We　propose　how　to　realize　a　multiqubit　tunable　phase　gate　of　one　qubit　simultaneously　controlling　n　qubits　with　four-level　quantum　systems　in　a　cavity　or　coupled　to　a　resonator.　Each　of　the　n　two-qubit　controlled-phase　(cp)　gates　involved　in　this　multiqubit　phase　gate　has　a　shared　control　qubit　but　a　different　target　qubit.　In　this　proposal,　the　two　lowest　levels　of　each　system　represent　the　two　logical　states　of　a　qubit　while　the　two　higher-energy　intermediate　levels　are　used　for　the　gate　implementation.　The　method　presented　here　operates　essentially　by　creating　a　single　photon　through　the　control　qubit,　which　then　induces　a　phase　shift　to　the　state　of　each　target　qubit.　The　phase　shifts　on　each　target　qubit　can　be　adjusted　by　changing　the　Rabi　frequencies　of　the　pulses　applied　to　the　target　qubit　systems.　The　operation　time　for　the　gate　implementation　is　independent　of　the　number　of　qubits,　and　neither　adjustment　of　the　qubit　level　spacings　nor　adjustment　of　the　cavity　mode　frequency　during　the　gate　operation　is　required　by　this　proposal.　It　is　also　noted　that　this　approach　can　be　applied　to　implement　certain　types　of　significant　multiqubit　phase　gates　(e.g.,　the　multiqubit　phase　gate　consisting　of　n　two-qubit　cp　gates　which　are　key　elements　in　quantum　Fourier　transforms).　A　possible　physical　implementation　of　our　approach　is　presented.　Our　proposal　is　quite　general　and　can　be　applied　to　physical　systems　such　as　various　types　of　superconducting　devices　coupled　to　a　resonator　and　trapped　atoms　in　a　cavity.　©　2010　The　American　Physical　Society.