On quantum circuits employing roots of the Pauli matrices

TL;DR

This paper explores roots of Pauli matrices and their application in quantum circuits, providing methods to simplify circuits and convert them into Clifford+T gate form from NCV library circuits.

Contribution

It introduces techniques for simplifying quantum circuits involving roots of Pauli matrices and demonstrates how to convert these into Clifford+T gate circuits from NCV circuits.

Findings

Techniques for simplifying circuits with roots of Pauli matrices

Method to convert NCV circuits to Clifford+T circuits

Enhanced understanding of gate relationships in quantum circuits

Abstract

The Pauli matrices are a set of three 2x2 complex Hermitian, unitary matrices. In this article, we investigate the relationships between certain roots of the Pauli matrices and how gates implementing those roots are used in quantum circuits. Techniques for simplifying such circuits are given. In particular, we show how those techniques can be used to find a circuit of Clifford+T gates starting from a circuit composed of gates from the well studied NCV library.