I don't think we know anywhere near enough about quantum gravity to be sure of that.
Not that I'd be super-optimistic about "quantum gravitational computers" actually being any use relative to ordinary quantum computers -- but in the absence of an actual working quantum theory of gravity I don't see how we can know they wouldn't make a difference in calef's hypothetical world.
We actually know quite a bit about quantum gravity: it must fall under a quantum mechanical framework, and it needs to result in gravity, and gravitons haven't been directly detected yet. This isn't enough to determine what the theory is, but it is enough to say some things about it. The main two things are:
1: Since it's just quantum mechanics, whatever it does, it'll just set another Hamiltonian. If it changes the ground rules, then it's not a theory of quantum gravity. It's a theory of something else gravity.
2: Gravity is weak. Ridiculously weak. Simply...
Speculation is important for forecasting; it's also fun. Speculation is usually conveyed in two forms: in the form of an argument, or encapsulated in fiction; each has their advantages, but both tend to be time-consuming. Presenting speculation in the form of an argument involves researching relevant background and formulating logical arguments. Presenting speculation in the form of fiction requires world-building and storytelling skills, but it can quickly give the reader an impression of the "big picture" implications of the speculation; this can be more effective at establishing the "emotional plausibility" of the speculation.
I suggest a storytelling medium which can combine attributes of both arguments and fiction, but requires less work than either. That is the "wikipedia article from the future." Fiction written by inexperienced sci-fi writers tends to generate into a speculative encyclopedia anyways--why not just admit that you want to write an encyclopedia in the first place? Post your "Wikipedia articles from the future" below.