  It is known that high intensity fields are usually required to implement
shortcuts to adiabaticity via Transitionless Quantum Driving (TQD). Here, we
show that this requirement can be relaxed by exploiting the gauge freedom of
generalized TQD, which is expressed in terms of an arbitrary phase when
mimicking the adiabatic evolution. We experimentally investigate the
performance of generalized TQD in comparison with both traditional TQD and
adiabatic dynamics. By using a $^{171}$Yb$^+$ trapped ion hyperfine qubit, we
implement a Landau-Zener adiabatic Hamiltonian and its (traditional and
generalized) TQD counterparts. We show that the generalized theory provides
optimally implementable Hamiltonians for TQD, with no additional fields
required. In addition, the energetically optimal TQD Hamiltonian for the
Landau-Zener model is investigated under dephasing. Remarkably, even using less
intense fields, optimal TQD exhibits fidelities that are more robust against a
decohering environment, with performance superior than that provided by the
adiabatic dynamics.
