  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.
