Virtual Z gates and symmetric gate compilation

Abstract: 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 all other gates using combinations of X-type 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. An important example is 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. This holds even for DD sequences designed to be robust against systematic control 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.