Dynamical decoupling sequence construction as a filter-design problem

TL;DR

This paper presents a novel approach to designing dynamical decoupling sequences by framing it as a filter-design problem, integrating control theory to optimize quantum coherence preservation.

Contribution

It introduces a filter-design framework for dynamical decoupling sequence construction, connecting quantum control with classical filter design and providing new insights and optimization techniques.

Findings

Mathematical reduction of dephasing suppression to a linear control problem

Comparison of standard and optimized sequences using the filter-design perspective

Identification of limitations such as digital clocking effects on sequence performance

Abstract

Over the past decade we have seen an explosion of demonstrations of quantum coherence in atomic, optical, and condensed matter systems. These developments have placed a new emphasis on the production of robust and optimal quantum control techniques in the presence of environmental noise. We discuss the use of dynamical decoupling as a form of open-loop quantum control capable of suppressing the effects of dephasing in quantum coherent systems. We introduce the concept of dynamical decoupling pulse-sequence construction as a filter-design problem, making connections with filter design from control theory and electrical engineering in the analysis of pulse-sequence performance for the preservation of the phase degree of freedom in a quantum superposition. A detailed mathematical description of how dephasing and the suppression of dephasing can be reduced to a linear control problem is provided, and used as motivation and context for studies of the filtration properties of various dynamical decoupling sequences. Our work then takes this practical perspective in addressing both "standard" sequences derived from nuclear magnetic resonance and novel optimized sequences developed in the context of quantum information. Additionally, we review new techniques for the numerical construction of optimized pulse sequences using the filter-design perspective. We show how the filter-design perspective permits concise comparisons of the relative capabilities of these sequences and reveals the physics underlying their functionality. The use of this new analytical framework allows us to derive new insights into the performance of these sequences and reveals important limiting issues, such as the effect of digital clocking on optimized sequence performance.