Trotterization in Quantum Theory

Abstract: Trotterization in quantum mechanics is an important theoretical concept in handling the exponential of noncommutative operators. In this communication, we give a mathematical formulation of the Trotter Product Formula, and apply it to basic examples in which the utility of Trotterization is evident. Originally, this article was completed in December 2020 as a report under the mentorship of Esteban C\'ardenas for the University of Texas at Austin Mathematics Directed Reading Program (DRP). However, the relevance of Trotterization in reducing quantum circuit complexity has warranted the release of a revised and more formal version of the original. Thus, we present a mathematical perspective on Trotterization, including a detailed sketch of a formal proof of the Trotter Product Formula.