Optimal and asymptotically optimal NCT reversible circuits by the gate types

TL;DR

This paper presents methods for constructing optimal and asymptotically optimal reversible circuits using NCT gates, refining complexity measures and highlighting limitations of T-count metrics in quantum circuit design.

Contribution

It introduces optimized NCT reversible circuits and analyzes their complexity, providing insights into the limitations of T-count in quantum applications.

Findings

Optimal NCT circuits achieved for various functions

Asymptotic bounds established for circuit complexity

Limitations of T-count metric in quantum circuits

Abstract

We report optimal and asymptotically optimal reversible circuits composed of NOT, CNOT, and Toffoli (NCT) gates, keeping the count by the subsets of the gate types used. This study fine tunes the circuit complexity figures for the realization of reversible functions via reversible NCT circuits. An important consequence is a result on the limitation of the use of the $T$-count quantum circuit metric popular in applications.