  The virtual Z gate has been established as an important tool for performing
quantum gates on various platforms, including but not limited to
superconducting systems. Many such platforms offer a limited set of calibrated
gates and compile other gates, such as the Y gate, using combinations of X and
virtual Z gates. Here, we show that the method of compilation has important
consequences in an open quantum system setting. Specifically, we experimentally
demonstrate that it is crucial to choose a compilation that is symmetric with
respect to virtual Z rotations. This is particularly pronounced in dynamical
decoupling (DD) sequences, where improper gate decomposition can result in
unintended effects such as the implementation of the wrong sequence. Our
findings indicate that in many cases the performance of DD is adversely
affected by the incorrect use of virtual Z gates, compounding other coherent
pulse errors. In addition, we identify another source of coherent errors:
interference between consecutive pulses that follow each other too closely.
This work provides insights into improving general quantum gate performance and
optimizing DD sequences in particular.
