  Shortcuts to adiabaticity is a general method for speeding up adiabatic
quantum protocols, and has many potential applications in quantum information
processing. Unfortunately, analytically constructing shortcuts to adiabaticity
for systems having complex interactions and more than a few levels is a
challenging task. This is usually overcome by assuming an idealized Hamiltonian
[e.g., only a limited subset of energy levels are retained, and the
rotating-wave approximation (RWA) is made]. Here we develop an $analytic$
approach that allows one to go beyond these limitations. Our method is general
and results in analytically derived pulse shapes that correct both nonadiabatic
errors as well as non-RWA errors. We also show that our approach can yield
pulses requiring a smaller driving power than conventional nonadiabatic
protocols. We show in detail how our ideas can be used to analytically design
high-fidelity single-qubit "tripod" gates in a realistic superconducting
fluxonium qubit.
