Reducing the Gate Count with Efficient Trotter-Suzuki Schemes

Abstract

Hamiltonian formulations of lattice field theories provide access to real-time dynamics, but their simulation is difficult to implement efficiently. Trotter-Suzuki decompositions are at the center of time evolution computation, either on quantum hardware or classically, for instance with the use of tensor networks. While low-order Trotterizations remain the standard choice due to their simplicity, higher-order schemes offer the potential for improved efficiency. In this work we outline a short guide to Trotter-Suzuki schemes and their implementations in general. To help with this, we highlight new efficient schemes found by our optimization framework, and demonstrate their performance on the Heisenberg model.

Comments: 10 pages, 3 figures, 3 tables and 1 algorithm - Proceedings of the 42nd International Symposium on Lattice Field Theory (Lattice 2025), TIFR Mumbai, India, 2025; v2: Fixed grouping mistake