GF(4) Based Synthesis of Quaternary Reversible/Quantum Logic Circuits

• Published in: 37th International Symposium on Multiple-Valued Logic (ISMVL'07) p. 11
• Main Authors: Khan, M.H.A., Perkowski, M.A.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01-05-2007
• Subjects: Circuit synthesis; Computer science; Decoding; DH-HEMTs; Galois fields; Input variables; Logic circuits; Logic functions; Multivalued logic; Quantum computing
• ISBN: 9780769528311; 0769528317
• ISSN: 0195-623X; 2378-2226
• DOI: 10.1109/ISMVL.2007.26

Galois field sum of products (GFSOP) has been found to be very promising for reversible/quantum implementation of multiple-valued logic. In this paper, we show ten quaternary Galois field expansions, using which quaternary Galois field decision diagrams (QGFDD) can be constructed. Flattening of the QGFDD generates quaternary GFSOP (QGFSOP). These QGFSOP can be implemented as cascade of quaternary 1-qudit gates and multi-qudit Feynman and Toffoli gates. We also show the realization of quaternary Feynman and Toffoli gates using liquid ion-trap realizable 1-qudit gates and 2-qudit Muthukrishnan-Stroud gates. Besides the quaternary functions, this approach can also be used for synthesis of encoded binary functions by grouping 2-bits together into quaternary value. For this purpose, we show binary-to-quaternary encoder and quaternary-to- binary decoder circuits using quaternary 1-quidit gates and 2-qudit Muthukrishnan-Stroud gates.