The characteristic polynomial in calculation of exponential and elementary functions in Clifford algebras

TL;DR

This paper introduces formulas for calculating multivector exponentials in Clifford algebras using characteristic polynomial roots, with practical examples relevant to quantum computing and quantum state evolution.

Contribution

It provides new formulas for multivector exponentials in Clifford algebras based on characteristic polynomial roots, applicable in quantum physics.

Findings

Formulas for multivector exponentials in Clifford algebras are derived.

Examples demonstrate practical application of the formulas.

Potential relevance to quantum circuits and entangled state analysis.

Abstract

Formulas to calculate multivector exponentials in a base-free representation and in a orthonormal basis are presented for an arbitrary Clifford geometric algebra Cl(p,q). The formulas are based on the analysis of roots of characteristic polynomial of a multivector. Elaborate examples how to use the formulas in practice are presented. The results may be useful in the quantum circuits or in the problems of analysis of evolution of the entangled quantum states.