an algorithm to perform this factorization, and thus provide a method of implementing an arbitrary reversible gate into hardware. The algorithm can be used to automate the implementation of a reversible function in future (c-MOS) technologies, realizing low-cost computing.

Journal

Journal of Physics A: Mathematical and GeneralIOP Publishing

Published: Apr 22, 2005

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