  In quantum computing, the nonstabilizerness of quantum operations is crucial
for understanding and quantifying quantum speedups. In this study, we explore
the phenomena of nonstabilizerness of the quantum SWITCH, a novel structure
that allows quantum states to pass through operations in a superposition of
different orders, outperforming traditional circuits in numerous tasks. To
assess its nonstabilizerness, we propose the magic resource capacity of a
quantum process to quantitatively examine the nonstabilizerness of general
quantum transformations. We find that the completely stabilizer-preserving
operations, which cannot generate magic states under standard conditions, can
be transformed to do so when processed by the quantum SWITCH. Furthermore, when
considering the impact of noise, although the nonstabilizerness of each path
may be annihilated, their superposition could still preserve the overall
nonstabilizerness. These findings reveal the unique properties of the quantum
SWITCH and open avenues in research on nonstabilizer resources of general
quantum architecture.
