Decomposition of orthogonal matrix and synthesis of two-qubit and three-qubit orthogonal gates

TL;DR

This paper explores the decomposition and synthesis of two-qubit and three-qubit orthogonal gates, providing optimal methods and gate counts for their implementation in quantum computing.

Contribution

It introduces an optimal synthesis method for general two-qubit orthogonal gates and details the gate counts needed for three-qubit unimodular orthogonal gates.

Findings

Two-qubit unimodular orthogonal gate requires at most 2 CNOT and 6 Ry gates.

Three-qubit unimodular orthogonal gate can be synthesized with 16 CNOT and 36 Ry/Rz gates.

Provides optimal synthesis strategies for these quantum gates.

Abstract

The decomposition of matrices associated to two-qubit and three-qubit orthogonal gates is studied, and based on the decomposition the synthesis of these gates is investigated. The optimal synthesis of general two-qubit orthogonal gate is obtained. For two-qubit unimodular orthogonal gate, it requires at most 2 CNOT gates and 6 one-qubit Ry gates. For the general three-qubit unimodular orthogonal gate, it can be synthesized by 16 CNOT gates and 36 one-qubit Ry and Rz gates in the worst case.