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Journal of Software

Algorithm of Optimizing Quantum Reversible Logic Synthesis

Zhiqiang Li, Wenqian Li, Hanwu Chen

Published Nov 13, 2009• 0 citations
Publisher

Abstract

最优化量子可逆逻辑的关键在于用最小的量子代价自动构造量子可逆逻辑.为了提高可逆逻辑自动生成与优化的效率,提出了类模板技术和一种快速算法.模板技术是一个有效的优化工具,类模板技术可以显著提高模板技术的匹配效率;R-M算法是可逆逻辑综合的一种较好的迭代方法,基于R-M算法的原始思想,构造了一个Hash函数,并在此基础上提出了一种可逆逻辑综合的快速算法.实验结果表明,在同等实验环境下使用类模板技术与快速算法,其优化的效果与效率远远优于已知的其他算法.;The key of optimizing quantum reversible logic lies in automatically constructing quantum reversible logic circuits with the minimal quantum cost. In order to improve the efficiency of an automatic synthesis and optimization of the reversible logic, a semi-template technique and a fast algorithm was proposed. Template is an efficient optimizing tool, and the semi-template technique can significantly improve the matching efficiency in optimization. R-M synthesis arithmetic is a good iterative method in reversible logic synthesis. Based on the original idea of R-M arithmetic, by constructing an optimal and collision-free Hash function, a new fast algorithm for synthesizing the quantum reversible logic circuits was proposed. This algorithm can construct optimal quantum reversible logic circuits with various types of gates and quantum cost. The experimental results show that to the best of the knowledge in the same testing environment, the results are much better than others.

DOI
10.3724/sp.j.1001.2009.03407

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最优化量子可逆逻辑的关键在于用最小的量子代价自动构造量子可逆逻辑.为了提高可逆逻辑自动生成与优化的效率,提出了类模板技术和一种快速算法.模板技术是一个有效的优化工具,类模板技术可以显著提高模板技术的匹配效率;R-M算法是可逆逻辑综合的一种较好的迭代方法,基于R-M算法的原始思想,构造了一个Hash函数,并在此基础上提出了一种可逆逻辑综合的快速算法.实验结果表明,在同等实验环境下使用类模板技术与快速算法,其优化的效果与效率远远优于已知的其他算法.;The key of optimizing quantum reversible logic lies in automatically constructing quantum reversible logic circuits with the minimal quantum cost. In order to improve the efficiency of an automatic synthesis and optimization of the reversible logic, a semi-template technique and a fast algorithm was proposed. Template is an efficient optimizing tool, and the semi-template technique can significantly improve the matching efficiency in optimization. R-M synthesis arithmetic is a good iterative method in reversible logic synthesis. Based on the original idea of R-M arithmetic, by constructing an optimal and collision-free Hash function, a new fast algorithm for synthesizing the quantum reversible logic circuits was proposed. This algorithm can construct optimal quantum reversible logic circuits with various types of gates and quantum cost. The experimental results show that to the best of the knowledge in the same testing environment, the results are much better than others.
We use bit operation to construct the novel and perfect Hash function and present an efficient algorithm which can construct optimal quantum reversible logic circuits with various types of gates by using the Hash table and produce quantum circuits with minimal cost in theory. Judging by the internationally recognized reversible functions of three variables, the algorithm not only synthesizes all optimal reversible logic circuits, but also runs extremely faster than other ones. The experimental results show that the average speed of the algorithm which synthesizes circuit with minimum length is 69.8 times that of currently best result [9].
Combining several kinds of ideas of synthesis of reversible logic circuits,this paper presents a novel and efficient algorithm which can automatically derive the positive polarity Reed-Muller expansion(RM).A solution space tree of creating quantum reversible logic circuits is constructed.Firstly floor traversal is used in whole,and depth-first search is used in local.Secondly according to the technique of template optimization,the bound function is created which can rapidly eliminate the branches of none result or none optimal result.Thirdly factors of RM are considered first.Therefore the algorithm can effectively construct optimal result and saves computational cost significantly.
Programmable reversible logic is emerging as a prospective logic design style for implementation in modern nanotechnology and quantum computing with minimal impact on circuit heat generation. Recent advances in reversible logic using and quantum computer algorithms allow for improved computer architecture and arithmetic logic unit designs. We present an optimization method for reversible logic synthesis based on the Integrated Qubit (IQ) library. This method works in conjunction with existing methods to further improve quantum cost and delay of a synthesized reversible logic circuit. This algorithm runs in O(N) time, and reduces the quantum cost of synthesized circuit by up to 45 percent. In addition, the process of replacing the gates in the synthesized circuits with IQ gates uses a locally optimal technique whose major benefits include reduction of cost as well as delay.
We present an effective algorithm which can construct optimal 3-qubit reversible logic circuits for any given reversible logic gates and costs by constructing a minimal perfect hash function. We also present an algorithm which can automatically construct quantum gate library. In the experiments on 3-qubit synthesis, our algorithm synthesizes all optimal reversible circuits with extremely fast speed--the average speed which synthesizes circuits with minimum cost is 365 times faster than that of best result.
Synthesis of quantum reversible logic circuits means to automatically construct desired quantum reversible logic circuit with minimal quantum cost.We present a novel and efficient algorithm which can construct almost all optimal 4-qubit reversible logic circuits with various types of gates and minimum length cost based on constructing the shortest coding and the specific topological compression, whose lossless compression ratios of the space of n-qubit circuits is near2×n!.We firstly have created all 3120218828 optimal 4-qubit circuits whose length is less than 9 for the Controlled-Not gate,NOT gate and Toffoli gate library,and our method can achieve 16 steps through cascading created circuits.Our algorithm can not only synthesizes all the 4-qubit benchmark circuits,but also runs extremely fast.
Quantum computers, more specifically quantum circuits, take on the eyes with their computational promises such as reversibility. In this paper, we perform synthesis and optimization of quantum circuits. In the first part, we propose a fast synthesis algorithm that implements any given reversible Boolean function with quantum gates. Instead of an exhaustive search on every given function, our algorithm creates a library of essential functions and performs sorting. As an example, to implement 4 bit circuits we only use 120 essential functions out of all 20922789888000 functions. In the second part, we optimize our circuits by using new templates. The proposed templates mainly consist of Toffoli gates with negative and positive controlling lines. These templates also show us that optimum area solutions proposed in the literature are not actually optimum; they can be improved.