Quantum slipstream drive, also later known as transwarp slipstream drive, was an advanced form of transwarp drive. The USS Voyager obtained and tested slipstream drive technology in the 2370s (VOY: "Hope and Fear", "Timeless").
Though largely unsuccessful for Voyager, QSD became a major development in several fan fiction continuities.
Star Trek: Arcadia
In Star Trek: Arcadia, the Voyager transmitted their slipstream data to Starfleet in late 2376. By 2377 Starfleet R&D developed a slipstream drive vessel incorporating other innovative technologies, including a spatial deflector array, improved energy feeds and automated computer systems, which made stable slipstream transit possible. By the mid-2380s, continuous refinement of slipstream drive (scientifically known as reversible-field quantum restructuring quadraxial drive) enabled Quantum-class vessels such as the UFS Arcadia to reach speeds approximating warp 81,250. At maximum velocity, a non-stop, one-way trip using this form of QSD would cover the Milky Way Galaxy in roughly six months. Due to its tactical advantages, Starfleet closely guarded slipstream drive to prevent it from falling into hostile hands.
Star Trek: Challenger
Star Trek: Interpreter
In Star Trek: Interpreter, the USS Interpreter was a prototype vessel fitted with the first Federation prototype quantum slipstream drive (sometimes referred to as quantum drive) in 2426. The research and development teams had thought they finally got it right after almost half a century working on it. The Interpreter on its maiden voyage tested its warp engines before docking but Captain Waters was a little hesitant with the slipstream drive.
In the Pendragon timeline, Starfleet Research and Development and the Starfleet Corps of Engineers began working on quantum slipstream drive in 2378, almost immediately after the USS Voyager's return to the Alpha Quadrant. The USS Spirit served as an early testbed for the drive, though the technology's existence was kept classified for several years. Limited supplies of the necessary benamite crystals hampered the widespread application of the drive as well. Due to the nature of the quantum slipstream's interactions with subspace, there were many starship types whose hull design and warp field geometry were incompatible with the drive tech, including the Galaxy-class, Pendragon-class and Sovereign-class. In contrast, vessels of the Intrepid-class were able to easily implement slipstream drives.
By early 2381, ships of the Vesta-class were equipped with the technology, including the USS Aventine. The success of the drive on these vessels and others, led to the implementation of Project Full Circle, a long-term exploration and diplomatic initiative in the Delta Quadrant, led by Voyager.
Star Trek: Phoenix-X
In Star Trek: Phoenix-X, the USS Phoenix-X utilized slipstream torpedoes beginning around stardate 52339.1 (2375). A Romulan warbird, led by Plutark, intercepted a secret transmission of torpedo schematics between the Phoenix-X and Starfleet Intelligence. The Gordarions also obtained this technology from the Phoenix-X.
After the USS Voyager returned in 2378, Federation and Starfleet scientists poured over the designs and schematics for the quantum slipstream drive. Then in 2379, the Starfleet Corps of Engineers began development of a working slipstream drive. Starfleet Command, in agreement with the Federation Council, concluded that a new class of starship was needed. So they developed the Cosmos-class starship. The first starship was constructed in 2380, but during a test flight the QSD drive malfunctioned, causing an explosion. Starfleet suspended testing and had the Starfleet Corps of Engineers re-examine the slipstream drive. ("The Teacher")
Federation prototype Cosmos-class starships
In Star Trek: Prometheus, as in Star Trek: Arcadia, the starship Voyager transmitted their slipstream data to Starfleet in late 2376. However in Star Trek: Prometheus the study group assembled to study the data deemed that it was not possible for Starfleet to develop a working slipstream drive given the current level of technology.
Following receiving the data on quantum slipstream propulsion from Voyager the technology became a major project and priority for the Starfleet Corps of Engineers culminating in the successful development of the drive and fitting the new Vesta-class with the drive as a supplement to its warp and impulse drives.
Following Voyager 's return to the Federation and the study of the data and logs brought back Project Full Circle was conceived with the express purpose of following up on Voyager 's travels in an official manner with a dedicated fleet equipped with quantum slipstream drives to allow the mission duration to be practical and not a long term/generational mission.
By 2386, the Prometheus had as yet to be fitted with a quantum slipstream drive like those found on the Project Full Circle fleet and on Vesta-class starships such as the USS Aventine due to delays in the fleet wide roll out of the technology related to the availability of suitable benamite crystals and long lead times in synthasizing suitable crystals and fabricating the technology.
By 2387, the Prometheus had been eqipped with a quantum slipstream drive for field testing for inclusion as a standard feature of the Prometheus class.