Exact Results on Dynamical Decoupling by $\pi$-Pulses in Quantum Information Processes

TL;DR

This paper provides exact analytical results on how optimized sequences of $$ pulses can effectively suppress decoherence in quantum bits, considering different environmental spectral cutoffs, and introduces iterated optimized sequences for intermediate cases.

Contribution

It offers the first exact results on dynamical decoupling with $$ pulses and proposes iterated optimized sequences for environments with intermediate spectral cutoffs.

Findings

Harder spectral cutoffs lead to better suppression by optimized sequences.

Iterated optimized sequences improve performance for intermediate cutoffs.

Exact results clarify the effectiveness of $$-pulse sequences in various environmental conditions.

Abstract

The aim of dynamical decoupling consists in the suppression of decoherence by appropriate coherent control of a quantum register. Effectively, the interaction with the environment is reduced. In particular, a sequence of $\pi$ pulses is considered. Here we present exact results on the suppression of the coupling of a quantum bit to its environment by optimized sequences of $\pi$ pulses. The effect of various cutoffs of the spectral density of the environment is investigated. As a result we show that the harder the cutoff is the better an optimized pulse sequence can deal with it. For cutoffs which are neither completely hard nor very soft we advocate iterated optimized sequences.