We describe a simple protocol for the single-step generation of N-body entangling interactions between trapped atomic ion qubits. We show that qubit state-dependent squeezing operations and displacement forces on the collective atomic motion can generate full N-body interactions. Similar to the M{\o}lmer-S{\o}rensen two-body Ising interaction at the core of most trapped ion quantum computers and simulators, the proposed operation is relatively insensitive to the state of motion. We show how this N-body gate operation allows the single-step implementation of a family of N-bit gate operations such as the powerful N-Toffoli gate, which flips a single qubit if and only if all other N-1 qubits are in a particular state.
Cite
@article{arxiv.2202.04230,
title = {$N$-body interactions between trapped ion qubits via spin-dependent squeezing},
author = {Or Katz and Marko Cetina and Christopher Monroe},
journal= {arXiv preprint arXiv:2202.04230},
year = {2022}
}