Multibit C$_k$NOT quantum gates via Rydberg blockade

Abstract

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 $π$ 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 $k=35$.

submitted to "Quantum Information Processing" special issue on "Quantum Information with Neutral Particles". v2, discussion of estimated errors expanded