Quantum interpolation 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 quantum digital simulators is the fidelity of the engineered dynamics, which stems from practical experimental constraints. While the approximation in building the target Hamiltonian by a Trotter construction could be improved by taking smaller steps, this is not always possible experimentally. Here we provide an alternative construction, which we call Quantum Interpolation, that locally minimizes the error and achieves better fidelity than the Trotter expansion for the same minimum time step and time-step resolution. Our Quantum Interpolation construction can be found from a simple geometric condition, thus is computationally efficient. Thanks to its improved fidelity, Quantum Interpolation can form the basis for experimental-constrained quantum digital simulation.