Improved Time-independent Hamiltonian Simulation

We describe a simple method for simulating time-independent Hamiltonian H that could be decomposed as H = sum_i=1^m H_i where each H_i can be efficiently simulated. Approaches relying on product formula generally work by splitting the evolution time into segments, and approximate the evolution in each segment by the evolution of composing Hamiltonian H_i. This key step incur a constraint, that prohibits a (poly)logarithmic scaling on approximation error. We employ the recently introduced quantum singular value transformation framework to utilize the ability to simulate H_i in an alternative way, which then allows us to construct and simulate the main Hamiltonian H with polylogarithmical scaling on the inverse of desired error, which is a major improvement with respect to product formula approaches.