circuit is always an interesting one. Quantum circuits, DNA technologies, nano‐technologies and optical computing are the most common applications of quantum theory. Every reversible gate can be calculated in terms of quantum cost and hence the reversible circuits can be measured in terms of quantum cost. Reducing the quantum cost from reversible circuit is always a challenging issue and research are still going on in this area. In this section, the quantum equivalent diagram of some popular reversible gate is presented.
Property 1.17.1
The quantum cost of every 2
1.17.1 Reversible NOT Gate (Feynman Gate)
Example 1.13
A 2
1.17.2 Toffoli Gate
Figure 1.10 shows the equivalent quantum realization of three input Toffoli gate. The cost of the Toffoli gate is five 2
Figure 1.9 Quantum cost calculation of Feynman gate.
Figure 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
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
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.
Конец ознакомительного фрагмента.
Текст предоставлен ООО «ЛитРес».
Прочитайте эту книгу целиком, купив полную легальную версию на ЛитРес.
Безопасно оплатить книгу можно банковской картой Visa, MasterCard, Maestro, со счета мобильного телефона, с платежного терминала, в салоне МТС или Связной, через PayPal,
