Abstract
The paper discusses various applications of permutation group theory in the synthesis of reversible logic circuits consisting of Toffoli gates with negative control lines. An asymptotically optimal synthesis algorithm for circuits consisting of gates from the NCT library is described. An algorithm for gate complexity reduction, based on equivalent replacements of gates compositions, is introduced. A new approach for combining a group-theory-based synthesis algorithm with a Reed–Muller-spectra-based synthesis algorithm is described. Experimental results are presented to show that the proposed synthesis techniques allow a reduction in input lines count, gate complexity or quantum cost of reversible circuits for various benchmark functions.
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Notes
- 1.
Hereinafter a multiplication of permutations is left-associative: \((f \circ g)(x) = g(f(x))\).
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Acknowledgments
The reported study was partially supported by RFBR, research project No. 16-01-00196 A.
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Zakablukov, D.V. (2016). Application of Permutation Group Theory in Reversible Logic Synthesis. In: Devitt, S., Lanese, I. (eds) Reversible Computation. RC 2016. Lecture Notes in Computer Science(), vol 9720. Springer, Cham. https://doi.org/10.1007/978-3-319-40578-0_17
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DOI: https://doi.org/10.1007/978-3-319-40578-0_17
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