# Crosstalk Insensitive Trapped-Ion Entanglement through Coupling Matrix Engineering

## TL;DR

This paper introduces a novel method to design entangling gates in trapped-ion systems that are inherently resistant to optical crosstalk by engineering the coupling matrix, improving fidelity without extra operations.

## Contribution

It presents a new approach to create crosstalk-insensitive entangling gates by controlling geometric phases, without needing prior crosstalk knowledge or additional hardware.

## Key findings

- Successfully designed crosstalk-insensitive entangling pulses for 20-ion strings.
- Experimentally validated crosstalk-insensitive entanglement in a three-ion system.
- Numerical simulations show robustness of the method against crosstalk variations.

## Abstract

Optical crosstalk due to imperfect addressing in trapped-ion entangling gates generates unwanted non-local entanglement between target ions and their neighbors that is difficult to mitigate using standard quantum error correction. We present a method to design entangling operations that are inherently insensitive to crosstalk by engineering the effective qubit coupling matrix. By controlling the geometric phases generated in the motional modes of the ion string, we construct a coupling matrix that selectively excludes crosstalk-affected neighbor ions from the entangling operation. This approach requires no knowledge of the amount of crosstalk present and avoids the need for additional gate operations or modifications to the optical setup. We numerically demonstrate the construction of crosstalk-insensitive entangling pulses for target ion pairs within an equispaced 20-ion string and provide experimental validation of crosstalk-insensitive entanglement in a three-ion string.