We　present　a　scheme　for　implementation　of　controlled-Z　and　controlled-NOT　gates　via　rapid　adiabatic　passage　and　Stark-tuned　Frster　resonance.　By　sweeping　the　Frster　resonance　once　without　passing　through　it　and　adiabatically　tuning　the　angle-dependent　RydbergRydberg　interaction　of　the　dipolar　nature,　the　system　can　be　effectively　described　by　a　two-level　system　with　the　adiabatic　theorem.　The　single　adiabatic　passage　leads　to　a　gate　fidelity　as　high　as　0.999　and　a　greatly　reduced　gate　operation　time.　We　investigate　the　scheme　by　considering　an　actual　atomic　level　configuration　with　rubidium　atoms,　where　the　fidelity　of　the　controlled-Z　gate　is　still　higher　than　0.99　under　the　influence　of　the　Zeeman　effect.　©　2018　Astro　Ltd.