Real 3-qubit gate decompositions via triality

TL;DR

This paper introduces a new decomposition method for real 3-qubit gates using triality symmetry, reducing the number of CNOT gates needed and advancing quantum circuit optimization.

Contribution

It presents a novel approach leveraging triality symmetry of PSO(8) to decompose real 3-qubit gates more efficiently than previous methods.

Findings

Any unimodular real 3-qubit gate can be decomposed with at most 14 CNOTs.

The method improves the previous bound of 16 CNOTs.

Utilizes the exotic triality symmetry of PSO(8) for gate decomposition.

Abstract

We show that any unimodular real 3-qubit gate can be expressed as the product of at most 14 CNOT gates plus single-qubit gates, improving on the bound of 16 CNOTs due to Wei and Di. Our method uses the exotic triality symmetry of $\operatorname{PSO}(8)$, and we explore some of the useful properties of this map in relation to the study of real 3-qubit gates.