Quinn was a name chosen by Q, a member of the Q Continuum who decided that he wanted to commit suicide. Once a respected philosopher among the Q, he would claim later that Q's irresponsible and inappropriate behavior, which he believed originated from his need for amusement, gave the Continuum something to talk about, and forced Quinn to think. Q was later made mortal as a punishment, until he was again readmitted in the Continuum. However, Q's "rebellion" against his existence became an inspiration for Quinn.
Quinn caused quite a stir within the Continuum when he published his views. He claimed he wished to die rather than have immortality forced upon him. In one of his "self-destructive stunts", he failed to terminate his existence, and instigated a hundred-year war between the Vulcans and the Romulans.
The starship USS Voyager encountered Quinn and released him from his imprisonment. When he told them who he was, Captain Kathryn Janeway mistook him for the Q who had visited the USS Enterprise-D. He then tried to commit suicide again but made all the men disappear instead. The Enterprise's Q turned up to apprehend him, and restored the men to Voyager but Quinn attempted to hide by whisking himself and Voyager to various places in the universe such as the beginning of the universe, subatomic proportions, even a Christmas tree. Q knew all the hiding places, but before he was able to re-imprison him, Quinn made a plea for political asylum to Captain Janeway. A courtroom hearing took place aboard Voyager to determine if asylum should be granted. Lieutenant Tuvok served as his defense. He stated that Quinn was sick of immortality. There was nothing left for him to explore and his life was pointless. Q tried to prove the worth of Quinn's life by calling witnesses such as Isaac Newton, Maury Ginsberg, and William T. Riker, pointing out how Quinn had affected their lives for the better. For Newton, he jostled the tree before the apple fell, leading to the discovery of gravity; Maury so that he could get to Woodstock to save it and then live a successful life; saving Riker's ancestor, Thaddius, so that his descendant would be born and save the Federation from the Borg (and so that Q could insult him).
Quinn attempted to prove his life was pointless and caused him unendurable boredom. He did this by taking Janeway to the Q Continuum, which was presented in the Human-comprehensible form of a house in the middle of a desert with a road running by it. The road, he told her, represented the universe's edge and there was nothing left for him to explore. None of the Q in the Continuum spoke anymore, because all things had been discussed and all things were known. Quinn told Janeway that his life's work was complete and that he had done everything there was possible to do, yet was forced by his people to continue to live. Captain Janeway ruled in favor of Quinn, despite Q's attempted bribe of whisking Voyager back to Earth. Reluctantly keeping his word, Q turned Quinn into a mortal, after the verdict. Janeway tried to convince Quinn not to commit suicide, since he now had a whole new mortal life to experience. As a mortal, Quinn briefly served as a crewman aboard Voyager. Janeway and Chakotay wondered whether he should be assigned to stellar cartography, noting that they might as well shut down that department given Quinn's vast knowledge. Knowing he would never truly fit in as a mortal, Quinn ultimately committed suicide with a sample of Nogatch hemlock procured by Q, who was inspired by Quinn's "rebelliousness." (VOY: "Death Wish")
Quinn's death ultimately caused a disruption in the Continuum, as Q had predicted. Many of his followers pushed for changes to the "status quo". When the Continuum leadership refused, Q led the dissidents in a civil war. (VOY: "The Q and the Grey")
Quinn was played by Gerrit Graham. While still a Q, Quinn was referred to as "Q" just like all other Q. He assumed the name "Quinn" only after becoming mortal.
The script of "Death Wish" consistently referred to this character as "Q2", even though he appears in the story before Q (who was referred to in the script as "Q1"). In his humanoid form, Quinn was also described in the script as "about forty."
In the first draft script of "Death Wish", which would have featured Geordi La Forge and not William Riker, it was established that Quinn somehow caused La Forge's birth. In that case, Tuvok would have ended up as chief engineer aboard the USS Enterprise-D.
Quinn would actually be the third known Q to die, as, according to Q, Amanda Rogers' father and mother were killed by the Continuum while living on Earth in Topeka, Kansas as Humans; ("True Q") Tuvok indirectly referenced this during the trial when noting that they were an example of Q practicing capital punishment, but Q justified the distinction on the grounds that they had already destabilized the Continuum by their actions in life and their deaths had restored stability.
Even though Quinn inspired him, Quinn cited the life of Q as his inspiration to rebel and argue for self termination because Q's antics forced him to think.