Application of Permutation Group Theory in Reversible Logic Synthesis

TL;DR

This paper explores the use of permutation group theory to improve reversible logic circuit synthesis, introducing algorithms that optimize gate complexity and circuit parameters, with experimental validation on benchmark functions.

Contribution

It presents novel algorithms combining group theory and Reed-Muller spectra for more efficient reversible circuit synthesis, reducing input lines and quantum cost.

Findings

Reduction in input lines for benchmark circuits

Decreased gate complexity and quantum cost

Effective combination of group-theory and Reed-Muller methods

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.