Efficient Algorithms for Optimal 4-Bit Reversible Logic System Synthesis

Zhiqiang Li,Hanwu Chen,Guowu Yang,Wenjie Liu

doi:10.1155/2013/291410

Abstract

Owing to the exponential nature of the memory and run-time complexity, many methods can only synthesize 3-bit reversible circuits and cannot synthesize 4-bit reversible circuits well. We mainly absorb the ideas of our 3-bit synthesis algorithms based on hash table and present the efficient algorithms which can construct almost all optimal 4-bit reversible logic circuits with many types of gates and at mini-length cost based on constructing the shortest coding and the specific topological compression; thus, the lossless compression ratio of the space ofn-bit circuits reaches near2×n!. This paper presents the first work to create all 3120218828 optimal 4-bit reversible circuits with up to 8 gates for the CNT (Controlled-NOT gate, NOT gate, and Toffoli gate) library, and it can quickly achieve 16 steps through specific cascading created circuits.

Highlights

Quantum computer is equivalent to quantum Turing machine, and quantum Turing machine is equivalent to a quantum logic circuit
Yang et al [11] reduced the synthesis for reversible logic circuit to group theory and presented a novel algorithm based on group-theory algebraic software GAP, while its performance was better than most others
We mainly absorb the ideas of our efficient 3-bit synthesis algorithms based on hash table and present the novel and efficient algorithms which can construct almost all optimal 4-bit reversible logic circuits [17]

Summary

Introduction

Quantum computer is equivalent to quantum Turing machine, and quantum Turing machine is equivalent to a quantum logic circuit. Several approaches for reversible logic circuit synthesis have been presented. Mishchenko and Perkowski [6] proposed a Reed Muller-based algorithm for optimizing quantum circuit. Shende et al [9, 10] reduced the synthesis for reversible logic circuit to permutation and gave an effective recursive algorithm. Yang et al [11] reduced the synthesis for reversible logic circuit to group theory and presented a novel algorithm based on group-theory algebraic software GAP, while its performance was better than most others. We mainly absorb the ideas of our efficient 3-bit synthesis algorithms based on hash table and present the novel and efficient algorithms which can construct almost all optimal 4-bit reversible logic circuits [17]. 1 00 all the optimal 16-gate mini-length circuits for the CNT library

Background

Coding 28679 34439 16985 18903 32969 29241

New Synthesis Algorithm

Experimental Results

Conclusions