# Second order phase dispersion by optimised rotation pulses

## TL;DR

This paper introduces a method to design shorter broadband control pulses for two-level systems by optimizing phase dispersion functions, improving control efficiency in quantum systems.

## Contribution

It proposes a novel quadratic phase dispersion approach and an optimal control method to create shorter, broadband universal rotation pulses avoiding local extrema traps.

## Key findings

- Pulse duration is halved with quadratic phase dispersion control.
- The method achieves broadband universal rotations efficiently.
- Optimal control avoids convergence to local extrema.

## Abstract

We show that the duration of broadband universal control pulses can be halved by choosing control targets with a quadratic function of phase dispersion. This class of control pulses perform a broadband universal rotation around an axis, in the Bloch sphere representation of two-level systems, given by this phase dispersion function. We present an effective optimal control method to avoid the problem of convergence to local extrema traps.