# Fast dynamical decoupling of the Molmer-Sorensen entangling gate

## TL;DR

This paper introduces a fast dynamical decoupling method for boson-mediated entangling gates that maintains high fidelity even during entanglement, significantly reducing gate time increase compared to previous schemes.

## Contribution

The authors develop and experimentally demonstrate a novel dynamical decoupling technique allowing pulses during entanglement, reducing gate time overhead independent of pulse number.

## Key findings

- Achieved robust entangling gates with minimal time increase.
- Demonstrated effectiveness against $\sigma_z$ noise in ion traps.
- Reduced gate time scaling from $\

## Abstract

Engineering entanglement between quantum systems often involves coupling through a bosonic mediator, which should be disentangled from the systems at the operation's end. The quality of such an operation is generally limited by environmental and control noise. One of the prime techniques for suppressing noise is by dynamical decoupling, where one actively applies pulses at a rate that is faster than the typical time scale of the noise. However, for boson-mediated gates, current dynamical decoupling schemes require executing the pulses only when the boson and the quantum systems are disentangled. This restriction implies an increase of the gate time by a factor of $\sqrt{N}$, with $N$ being the number of pulses applied. Here we propose and realize a method that enables dynamical decoupling in a boson mediated system where the pulses can be applied while spin-boson entanglement persists, resulting in an increase in time that is at most a factor of $\frac{\pi}{2}$, independently of the number of pulses applied. We experimentally demonstrate the robustness of our fast dynamically decoupled entangling gate to $\sigma_z$ noise with ions in a Paul trap.