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 Mølmer-Sørensen 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 for 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 $N\text{−}1$ qubits are in a particular state.

中文翻译：

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通过自旋依赖挤压的捕获离子量子比特之间的 N 体相互作用

我们描述了一个简单的协议，用于单步生成$ñ$- 被困原子离子量子比特之间的身体纠缠相互作用。我们表明，量子比特状态相关的挤压操作和集体原子运动上的位移力可以产生完整的$ñ$- 身体互动。与大多数捕获离子量子计算机和模拟器核心的 Mølmer-Sørensen 二体伊辛相互作用类似，所提出的操作对运动状态相对不敏感。我们展示了这是如何$ñ$-体门操作允许单步实现一系列$ñ$位门操作等功能强大$ñ$-Toffoli 门，当且仅当所有其他量子位翻转单个量子位$ñ\text{-}1$量子位处于特定状态。