The Quantum Teleportation Data Stream was used in the series finale episode Just Another Day to teleport data.
The teleportation stream was only shown in the final episode, so there is no way of knowing if it might have been used in another episode later, had the show not ended. However, considering the fact that they were using it to transfer all of the GD research and technology information to Washington D.C. (because they were closing down the whole town of Eureka) it's very unlikely that it would have been needed again.
No one knows who invented it, though it's been hypothesized that it might've been Zane Donovan.