Trotterization and Trotter Error (YQIS 2021)

Abstract

The Lie-Trotter formula, together with its higher-order generalizations, provides a simple approach to decomposing the exponential of a sum of operators, an approach commonly known as Trotterization in quantum computation. This talk will present some of our recent results on the application of these formulas to digital quantum simulation. Topics to be covered include the implementation of Trotterization in the quantum circuit model, vanilla bound on the Trotter error with $1$-norm scaling, faster Trotterization by randomization and symmetry protection, and improved analysis of Trotter error with commutator scaling. Based on arXiv:1711.10980, arXiv:1805.08385, arXiv:1901.00564, arXiv:1912.08854, arXiv:2006.16248, arXiv:2012.09194.