Novel Trotter formulas for digital quantum simulation

Quantum simulation promises to address many challenges in fields ranging from quantum chemistry to material science and high-energy physics, and could be implemented in noisy intermediate scale quantum devices. A challenge in building good digital quantum simulators is the fidelity of the engineered dynamics given a finite set of elementary operations. The goal of this work is to find a proper ordering of elementary operations so that they approximate as well as possible the desired evolution. However, when the quantum system is large, even calculating one elementary operation is computationally expensive. In this talk, I will introduce a geometric framework for optimizing the order of operations without considering the details of the operations themselves, thus achieving computational efficiency. Based on the geometric framework, I will present two alternative orderings. One has optimal fidelity at a short time scale, and the other one is robust at a long time scale. Thanks to the improved fidelity at different time scales, the two different orderings can form the basis for experimental-constrained digital quantum simulation.