Results 1  10
of
44
A transformation based algorithm for reversible logic synthesis
 in Design Automation Conf
"... A digital combinational logic circuit is reversible if it maps each input pattern to a unique output pattern. Such circuits are of interest in quantum computing, optical computing, nanotechnology and lowpower CMOS design. Synthesis approaches are not well developed for reversible circuits even for ..."
Abstract

Cited by 107 (23 self)
 Add to MetaCart
(Show Context)
A digital combinational logic circuit is reversible if it maps each input pattern to a unique output pattern. Such circuits are of interest in quantum computing, optical computing, nanotechnology and lowpower CMOS design. Synthesis approaches are not well developed for reversible circuits even for small numbers of inputs and outputs. In this paper, a transformation based algorithm for the synthesis of such a reversible circuit in terms of n n Toffoli gates is presented. Initially, a circuit is constructed by a single pass through the specication with minimal lookahead and no backtracking. Reduction rules are then applied by simple template matching. The method produces nearoptimal results for 3input circuits and also produces very good results for larger problems.
Toffoli network synthesis with templates
 IEEE Trans. on CAD of Integrated Circuits and Systems
, 2005
"... Abstract—Reversible logic functions can be realized as networks of Toffoli gates. The synthesis of Toffoli networks can be divided into two steps. First, find a network that realizes the desired function. Second, transform the network such that it uses fewer gates, while realizing the same function. ..."
Abstract

Cited by 41 (9 self)
 Add to MetaCart
Abstract—Reversible logic functions can be realized as networks of Toffoli gates. The synthesis of Toffoli networks can be divided into two steps. First, find a network that realizes the desired function. Second, transform the network such that it uses fewer gates, while realizing the same function. This paper addresses the above synthesis approach. We present a basic method and, based on that, a bidirectional synthesis algorithm which produces a network of Toffoli gates realizing a given reversible specification. An asymptotically optimal modification of the basic synthesis algorithm employing generalized mEXOR gates is also presented. Transformations are then applied using template matching. The basis for a template is a network of gates that realizes the identity function. If a sequence of gates in the synthesized network matches a sequence comprised of more than half the gates in a template, then a transformation using the remaining gates in the template can be applied resulting in a reduction in the gate count for the synthesized network. All templates with up to six gates are described in this paper. Experimental results including an exhaustive examination of all 3variable reversible functions and a collection of benchmark problems are presented. The paper concludes with suggestions for further research. Index Terms—Logic synthesis, quantum computing, reversible logic. I.
Reversible Cascades With Minimal Garbage
, 2004
"... The problem of minimizing the number of garbage outputs is an important issue in reversible logic design. We start with the analysis of the number of garbage outputs that must be added to a multiple output function to make it reversible. We give a precise formula for the theoretical minimum of the ..."
Abstract

Cited by 38 (12 self)
 Add to MetaCart
(Show Context)
The problem of minimizing the number of garbage outputs is an important issue in reversible logic design. We start with the analysis of the number of garbage outputs that must be added to a multiple output function to make it reversible. We give a precise formula for the theoretical minimum of the required number of garbage outputs. For some benchmark functions, we calculate the garbage required by some proposed reversible design methods and compare it to the theoretical minimum. Based on the information about minimal garbage, we suggest a new reversible design method that uses the minimum number of garbage outputs. We show that any Boolean function can be realized as a reversible network in terms of this new approach by giving the theoretical method of finding such a network. Using a heuristics synthesis approach, we create a program and run it to compare results of our synthesis to the previously reported synthesis results for the benchmark functions with up to ten variables. Finally, we show that the synthesis for the proposed model can be accomplished with lower cost than the synthesis of EXOR programmable logic arrays.
Quantum circuit simplification using templates
 in Proc
, 2005
"... Optimal synthesis of quantum circuits is intractable and heuristic methods must be employed. Templates are a general approach to reversible and quantum circuit simplification. In this paper, we consider the use of templates to simplify a quantum circuit initially found by other means. We present a ..."
Abstract

Cited by 33 (10 self)
 Add to MetaCart
(Show Context)
Optimal synthesis of quantum circuits is intractable and heuristic methods must be employed. Templates are a general approach to reversible and quantum circuit simplification. In this paper, we consider the use of templates to simplify a quantum circuit initially found by other means. We present and analyze templates in the general case, and then provide particular details for circuits composed of NOT, CNOT and controlledsqrtofNOT gates. We introduce templates for this set of gates and apply them to simplify both known quantum realizations of Toffoli gates and circuits found by earlier heuristic Fredkin and Toffoli gate synthesis algorithms. While the number of templates is quite small, the reduction in quantum cost is often significant. 1.
Garbage in reversible design of multiple output functions
 In 6th International Symposium on Representations and Methodology of Future Computing Technologies
, 2003
"... In this paper we analyze the number of garbage outputs that must be added to a multiple output function to make it reversible. We give the precise formula for the theoretical minimum. For some benchmark functions, we calculate the garbage required by some proposed reversible design methods and com ..."
Abstract

Cited by 32 (7 self)
 Add to MetaCart
(Show Context)
In this paper we analyze the number of garbage outputs that must be added to a multiple output function to make it reversible. We give the precise formula for the theoretical minimum. For some benchmark functions, we calculate the garbage required by some proposed reversible design methods and compared it to the theoretical minimum. Based on the information about garbage we suggest a new reversible design method, that produces the minimum number of garbage outputs. Finally, we show that our proposed reversible logic structure may have some application in conventional logic design. 1
Techniques for the synthesis of reversible Toffoli networks
 ACM TRANS. DESIGN AUTOM. ELECTR. SYST
, 2006
"... This paper presents novel techniques for the synthesis of reversible networks of Toffoli gates, as well as improvements to previous methods. Gate count and a technology oriented cost metrices are used. Our synthesis techniques are independent of the cost metrics. Two new iterative synthesis procedur ..."
Abstract

Cited by 29 (3 self)
 Add to MetaCart
This paper presents novel techniques for the synthesis of reversible networks of Toffoli gates, as well as improvements to previous methods. Gate count and a technology oriented cost metrices are used. Our synthesis techniques are independent of the cost metrics. Two new iterative synthesis procedure employing ReedMuller spectra are introduced and shown to complement earlier synthesis approaches. The template simplification introduced in earlier work is enhanced and new templates of sizes 7 and 9 are presented. A novel “resynthesis” approach is introduced wherein a sequence of gates is chosen from a network, and the reversible specification it realizes is resynthesized as an independent problem in hopes of reducing the network cost. Empirical results are presented to show that the methods are effective both in terms of the realization of all 3 × 3 reversible functions and larger reversible benchmark specifications.
Quantum Circuit Simplification and Level Compaction
 in IEEE Transactions on ComputerAided Design of Integrated Circuits and Systems, 2008
"... Abstract—Quantum circuits are timedependent diagrams describing the process of quantum computation. Usually, a quantum algorithm must be mapped into a quantum circuit. Optimal synthesis of quantum circuits is intractable, and heuristic methods must be employed. With the use of heuristics, the optim ..."
Abstract

Cited by 25 (4 self)
 Add to MetaCart
(Show Context)
Abstract—Quantum circuits are timedependent diagrams describing the process of quantum computation. Usually, a quantum algorithm must be mapped into a quantum circuit. Optimal synthesis of quantum circuits is intractable, and heuristic methods must be employed. With the use of heuristics, the optimality of circuits is no longer guaranteed. In this paper, we consider a local optimization technique based on templates to simplify and reduce the depth of nonoptimal quantum circuits. We present and analyze templates in the general case and provide particular details for the circuits composed of NOT, CNOT, and controlledsqrtofNOT gates. We apply templates to optimize various common circuits implementing multiple control Toffoli gates and quantum Boolean arithmetic circuits. We also show how templates can be used to compact the number of levels of a quantum circuit. The runtime of our implementation is small, whereas the reduction in the number of quantum gates and number of levels is significant. Index Terms—Circuit optimization, quantum circuits, time optimization. I.
Synthesis of reversible logic
 In Design, Automation and Test in Europe
, 2004
"... Abstract — A function is reversible if each input vector produces a unique output vector. Reversible functions find applications in low power design, quantum computing, and nanotechnology. Logic synthesis for reversible circuits differs substantially from traditional logic synthesis. In this paper, ..."
Abstract

Cited by 20 (0 self)
 Add to MetaCart
(Show Context)
Abstract — A function is reversible if each input vector produces a unique output vector. Reversible functions find applications in low power design, quantum computing, and nanotechnology. Logic synthesis for reversible circuits differs substantially from traditional logic synthesis. In this paper, we present the first practical synthesis algorithm and tool for reversible functions with a large number of inputs. It uses positivepolarity ReedMuller decomposition at each stage to synthesize the function as a network of Toffoli gates. The heuristic uses a priority queue based search tree and explores candidate factors at each stage in order of attractiveness. The algorithm produces nearoptimal results for the examples discussed in the literature. The key contribution of the work is that the heuristic finds very good solutions for reversible functions with a large number of inputs. I.
Comparison of the cost metrics for reversible and quantum logic synthesis
, 2005
"... A breadthfirst search method for determining optimal 3line circuits composed of quantum NOT, CNOT, controlledV and controlledV + (NCV) gates is introduced. Results are presented for simple gate count and for technology motivated cost metrics. The optimal NCV circuits are also compared to NCV cir ..."
Abstract

Cited by 19 (5 self)
 Add to MetaCart
(Show Context)
A breadthfirst search method for determining optimal 3line circuits composed of quantum NOT, CNOT, controlledV and controlledV + (NCV) gates is introduced. Results are presented for simple gate count and for technology motivated cost metrics. The optimal NCV circuits are also compared to NCV circuits derived from optimal NOT, CNOT and Toffoli (NCT) gate circuits. The work presented here provides basic results and motivation for continued study of the direct synthesis of NCV circuits, and establishes relations between function realizations in different circuit cost metrics. 1
Simplification of Toffoli Networks via Templates
 In Symposium on Integrated Circuits and System Design
, 2003
"... Reversible logic functions can be realized as networks of Toffoli gates. The synthesis of Toffoli networks can be divided into two steps. First, find a network that realizes the desired function. Second, transform the network such that it uses fewer gates, while realizing the same function. This pap ..."
Abstract

Cited by 18 (4 self)
 Add to MetaCart
Reversible logic functions can be realized as networks of Toffoli gates. The synthesis of Toffoli networks can be divided into two steps. First, find a network that realizes the desired function. Second, transform the network such that it uses fewer gates, while realizing the same function. This paper addresses the second step. Transformations are accomplished via template matching. The basis for a template is a network with Ñ gates that realizes the identity function. If a sequence in the network to be synthesized matches more than half of a template, then a transformation reducing the gate count can be applied. All templates for Ñ � � are described in this paper. 1