We don't understand gravity to the point where we have a consistent algorithmic explanation for it. As suggested, there are competing theories, all of which are algorithmically based. The holy grail of modern physics is to find the algorithm that explains gravity as that is the last missing piece to finalize the theory of everything.

The results of this research are implying that it is not possible to prove, algorithmically, that gravity is quantum but rather that quantum gravity as the foundation of the universe is non-algorithmic and therefore non-computational. And so a theory of everything is impossible, implying that the universe cannot be simulated by computing the theory of everything.

This research builds on a lot of the work that Roger Penrose did in the 90s in exploring the potential non-algorithmic nature of consciousness (https://en.wikipedia.org/wiki/Roger_Penrose#Consciousness). If you read his book "Shadows of the Mind" published in 1993 you will find a prediction of future computational abilities that is a shockingly accurate description of AI deep fakes and the AI slop we see today with LLMs.

The no-simulated universe idea is one interesting conclusion of this research, but in my opinion, a more interesting conclusion of this research is that if you believe Penrose's argument for consciousness being non-algorithmic, than this research is implying that AGI is also impossible.

Yeah, there is no consensus on quantum gravity. There are competing theories, none of which have any viable path to test.

Here's the abstract from a paper from last year at https://arxiv.org/pdf/gr-qc/0601043 (PDF, unfortunately):

Freeman Dyson has questioned whether any conceivable experiment in the real universe can detect a single graviton. If not, is it meaningful to talk about gravitons as physical entities? We attempt to answer Dyson’s question and find it is possible concoct an idealized thought experiment capable of detecting one graviton; however, when anything remotely resembling realistic physics is taken into account, detection becomes impossible, indicating that Dyson’s conjecture is very likely true. We also point out several mistakes in the literature dealing with graviton detection and production.

Edit: That said, the paper does address this. They cover a variety of QG theories and try to address the fundamental requirements any theory must meet.

As we do not have a fully consistent theory of quantum gravity, several different axiomatic systems have been proposed to model quantum gravity Witten:1985cc ; Ziaeepour:2021ubo ; Faizal2024 ; bombelli1987spacetime ; Majid:2017bul ; DAriano:2016njq ; Arsiwalla:2021eao . In all these programs, it is assumed a candidate theory of quantum gravity is encoded as a computational formal system

ℱQ​G={ℒQ​G,ΣQ​G,ℛalg}.

It's over my head, personally.