Synthesis methods for reversible circuits consisting of NOT, CNOT and 2-CNOT gates (Ph.D. thesis)

TL;DR

This thesis explores synthesis methods for reversible circuits with NOT, CNOT, and 2-CNOT gates, demonstrating that additional inputs can significantly reduce circuit complexity, depth, and weight.

Contribution

It introduces asymptotically optimal synthesis methods and discusses complexity reduction techniques for reversible circuits, including implementing discrete logarithm.

Findings

Additional inputs reduce circuit complexity, depth, and weight

Asymptotically optimal synthesis methods are described

Implementation of discrete logarithm within reversible circuits is discussed

Abstract

In this paper, reversible circuits consisting of NOT, CNOT and 2-CNOT gates are studied. Several asymptotically optimal by the order of magnitude synthesis methods are described. Some circuit's complexity reduction approaches are considered. Implementation of discrete logarithm within a reversible circuit is discussed. The main conclusion in the paper is that the usage of additional inputs (additional memory) in reversible circuits almost always allow to reduce their complexity, depth and weight.