  We analyze numerically the performance of the near-optimal quadratic
dynamical decoupling (QDD) single-qubit decoherence errors suppression method
[J. West et al., Phys. Rev. Lett. 104, 130501 (2010)]. The QDD sequence is
formed by nesting two optimal Uhrig dynamical decoupling sequences for two
orthogonal axes, comprising N1 and N2 pulses, respectively. Varying these
numbers, we study the decoherence suppression properties of QDD directly by
isolating the errors associated with each system basis operator present in the
system-bath interaction Hamiltonian. Each individual error scales with the
lowest order of the Dyson series, therefore immediately yielding the order of
decoherence suppression. We show that the error suppression properties of QDD
are dependent upon the parities of N1 and N2, and near-optimal performance is
achieved for general single-qubit interactions when N1=N2.
