Stability and convergence of dynamical decoupling with finite amplitude control

TL;DR

This paper investigates the effectiveness of dynamical decoupling using finite amplitude controls in quantum systems, establishing conditions for success and connecting it to the ideal bangbang model as a limiting case.

Contribution

It provides a theoretical analysis of finite amplitude dynamical decoupling, bridging the gap with the idealized bangbang approach and clarifying its physical validity.

Findings

Finite amplitude controls can effectively achieve dynamical decoupling under certain conditions.

The bangbang model is shown to be a limiting case of finite amplitude controls.

Conditions for the success of finite amplitude dynamical decoupling are established.

Abstract

Dynamical decoupling is a key method to mitigate errors in a quantum mechanical system, and we studied it in a series of papers dealing in particular with the problems arising from unbounded Hamiltonians. The standard bangbang model of dynamical decoupling, which we also used in those papers, requires decoupling operations with infinite amplitude, which is strictly speaking unrealistic from a physical point of view. In this paper we look at decoupling operations of finite amplitude, discuss under what assumptions dynamical decoupling works with such finite amplitude operations, and show how the bangbang description arises as a limit, hence justifying it as a reasonable approximation.