Overview
The term quantum singularity is used to refer to many different phenomena in fiction. They often only approximate a gravitational singularity in the scientific sense in that they are massive, localized distortions of space and time. The name invokes one of the most fundamental problems remaining in modern physics: the difficulty in uniting Einstein's theory of relativity, which includes singularities within its models of black holes, and quantum mechanics. In fact, since according to relativity, singularities, by definition, are infinitely small, and expected to be quantum mechanical by nature, a theory of quantum gravity would be required to describe their behavior. No such theory has yet been formulated.
Star Trek
A Star Trek quantum singularity is a phenomenon of multiple varieties. One such variety appears in the Star Trek: Voyager episode "Parallax" which creates a mirror image along with a temporal distortion. Voyager flies into the singularity after seeing an image of itself inside, and becomes trapped. To escape, the crew uses a shuttle to fire a tachyon beam at the entry. In the Voyager episode "Hunters", the crew discover a Hirogen relay station almost 100,000 years old, powered by a quantum singularity, also referred to by Tom Paris as a black hole. The word "tiny" being used to describe a quantum singularity, about "a centimeter" in diameter, making it relatively large, although it is more likely that the stated diameter instead refers to the singularity's event horizon. In the episode "Scorpion", Species 8472 and the Borg, make use of quantum singularities to travel to and from fluidic space.
Artificial quantum singularities are also used to power Romulan Warbirds as first described in the Star Trek: The Next Generation episode "Face of the Enemy". Additionally, in the Star Trek: Deep Space Nine episode "Visionary", the side effects from quantum singularities cause Miles O'Brien to shift through time.
Futurama
In the Futurama episode "Love and Rocket", after Bender breaks up with the Planet Express Ship, whom he only dated during this episode, the ship, which took the break-up pretty hard, threatens to fly into a giant quasar.
From Wikipedia (CC BY-SA 4.0).