  We propose schemes of controlled-Z and controlled-NOT gates with ultracold
neutral atoms based on deterministic phase accumulation during double adiabatic
passage of the Stark-tuned F\"{o}rster resonance of Rydberg states. The effect
of deterministic phase accumulation during double adiabatic passage in a
two-level quantum system has been analyzed in detail. Adiabatic rapid passage
using nonlinearly chirped pulses with rectangle intensity profile has been
discussed. Nonlinear time dependence of the energy detuning from the
F\"{o}rster resonance is used to achieve a high fidelity of population transfer
between Rydberg states. Fidelity of two-qubit gates has been studied with an
example of the $90S+96S\to 90P+95P$ Stark-tuned F\"{o}rster resonance in Cs
Rydberg atoms.
