Synthesis of reversible circuits for large reversible functions (original) (raw)

Synthesis of reversible circuits using a moving forward strategy

IEICE Electronics Express, 2008

Reversible circuits have applications in various research areas including signal processing, cryptography and quantum computation. In this paper, a non-search based moving forward synthesis algorithm (MOSAIC) for Boolean reversible circuits is proposed to convert an arbitrary well-formed matrix into an identity matrix using a set of reversible gates. In contrast with the widely used search-based methods, MOSAIC is guaranteed to produce a result and can lead to a solution in much fewer algorithmic steps. To evaluate the proposed algorithms, different circuits and benchmarks were used that show the efficiency of the proposed algorithm to lead a result.

Efficient Synthesis of Linear Reversible Circuits

Iwls, 2003

In this paper we consider circuit synthesis for n-wire linear reversible circuits using the C-NOT gate library. These circuits are an important class of reversible circuits with applications to quantum computation. Previous algorithms, based on Gaussian elimination and LU-decomposition, yield circuits with O n 2 gates in the worst-case. However, an information theoretic bound suggests that it may be possible to reduce this to as few as O n 2 / log n gates. We present an algorithm that is optimal up to a multiplicative constant, as well as Θ(log n) times faster than previous methods. While our results are primarily asymptotic, simulation results show that even for relatively small n our algorithm is faster and yields more efficient circuits than the standard method. Generically our algorithm can be interpreted as a matrix decomposition algorithm, yielding an asymptotically efficient decomposition of a binary matrix into a product of elementary matrices.

A Fast Transformation-Based Synthesis Algorithm for Reversible Circuits

2008 11th EUROMICRO Conference on Digital System Design Architectures, Methods and Tools, 2008

In this paper, a simple and fast algorithm for the synthesis of reversible circuits is presented. This algorithm considers the synthesis process as a kind of sorting problem, generating a reversible circuit composed of CNOT-based gates. We prove that the proposed algorithm converges for any given specification. The empirical results of realizing examples discussed in the literature are reported. The results show that the algorithm leads to a near optimum solution for all 3*3 specifications and very good results for other larger specifications in much fewer steps compared to the search based and other previous algorithms.

Data structures and algorithms for simplifying reversible circuits

2006

Abstract Reversible logic is motivated by low-power design, quantum circuits, and nanotechnology. We develop a compact representation of small reversible circuits to generate and store optimal circuits for all 40,320 three-input reversible functions, and millions of four-input circuits. This allows implementing a function optimally in constant time for use in the peephole optimization of larger circuits produced by existing techniques, and guarantees that every three-bit subcircuit is optimal.

BDD-based synthesis of reversible logic for large functions

… Conference, 2009. DAC'09. 46th ACM/ …, 2009

Reversible logic is the basis for several emerging technologies such as quantum computing, optical computing, or DNA computing and has further applications in domains like low-power design and nanotechnologies. However, current methods for the synthesis of reversible logic are limited, i.e. they are applicable to relatively small functions only. In this paper, we propose a synthesis approach, that can cope with Boolean functions containing more than a hundred of variables. We present a technique to derive reversible circuits for a function given by a Binary Decision Diagram (BDD). The circuit is obtained using an algorithm with linear worst case behavior regarding run-time and space requirements. Furthermore, the size of the resulting circuit is bounded by the BDD size. This allows to transfer theoretical results known from BDDs to reversible circuits. Experiments show better results (with respect to the circuit cost) and a significantly better scalability in comparison to previous synthesis approaches.

Realization and synthesis of reversible functions

Theoretical Computer Science, 2011

Reversible circuits play an important role in quantum computing. This paper studies the realization problem of reversible circuits. For any n-bit reversible function, we present a constructive synthesis algorithm. Given any n-bit reversible function, there are N distinct input patterns different from their corresponding outputs, where N ≤ 2 n , and the other (2 n − N) input patterns will be the same as their outputs. We show that this circuit can be synthesized by at most 2n · N '(n − 1)'-CNOT gates and 4n 2 · N NOT gates. The time and space complexities of the algorithm are Ω(n · 4 n ) and Ω(n · 2 n ), respectively. The computational complexity of our synthesis algorithm is exponentially lower than that of breadth-first search based synthesis algorithms.