Multibit CkNOT quantum gates via Rydberg blockade

Long range Rydberg blockade interactions have the potential for efficient implementation of quantum gates between multiple atoms. Here we present and analyze a protocol for implementation of a k-atom controlled NOT (CkNOT) neutral atom gate. This gate can be implemented using sequential or simultaneous addressing of the control atoms which requires only 2k + 3 or 5 Rydberg p pulses respectively. A detailed error analysis relevant for implementations based on alkali atom Rydberg states is provided which shows that gate errors less than 10% are possible for k = 35.