Reversible and DNA Computing. Hafiz M. H. Babu

1.10 Quantum circuit of Toffoli gate.

Figure 1.11 Quantum circuit of Fredkin gate.

Figure 1.12 Quantum circuit of a Peres gate.

      1.17.3 Fredkin Gate

The Fredkin gate costs the same as the Toffoli gate. The Toffoli gate includes a single Davio gate, while the Fredkin gate includes two multiplexers. The quantum equivalent Toffoli gate is shown in Figure 1.10. Each dotted rectangles in Figure 1.11 is equivalent to a 2 2 Feynman gate and so the cost is 1 for the particular case.

      1.17.4 Peres Gate

This gate can be realized with cost 4. It is just like a Toffoli gate but without the last Feynman gate from right. This is the cheapest realization of a complete (universal) 3 3 permutation gate. Figure 1.12 shows the quantum realization of a Peres gate.

1.18 Summary

      Maxwell's demon and Szilard's analysis of the demon at first suggested the connection between a single degree of freedom (one bit) and a minimum quantity of entropy. In the 1950s, this connection had been popularly interpreted to mean that computation must dissipate a corresponding minimum amount of energy during every elemental act of computation. Landauer later recognized that energy dissipation is only unavoidable when information is destroyed. Bennett and Toffoli first realized that a reversible computation, in which no information is destroyed, may dissipate arbitrarily small amounts of energy. The reversible circuits form the basic building block of quantum computers. This chapter presents some reversible gates. This chapter will help researchers/designers in designing higher complex computing circuits using reversible gates. It can further be extended toward the digital design development using reversible logic circuits, which are helpful in quantum computing, low‐power CMOS, nanotechnology, cryptography, optical computing, DNA computing, digital signal processing (DSP), quantum dot cellular automata, communication, and computer graphics.