Dual Toffoli and Peres-reversible gates

TL;DR

This paper introduces dual Toffoli and Peres reversible gates with disjunctive control, explores their properties, reduction techniques, and implementation on IBM quantum computers, advancing reversible circuit design.

Contribution

It presents novel dual Toffoli and Peres gates, their rewriting rules, and a Clifford+T implementation suitable for IBM quantum hardware.

Findings

Reversible gates operate under disjunctive control.

Rewriting rules reduce gate count and quantum cost.

Clifford+T implementation enables practical mapping to IBM quantum computers.

Abstract

The paper introduces dual Toffoli and Peres reversible gates, which operate under disjunctive control, and shows their functionality based on the Barenco et al. quantum model. Both uniform and mixed polarity are considered for the controls. Rewriting rules are presented, which provide a possible reduction of the number of gates and quantum cost of reversible (sub)circuits using standard Toffoli or Peres gates. Finally, a Clifford+T realization of a dual Toffoli and a dual Peres gate is shown, which may be used when mapping reversible circuits to the IBM quantum computers.