Some month ago, I was attending a lecture from a person who worked for LIGO, and eho is now a professor at MIT, about gravitational waves. At the end of the conference, though, time for questions ran out, but I sometime I have this curiosity: do gravitational waves have potential for computing? If so, how much potential do they have, compared to quantum computers ( althiugh I know quantum computers are still a "work in progress")? Are they studied somewhere, in order to achieve this goal?
There are people studying whether it is possible to build "quantum gravity quantum computers", that is, quantum computers harnessing things like quantum fluctuations in the causal structure of spacetime, to solve tasks more efficiently than what is possible with "regular" quantum computers. A quick google search will lead you to some of these studies.
If you instead mean whether it is possible to use gravitational waves to do "standard" quantum computing, I'd say the answer is no. To do something like this you would first of all need to quantize the gravitational waves, that is, have a consistent theory of quantum gravity.
Also, consider how harder it is to experimentally "see" the quantized nature of light (i.e. single photons) with respect to just detecting an electromagnetic wave. It took huge effort to detect "classical" gravitational waves. To detect their quantum nature (like gravitons, if that is even a thing in the real world) would be incredibly harder.
To summarize: it can be interesting, and is currently done, to study whether quantum gravity can allow (in theory) to perform things unachievable for regular quantum computers. But to harness gravitational waves for quantum computing is even further away from the realm of actually doable things.