  The loss of quantum information due to interaction with external degrees of
freedom, which is known as decoherence, remains one of the main obstacles for
large-scale implementations of quantum computing. Accordingly, different
measures are being explored for reducing its effect. One of them is dynamical
decoupling (DD) which offers a practical solution because it only requires the
application of control pulses to the system qubits. Starting from basic DD
sequences, more sophisticated schemes were developed that eliminate
higher-order terms of the system-environment interaction and are also more
robust against experimental imperfections. A particularly successful scheme,
called concatenated DD (CDD), gives a recipe for generating higher order
sequences by inserting lower order sequences into the delays of a generating
sequence. Here, we show how this scheme can be improved further by converting
some of the pulses to virtual (and thus ideal) pulses. The resulting scheme,
called vCDD, has lower power deposition and is more robust against pulse
imperfections than the original CDD scheme.
