Quantum interpolation for digital quantum simulation

Quantum simulation enables understanding complex dynamics with experimentally implementable dynamics. Digital quantum simulation enabled by Trotter expansion finds many applications due to its flexibility and universality. However, Trotter expansion higher than second order requires complicated coefficients that are hard to implement in experiment. Here we present Quantum Interpolation, a new exponential product second order approximation of exponential operators, motivated by realistic experimental limitations. We show that Quantum Interpolation has higher fidelity than the most commonly used second order Trotter expansion without any complicated coefficients. We also present the application of Quantum Interpolation in nano nuclear magnetic resonance imaging.