In the Star Trek: Discovery Episode Context is For Kings, we see the Spore Drive.
Their research was based on the insight that at a quantum level, there was no difference between biology or physics, and specifically that spores were not only the progenitors of panspermia, but also the building blocks of energy across the universe. This allowed Stamets and Straal to approach physics as biology. As such, the equations involved were reminiscent of both quantum astrophysics and biochemistry. (DIS: "Context Is for Kings")
The point being that the Spore drive appears to allow near instantaneous travel across the Galaxy.
Similarly the character Q appeared to have godlike powers, including the ability to instantaneously travel across the universe.
The following commentator writes:
AfterTrek spores "Q" like travel capabilities Hhmm
My question is: Is there any evidence to suggest Q has a mechanism of travel similar to the Spore drive?