  Speeding up the dynamics of a quantum system is of paramount importance for
quantum technologies. However, in finite dimensions and without full knowledge
of the details of the system, it is easily shown to be impossible. In contrast
we show that continuous variable systems described by a certain class of
quadratic Hamiltonians can be sped up without such detailed knowledge. We call
the resultant procedure Hamiltonian amplification (HA). The HA method relies on
the application of local squeezing operations allowing for amplifying even
unknown or noisy couplings and frequencies by acting on individual modes.
Furthermore, we show how to combine HA with dynamical decoupling to achieve
amplified Hamiltonians that are free from environmental noise. Finally, we
illustrate a significant reduction in gate times of cavity resonator qubits as
one potential use of HA.
