  In this work we derive novel ultrafast shortcuts for adiabatic rapid passage
for a qubit where the only control variable is the longitudinal $z$-field,
while the transverse $x$-field remains constant. This restrictive framework is
pertinent to some important tasks in quantum computing, for example the design
of a high fidelity controlled-phase gate can be mapped to the adiabatic quantum
control of such a qubit. We study this problem in the adiabatic reference frame
and with appropriately rescaled time, using as control input the derivative of
the total field polar angle (with respect to rescaled time). We first show that
a constant pulse can achieve perfect adiabatic rapid passage at only specific
times, corresponding to resonant shortcuts to adiabaticity. We next show that,
by using "on-off-on-...-on-off-on" pulse-sequences with appropriate
characteristics (amplitude, timing, and number of pulses), a perfect fidelity
can be obtained for every duration larger than the limit $\pi/\Omega$, where
$\Omega$ is the constant transverse $x$-field. We provide equations from which
these characteristics can be calculated. The proposed methodology for
generalized resonant shortcuts exploits the advantages of composite pulses in
the rescaled time, while the corresponding control $z$-field varies
continuously and monotonically in the original time. Of course, as the total
duration approaches the lower limit, the changes in the control signal become
more abrupt. These results are not restricted only to quantum information
processing applications, but is also expected to impact other areas, where
adiabatic rapid passage is used.

Quantum Physics