Fermionic quantum orthogonalizations I

TL;DR

This paper extends classical orthogonalization methods to fermionic quantum operations, providing insights and generalizations for quantum orthogonalization procedures, including the symmetric case.

Contribution

It introduces a framework for fermionic quantum orthogonalizations, generalizing classical procedures like Gram-Schmidt and symmetric orthogonalization.

Findings

Generalization of Gram-Schmidt to fermionic quantum operations

Insights into properties of fermionic quantum orthogonalizations

Extension of symmetric orthogonalization procedure

Abstract

We generalize classical orthogonalization procedures from real linear algebra to the setting of fermionic quantum (FQ) operations. In the case of the Gram-Schmidt orthogonalization procedure, the generalization is easy. This, however, helps to obtain general information regarding FQ operations, and to generalize the symmetric orthogonalization procedure.