  A shortcut-to-adiabatic protocol for the realization of a fast and
high-fidelity controlled-phase gate in Rydberg atoms is developed. The
adiabatic state transfer, driven in the high-blockade limit, is sped up by
compensating nonadiabatic transitions via oscillating fields that mimic a
counterdiabatic Hamiltonian. High fidelities are obtained in wide parameter
regions. The implementation of the bare effective counterdiabatic field,
without original adiabatic pulses, enables to bypass gate errors produced by
the accumulation of blockade-dependent dynamical phases, making the protocol
efficient also at low blockade values. As an application toward quantum
algorithms, how the fidelity of the gate impacts the efficiency of a minimal
quantum-error correction circuit is analyzed.
