Reversible Logic Synthesis by Quantum Rotation Gates

TL;DR

This paper introduces a rotation-based synthesis framework for reversible logic that combines Boolean logic and quantum computation techniques, achieving efficient quantum circuit constructions with optimized gate counts and depths.

Contribution

It presents a novel canonical representation and recursive synthesis approach for reversible logic using quantum rotation gates, improving efficiency without ancillae.

Findings

Quadratic gate count for multiple-control Toffoli gates

Linear depth for quantum carry-ripple adder

Quasilinear size for quantum multiplexer

Abstract

A rotation-based synthesis framework for reversible logic is proposed. We develop a canonical representation based on binary decision diagrams and introduce operators to manipulate the developed representation model. Furthermore, a recursive functional bi-decomposition approach is proposed to automatically synthesize a given function. While Boolean reversible logic is particularly addressed, our framework constructs intermediate quantum states that may be in superposition, hence we combine techniques from reversible Boolean logic and quantum computation. The proposed approach results in quadratic gate count for multiple-control Toffoli gates without ancillae, linear depth for quantum carry-ripple adder, and quasilinear size for quantum multiplexer.