$N$-body interactions between trapped ion qubits via spin-dependent squeezing

TL;DR

This paper introduces a protocol for generating N-body entangling interactions among trapped ion qubits using spin-dependent squeezing, enabling efficient implementation of complex multi-qubit gates like the N-Toffoli.

Contribution

The authors propose a novel single-step method for creating N-body interactions in trapped ion systems using spin-dependent squeezing and displacement, extending beyond traditional two-qubit gates.

Findings

Enables single-step N-body entangling operations

Insensitive to the motional state of ions

Facilitates implementation of complex N-qubit gates like N-Toffoli

Abstract

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.