  Simulating high-weight Hamiltonians can convert local noise on the original
Hamiltonian into undesirable nonlocal noise on the simulated Hamiltonian. Here
we show how starting from two-local Hamiltonian in the presence of
non-Markovian noise, a desired computation can be simulated as well as
protected using fast pulses, while maintaining an energy gap against the errors
created in the process.
