  Given the Hamiltonian, the evaluation of unitary operators has been at the
heart of many quantum algorithms. Motivated by existing deterministic and
random methods, we present a hybrid approach, where Hamiltonians with large
amplitude are evaluated at each time step, while the remaining terms are
evaluated at random. The bound for the mean square error is obtained, together
with a concentration bound. The mean square error consists of a variance term
and a bias term, arising respectively from the random sampling of the
Hamiltonian terms and the operator splitting error. Leveraging on the
bias/variance trade-off, the error can be minimized by balancing the two. The
concentration bound provides an estimate on the number of gates. The estimates
are verified by using numerical experiments on classical computers.
