(The Wahrian Space Gate is now known as Space Gate Alpha in Heart of Galaxy Horizons)
The Space Gate Alpha is a building that is unlocked by having at least Level 1 in the Research Secrets of Space-Time (which, in turn, needs Quantum Physics Level 2, Nuclear Physics Level 14, and conquering Xora Tauri).
The Space Gate Alpha may be constructed on any planet you own (from the "Other buildings" section, where you would also find the options to build Shipyards, Greenhouses, Battery Chargers, and Trade Hubs). The material requirements are:
Once constructed, clicking on the Space Gate Alpha in the Other Buildings section presents a new button labeled "Send a Fleet to Solidad". When clicked, you are shown a list of all of your fleets at the same planet at the Space Gate Alpha. Clicking on a fleet will teleport that fleet to the planet Solidad, the first planet in Andromeda Heart (which starts off uninhabited, so you will need a Heaven's Door.)
Antimatter cost = (Weight of Ships + Weight of cargo) / (100000 * SQRT(Number of Wahrian Space Gates) )
In other words, if you have 4 Space Gate Alphas built at Ishtar Gate, then you need 1 unit of antimatter at Ishtar Gate to send a 200 thousand weight fleet from Ishtar Gate to Solidad.
In the above formula, the "weight" of an empty ship is the exact same number as the "weight" used in combat calculations to determine what proportion of incoming enemy fire is directed at this ship. For example, for combat purposes a Babayaga always has a Weight of 1500 regardless of whether it is carrying cargo into battle or not; merely having cargo on board is NOT going to cause a particular Babayaga to get shot at more than usual. However, for the purposes of Space Gate Alpha, an empty Babayaga has a Weight of 1500 and a Babayaga packed full of cargo has a Weight of 101500; that's 67.66 times more Weight, so that's going to cost 67.66 times as much Antimatter.
Antimatter costs are always rounded up to the next integer.
As of Heart of Galaxy version 32 (published May 14, 2017), all Space Gates lead to Solidad. Wahrian Space Gates can only send fleets, they cannot recall fleets. A Space Gate Alpha built in Solidad is completely useless as it can only send fleets to itself. You can use Space Gate Alphas to send resupply fleets manually from Perseus Arm to Andromeda Heart, but fleets and resources can NOT be sent back from Andromeda Heart to Perseus Arm.