# Two-qubit entangling gates within arbitrarily long chains of trapped ions

## TL;DR

This paper demonstrates that high-fidelity two-qubit entangling gates can be achieved in large chains of trapped ions, overcoming spectral crowding challenges and enabling scalable quantum computing.

## Contribution

It provides analytical insights into crosstalk errors in parallel gates and experimentally achieves high-fidelity entangling gates in a 17-ion chain.

## Key findings

- Crosstalk error decreases with the cube of inter-ion distance.
- Achieved 97% fidelity in entangling gates on 17-ion chain.
- Analytical model guides scalable ion trap quantum computing.

## Abstract

Ion trap systems are a leading platform for large scale quantum computers. Trapped ion qubit crystals are fully-connected and reconfigurable, owing to their long range Coulomb interaction that can be modulated with external optical forces. However, the spectral crowding of collective motional modes could pose a challenge to the control of such interactions for large numbers of qubits. Here, we show that high-fidelity quantum gate operations are still possible with very large trapped ion crystals, simplifying the scaling of ion trap quantum computers. To this end, we present analytical work that determines how parallel entangling gates produce a crosstalk error that falls off as the inverse cube of the distance between the pairs. We also show experimental work demonstrating entangling gates on a fully-connected chain of seventeen $^{171}{\rm{Yb}}^{+}$ ions with fidelities as high as $97(1)\%$.