Finite Geometries with Qubit Operators

TL;DR

This paper explains the emergence of finite projective geometries, like the Fano plane, in multi-qubit quantum systems using Clifford algebras, revealing geometric structures underlying quantum gate operators.

Contribution

It introduces a Clifford algebra framework to elucidate the connection between finite geometries and multi-qubit quantum operators, providing a new theoretical perspective.

Findings

Finite geometries appear naturally in multi-qubit systems.

Clifford algebras explain the geometric structures in quantum operators.

The Fano plane and higher-dimensional geometries are linked to quantum gate properties.

Abstract

Finite projective geometries, especially the Fano plane, have been observed to arise in the context of certain quantum gate operators. We use Clifford algebras to explain why these geometries, both planar and higher dimensional, appear in the context of multi-qubit composite systems.