Optimally combining dynamical decoupling and quantum error correction

TL;DR

This paper develops an optimal method for combining dynamical decoupling and quantum error correction to enhance fault-tolerant quantum computing, reducing sequence length and relaxing assumptions for practical implementation.

Contribution

It identifies the optimal DD generator set aligned with stabilizer codes, improving hybrid DD-QEC schemes and easing practical realization.

Findings

Optimal DD generator set minimizes sequence length

Relaxation of local-bath assumption enhances scheme feasibility

Bridges gap between theory and practical quantum error correction

Abstract

We show how dynamical decoupling (DD) and quantum error correction (QEC) can be optimally combined in the setting of fault tolerant quantum computing. To this end we identify the optimal generator set of DD sequences designed to protect quantum information encoded into stabilizer subspace or subsystem codes. This generator set, comprising the stabilizers and logical operators of the code, minimizes a natural cost function associated with the length of DD sequences. We prove that with the optimal generator set the restrictive local-bath assumption used in earlier work on hybrid DD-QEC schemes, can be significantly relaxed, thus bringing hybrid DD-QEC schemes, and their potentially considerable advantages, closer to realization.