High-fidelity 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. Here we present a framework for optimizing the order of operations based on a geometric picture, thus abstracting from the operation details and achieving computational efficiency. Based on this geometric framework, we provide two alternative second-order Trotter expansions: one with optimal fidelity at a short timescale, and the second robust at a long timescale. Thanks to the improved fidelity at different timescales, the two expansions we introduce can form the basis for experimental-constrained digital quantum simulation.