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In this paper we propose an analytic approach to the variable sifting based on weighting of qubits and gates. The proposed scheme allows to optimally sift gates (multi-control single-target reversible gates) within a linear number of steps of computation and provides in general smaller amount of SWAP gates required to transform a reversible circuit into an Linear Nearest Neighbor (LNN) model than...
Reversible computation is one of the intensively developing research areas nowadays in the field of computer science and engineering. Although the field of reversible circuit synthesis has been studied during the last 15 years few attempts have been published to propose classification of reversible functions. In an earlier paper we considered whether all component functions of a reversible Boolean...
Recently an approach to encryption/decryption based on using reversible logic circuits has been proposed. The reason for this is that conventional microelectronic technologies are reaching their limits. On the other hand, reversible logic circuits can decrease energy dissipation theoretically to zero. This paper presents a solution to designing encryption schemes based entirely on reversible logic...
In this paper we present improvements to the cost of quantum circuits implemented with 2n-lines circuit implementation. The 2n-line circuit implementation is intended for the linear nearest neighbor quantum circuits and implements any quantum circuits in such manner that they can be directly mapped to quantum implementations. In this paper we propose a replacement strategy for 2- and 3-qubit patterns...
In this paper, a method for constructing sequences of reversible functions of large number of variables is presented. First, by using our database of all minimal reversible circuits for 3-variable reversible functions, and our tool for designing minimal circuits for 4-variable reversible functions, circuits with structural regularities are searched for. The aim is to find a pair, 3- and 4-variable...
In this paper we describe faults that can occur in reversible circuits. In particular, we focus on comparison of faults that can appear in classical circuits with faults that can occur in quantum technology. The analysis is generalized from the point of view of technologies such as information reversible and energy reversible. We show that contrary to classical non-reversible transistor based circuits,...
Multiple-control Toffoli gates are basic building blocks for reversible and quantum circuits. 3-bit Peres gate can be considered as a pair of 3-bit and 2-bit Toffoli gates, which can be implemented with fewer elementary quantum gates (what defines a metric called quantum cost) than the total number of elementary quantum gates required by each of Toffoli gates implemented separately. Due to this property,...
This paper reports on a method of the construction of new difficult benchmarks for reversible logic synthesis. It is shown how to extrapolate 3- and 4-variable reversible functions implemented by gate count minimal circuits having regular structure. In this way sequences of reversible functions of an arbitrary number of variables have been constructed for which we have built minimal circuits implementing...
This paper introduces a new synthesis approach called Products of EXOR-sums (POE) and demonstrates its utility when employed in an Exclusive-Or-Sum-of-Products (ESOP) based algorithm for reversible and permutative quantum circuits restricted to single output functions. Unlike previous ESOP approaches such as EXORCISM-4 which realize functions as an EXOR-ed sum of product literals, this new algorithm...
We present an analysis of the Reversible and Quantum Finite State Machines (QFSM) realized as Quantum Circuits using the three well known sequences applied in the analysis of the classical Finite State Machines (FSM). The synchronizing, the homing and the distinguishing sequences are applied to both strictly Reversible FSM (RFSM) and QFSM in order to determine the power of these new techniques in...
We provide several extensions of the new approach to the minimization of reversible circuits based on PSE gates and ESOPOS circuits. These circuits realize the Exclusive-Or-Sum-of-Product-Sums (ESOPOS) structure where every output is an exclusive-or of Product-Sum-Exor (PSE) gates which generalize the multi-input Toffoli gates. We also propose a new efficient realization of the PSE gate that uses...
Four main approaches to synthesis of reversible circuits are considered: cycle-based, transformation-based, ESOP-based and BDD-based as well as their advantages and disadvantages are discussed. It is indicated that the decisions in them are based on local information only what leads to very redundant designs. Suggestions for making global decisions are also presented. New directions of research are...
Optimal synthesis of reversible circuits is a very hard task. In 2010, a method and a tool of practical usage for finding optimal circuits built from multi-control Toffoli gates for any 4-bit reversible specification were finally developed. In 2011 we published an extension to the algorithm, which allows to reduce the quantum cost of the resulting circuits. In this paper we present another extension...
Recently, one of the main criteria used to evaluate reversible circuit designs is quantum cost. In this paper, an approach to reducing quantum cost of small-width reversible circuits is presented. Using our tool we have shown that for known benchmarks as well as designs taken from recent publications it is possible to obtain substantial savings in quantum cost (35% on average for 4-input benchmarks)...
Advances in LSI technology have led to problems concerning the selection of output functions for optimum complex logic modules. A natural criterion for the evaluation of possible designs is the structure of the set of all subfunctions of the function realized by a module. Thus studying properties of the sub-function sets of Boolean functions is an approach to solving the above problems. In the paper...
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