Multibit C$_k$NOT quantum gates via Rydberg blockade

Understand

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 (C$_k$NOT) 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 $\pi$ 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 $k=35$.