Reducing the Gate Count with Efficient Trotter-Suzuki Schemes

TL;DR

This paper explores advanced Trotter-Suzuki schemes to reduce gate counts in quantum simulations of lattice field theories, demonstrating their efficiency on the Heisenberg model.

Contribution

It introduces optimized higher-order Trotter-Suzuki schemes that improve simulation efficiency compared to standard methods.

Findings

New efficient Trotter-Suzuki schemes identified

Performance improvements demonstrated on the Heisenberg model

Reduction in gate count for quantum simulations

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.