# General solution to inhomogeneous dephasing and smooth pulse dynamical decoupling

## TL;DR

This paper introduces a new geometrical framework for designing smooth, high-fidelity pulse sequences that effectively decouple quantum systems from noise and inhomogeneities, overcoming experimental implementation challenges.

## Contribution

It presents a novel geometrical approach to generate unlimited smooth pulses for dynamical decoupling and corrected gates, improving quantum control fidelity.

## Key findings

- Enhanced single-qubit operation fidelity under noise.
- Ability to generate experimentally feasible smooth pulses.
- Significant improvement over traditional ideal pulses.

## Abstract

In order to achieve the high-fidelity quantum control needed for a broad range of quantum information technologies, reducing the effects of noise and system inhomogeneities is an essential task. It is well known that a system can be decoupled from noise or made insensitive to inhomogeneous dephasing dynamically by using carefully designed pulse sequences based on square or delta-function waveforms such as Hahn spin echo or CPMG. However, such ideal pulses are often challenging to implement experimentally with high fidelity. Here, we uncover a new geometrical framework for visualizing all possible driving fields, which enables one to generate an unlimited number of smooth, experimentally feasible pulses that perform dynamical decoupling or dynamically corrected gates to arbitrarily high order. We demonstrate that this scheme can significantly enhance the fidelity of single-qubit operations in the presence of noise and when realistic limitations on pulse rise times and amplitudes are taken into account.