Synthesis of the Optimal 4-bit Reversible Circuits

TL;DR

This paper introduces an algorithm for optimal synthesis of 4-bit reversible circuits, addressing the challenge of the vast search space and enabling efficient design of quantum and reversible computing systems.

Contribution

The paper presents a novel algorithm that efficiently synthesizes optimal 4-bit reversible circuits, overcoming the computational challenges posed by the large search space.

Findings

Successfully synthesized all 4-bit linear reversible circuits

Generated optimal circuits for various benchmark functions

Analyzed the distribution of optimal circuits in the search space

Abstract

Optimal synthesis of reversible functions is a non-trivial problem. One of the major limiting factors in computing such circuits is the sheer number of reversible functions. Even restricting synthesis to 4-bit reversible functions results in a huge search space (16!~2^44 functions). The output of such a search alone, counting only the space required to list Toffoli gates for every function, would require over 100 terabytes of storage. In this paper, we present an algorithm that synthesizes an optimal circuit for any 4-bit reversible specification. We employ several techniques to make the problem tractable. We report results from several experiments, including synthesis of random 4-bit permutations, optimal synthesis of all 4-bit linear reversible circuits, synthesis of existing benchmark functions, and distribution of optimal circuits. Our results have important implications for the design and optimization of quantum circuits, testing circuit synthesis heuristics, and performing experiments in the area of quantum information processing.