Comparison of the Cost Metrics for Reversible and Quantum Logic Synthesis

TL;DR

This paper compares cost metrics for reversible and quantum logic synthesis, introducing a BFS method for optimal 3-line quantum circuits and analyzing their costs in different metrics.

Contribution

It presents a BFS-based approach for optimal 3-line quantum circuits and compares NCV circuits with NCT-based circuits across various cost metrics.

Findings

Optimal NCV circuits are identified for simple cases.

Cost metrics influence circuit design choices.

Relations between different circuit realizations are established.

Abstract

A breadth-first search method for determining optimal 3-line circuits composed of quantum NOT, CNOT, controlled-V and controlled-V+ (NCV) gates is introduced. Results are presented for simple gate count and for technology motivated cost metrics. The optimal NCV circuits are also compared to NCV circuits derived from optimal NOT, CNOT and Toffoli (NCT) gate circuits. The work presented here provides basic results and motivation for continued study of the direct synthesis of NCV circuits, and establishes relations between function realizations in different circuit cost metrics.