Optimal Design of a Reversible Full Adder

Classical computing machines using irreversible logic gates unavoidably generate heat. This is due to the fact that each loss of one bit of information is accompanied by an increase of the environment’s entropy by an amount k log(2), where k is Boltzmann’s constant. In turn this means that an amount of thermal energy equal to kT log(2) is transferred to the environment, having a temperature T. According to Landauer’s principle [1,2], it is possible to construct a computer that dissipates an arbitrarily small amount of heat [3]. A necessary condition is that no information is thrown away. Therefore, logical reversibility is a necessary (although not sufficient) condition for physical reversibility. It is widely known that an arbitrary boolean function can be implemented into logic using only NAND-gates. A NAND-gate has two binary inputs (say A and B) but only one binary output (say P), and