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In principle, any reversible logic circuit can be built by using a single building block (having three logic inputs and three logic outputs). We demonstrate that, for a exible design, it is more advantageous to use a broad class of reversible gates, called control gates. They form a gen- eralization of Feynman's three gates (i.e. the NOT, the CONTR...
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... P i ), of C i+1 , and of S i ) together, we see that the logic depth d of the resulting n-bit c.l.a. adder is 3, independent of n. Note that we consider the NOT as a gate of zero depth. Indeed, in dual line hardware, the NOT gate is merely an interchange of the two lines and thus costs neither silicon area, nor time delay, nor power dissipation. Fig. 4 shows the 4-bit c.l.a. adder. For sake of clarity, the 8 preset input lines and the 12 garbage output lines are not shown, nor are the inverters (i.e. the NOT gates). Each logic gate has an equal number of logic inputs and logic outputs, a number we call the width w of the gate. The full circuit has depth d = 3, width w = 17, and ...
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... These results are identical with the minimum length for R 3 and NR 3 , but our results are different with the minimum quantum cost. For example, it can be shown using GAP [17] that a cyclic permutation equal (5,8,7,6) can be realized by NR 3 -based reversible circuit ...
... with minimum quantum cost equal 12 and minimum length equal 6 as shown in Fig. 18, while the same cyclic permutation equal (5,8,7,6) can be realized by NM 3 -based reversible circuit [M 3 231 , N 3 1 , M 3 123 , M 3 213 , N 3 1 , N 3 3 ] with minimum quantum cost equal 11 and minimum length equal 6 as shown in Fig. 19. ...
... For 3-bits reversible circuits built using M 3 -gate library, the maximum quantum cost is 36 and average quantum cost is 25.70 before optimization. After adding the N gate 19 The circuit representation for the cyclic permutation equal (5,8,7,6), where: a The NM 3 -based reversible circuit realize the cyclic permutation b The optimized decomposition of the NM 3 -based reversible circuit into its 17 elementary quantum gates with QC equal 11 ...
Reversible logic has been considered as an important solution to the power dissipation problem in the existing electronic devices. Many universal reversible libraries that include more than one type of gates have been proposed in the literature. This paper proposes a novel reversible n-bit gate that is proved to be universal for synthesizing reversible circuits. Reducing the reversible circuit synthesis problem to permutation group allows Schreier-Sims Algorithm for the strong generating set-finding problem to be used in the synthesize of reversible circuits using the proposed gate. A novel optimization rules will be proposed to further optimize the synthesized circuits in terms of the number of gates, the quantum cost and the utilization of library to achieve better results than that shown in the literature.
... Reversible logic [9,34] is one of the hot areas of research. It has many applications in quantum computation [37,51], low-power CMOS [21,67] and many more. Synthesis of reversible circuits cannot be done using conventional approaches [63]. ...
There have been efforts to find an automatic way to create efficient Boolean quantum circuits, because of their wide range of applications. This chapter shows how to build efficient Boolean quantum circuits. A direct synthesis method can be used to implement any Boolean function as a quantum circuit using its truth table, where the generated circuits are more efficient than ones generated using methods proposed by others. The chapter shows, using another method, that there is a direct correspondence between Boolean quantum operations and the classical Reed-Muller expansions. This relation makes it possible for the problem of synthesis and optimization of Boolean quantum circuits to be tackled within the domain of Reed-Muller logic under manufacturing constraints, for example, the interaction between qubits of the system.
... Reversible logic [1,9] is one of the hot areas of research. It has many applications in quantum computation [12,21], low-power CMOS [7,3] and many more. Synthesis of reversible circuits cannot be done using conventional ways [25]. ...
... The last bit is flipped unconditionally. For 3-in/out reversible circuits, there are 6 possible G3 gates as follows, 1,5,3,7,2,6,4,8), 5,2,6,3,7,4,8), 3,5,7,2,4,6,8), 3,2,4,5,7,6,8), 2,5,6,3,4,7,8), 2,3,4,5,6,7,8). ...
... The last bit is flipped unconditionally. For 3-in/out reversible circuits, there are 6 possible G3 gates as follows, 1,5,3,7,2,6,4,8), 5,2,6,3,7,4,8), 3,5,7,2,4,6,8), 3,2,4,5,7,6,8), 2,5,6,3,4,7,8), 2,3,4,5,6,7,8). ...
Many universal reversible libraries that contain more than one gate type have
been proposed in the literature. Practical implementation of reversible
circuits is much easier if a single gate type is used in the circuit
construction. This paper proposes a reversible n-bit gate that is universal for
reversible circuits synthesis. The proposed gate is extendable according to the
size of the circuit. The paper shows that the size of the synthesized circuits
using the proposed gate is comparable with the size of the synthesized circuits
using the hybrid reversible libraries for 3-in/out reversible circuits.
... Reversible logic [2,11] is one of the hot areas of research. It has many applications in quantum computation [14,23], low-power CMOS [9,5] and many more. Synthesis of reversible circuits cannot be done using conventional ways [29]. ...
The reversible circuit synthesis problem can be reduced to permutation group.
This allows Schreier-Sims Algorithm for the strong generating set-finding
problem to be used to find tight bounds on the synthesis of 3-bit reversible
circuits using the NFT library. The tight bounds include the maximum and
minimum length of 3-bit reversible circuits, the maximum and minimum cost of
3-bit reversible circuits. The analysis shows better results than that found in
the literature for the lower bound of the cost. The analysis also shows that
there are 1960 universal reversible sub-libraries from the main NFT library.
... Reversible logic [1,2] is an active area of research. It has many applications in quantum computing [3,4], low-power CMOS [5,6] and many more. Synthesis and optimization of Boolean reversible circuits cannot be done using classical methods [7]. ...
... The 6 possible gates for 3-bit reversible circuits. ...
... (1,8,7)(2,5) (3,6) [ 2 3 , 123 3 , 1 3 , 32 3 , 321 3 , 13 3 ] 12 6 (NAND, NOT, NOR) (1, 8,3,7) [ 1 3 , 3 3 , 21 3 , 132 3 , 3 3 , 123 21 3 , 31 3 , 13 3 ] 8 6 (NOR, NOT, NAND) (1,8,7)(2,5) (3,4) [ 23 3 , 2 3 , 132 3 , 23 3 , 21 3 ...
The reversible circuit synthesis problem can be reduced to permutation group. This allows Schreier-Sims Algorithm for the strong generating set-finding problem to be used to synthesize reversible circuits using the NCT library. Applying novel optimization rules to minimize the number of gates gives better quantum cost than that shown in the literature. Applications on how to integrate any three irreversible Boolean functions on a single 3-bit reversible circuit will be shown.
... Reversible logic [4,9] is one of the hot areas of research. It has many applications in quantum computation [11,19], low-power CMOS [7,6] and many more. Synthesis of reversible circuits cannot be done using conventional ways [24]. ...
... The paper recommends the proposed algorithm to be used together with any optimization algorithm to handle the problem of NTRIs. Optimized (g,c) [1] Optimized + NTRIs Removal (g,c) [12,7,2,5,0,15,14,11,6,3,10,1,8,9,4,13] APP2.1 (21, Table 2: Random reversible circuits with NTRIs optimized using [1] alone and optimized using a hybrid system from the proposed algorithm and [1]. where the pair (g, c) represents the number of gates (g) and the quantum cost (c). ...
Non-Trivial Reversible Identities (NTRIs) are reversible circuits that have
equal inputs and outputs. NTRIs cannot be detected using optimization
algorithms in the literature. Existence of NTRIs in a circuit will cause a slow
down by increasing the number of gates and the quantum cost. NTRIs might arise
due to integration between two or more optimal reversible circuits. In this
paper, an algorithm that detects and removes NTRIs in polynomial time will be
proposed. Experiments that show the bad effect of NTRIs and the enhancement
using the proposed algorithm will be presented.
... Reversible logic [4,11] is one of the hot areas of research. It has many applications in quantum computation [13,23], low-power CMOS [8,31] and many more. Synthesis and optimization of reversible circuits cannot be done using conventional ways [29]. ...
Homogenous Boolean function is an essential part of any cryptographic system. The ability to construct an optimized reversible circuits for homogeneous Boolean functions might arise the possibility of building cryptographic system on novel computing paradigms such as quantum computers. This paper shows a factorization algorithm to synthesize such circuits.
... (However, energy may be lost for input and output operations.) It was shown that reversible gates can be built in DNA, optical, quantum and other technologies but here we will concentrate on CMOS [1,4,5,18]. Developing systematic logic synthesis algorithms for reversible logic is still very immature, but some methods have been proposed [8,13,14]. ...
... This analysis created several new types of reversible gates. Most of reversible gates in literature are threeinput three-output (3*3) or four-input four-output (4*4) gates, the exceptions are [4,5,8,13,15]. In this research we will stay with reversible gates with maximum size of 4*4 (including 1*1, 2*2, 3*3). ...
A reversible circuit maps each output vector into a unique input vector, and vice versa. CMOS reversible / adiabatic circuits are currently the most important approaches to power optimization. This paper introduces an approach to synthesize generalized multi-rail reversible cascades for single- output Boolean functions. Minimizing the "garbage bits" is the main challenge of reversible logic synthesis. Experimental results over a set of single output functions (derived from Espresso PLAs) will be presented at IWLS 2002.
... It is a fast developing area of research due to its increasing importance to future computer technologies, especially quantum ones [16] because of possibility to solve some exponentially hard problems in polynomial time [7]. For example, during the last three years many papers have been written on reversible computing [1] [2] [3] [4] [5] [8] [12] [13] [14] [15] [20] [22] [23] [24] [25] [26] [28] [29] [30] [32] [33] [34] [35] [36] [40] [41] [42] [43] [44] [45] [46] [47] [50] [53] [54], some of them proposing new multiple-valued gates [47] [41] [5] [14] [1] [2] [3] [40] [43] [30]. In designing circuits built from such gates it is important to know which of the gates have the least cost. ...
A set of p-valued logic gates (primitives) is called universal if an arbitrary p-valued logic function can be realized by a logic circuit built up from a finite number of gates belonging to this set. In the paper, we consider the problem of determining the number of universal single-element sets of ternary reversible logic gates with two inputs and two outputs. We have established that over 97% of such sets are universal.
