Reversible Gates Using Quantum Phase Slip Junctions, Part A: Logical Reversible Design

Quantum phase slip junction (QPSJ) can offer very low power switching operation and represent near adiabatic switching operation for using in designing of the reversible logic gates. The reversible gates have logical reversibility, where the inputs can be logically reconstructed from the outputs and no data is lost, and physical (adiabatic) reversibility, where the energy dissipation can be decreased even below the Landauer limit. In this manuscript, for the first time, designing of the QPSJ-based basic reversible gates, namely Feynman, Toffoli, Peres, and Fredkin, from the logical reversibility point of view is represented. The main logic function in these gates is the
xor
function. First, a new two-input QPSJ-based
xor
gate with simple circuit is designed in which the outputs of the previous gate can be connected directly to its inputs without the need for splitter lines. Second, the proposed
xor
gate is used to design the Feynman and Toffoli gates. Further, the Peres and Fredkin gates are designed by using the proposed Feynman and Toffoli gates. Proper operations of the proposed gates are verified by simulation results. Logical reversibility of the Feynman and Toffoli gates is verified by cascading them and operating their logical function two times, i.e.,
f(f(x))
=
x
.