Filter-design perspective applying to dynamical decoupling of a multi-qubit system

TL;DR

This paper compares the effectiveness of nested Uhrig and symmetric dynamical decoupling sequences in protecting multi-qubit systems from decoherence, highlighting their performance under different bath conditions and control imperfections.

Contribution

It applies the filter-design perspective to analyze and compare NUDD and SDD in multi-qubit decoherence suppression within the spin-boson model.

Findings

SDD outperforms NUDD with a soft cutoff bath

NUDD approaches SDD with a hard cutoff

SDD preserves decoherence-free subspace with common reservoir

Abstract

We employ the filter-design perspective and derive the filter functions according to nested Uhrig dynamical decoupling (NUDD) and Symmetric dynamical decoupling (SDD) in the pure-dephasing spin-boson model with N qubits. The performances of NUDD and SDD are discussed in detail for a two-qubit system. The analysis shows that (i) SDD outperforms NUDD for the bath with a soft cutoff while NUDD approaches SDD as the cutoff becomes harder; (ii) if the qubits are coupled to a common reservoir, SDD helps to protect the decoherence-free subspace while NUDD destroys it; (iii) when the the imperfect control pulses with finite width are considered, NUDD is affected in both the high-fidelity regime and coherence time regime while SDD is affected in the coherence time regime only.