The Fredkin gate in reversible and quantum environments

Abstract

Reversible Computing circuits are characterized by low power consumption and their proximity to circuits for quantum computing. The Fredkin gate was one of the earliest proposed controlled reversible circuits, which however, was soon superseded by the Toffoli gate, the NOT, and CNOT gates, which constituting a flexible functionally complete set could also realize the Fredkin gate as a building block. In quantum computing circuits, the Fredkin gate (under the name controlled SWAP) plays an important role regarding the superposition of states. The present paper studies extensions of the Fredkin gate in terms of mixed polarity in the reversible domain and an application in quantum computing.