Gravity: Classical or Quantum? express
Gravity seems simple: it keeps us on the ground and makes planets orbit. But if it were classical (described by Einstein's equations as the curvature of spacetime, while all matter follows the quantum laws of the Standard Model) then an ordinary quantum bit (qubit) falling freely would solve unsolvable problems. It turns out gravity influences the qubit so that its trajectory becomes a computation. It's like a marble rolling through a bumpy labyrinth and finding the shortest path, and that path turns out to be the answer. Problems like perfectly packing a suitcase are beyond even supercomputers.
But there's a fundamental principle: nothing physical can compute faster than an ordinary computer. If gravity were classical, a falling qubit would break that rule. Since we don't witness such magic in reality, gravity must be quantum. So it's not physics but computation theory that demands quantum gravity — an unexpected twist. Hawking, Penrose, and Wheeler grappled with this: without quantum gravity, we can't understand black holes or the birth of the Universe.
Original abstract
as written by the authors arXiv:2606.14806
Assuming the gravitational field is classical and that it couples to quantum fields via the semiclassical Einstein field equations, we show that the weak-field dynamics of a massive and non-relativistic qubit can in principle be used to solve an $$\mathsf{NP}$$-complete problem in polynomial time. We attribute this vast computational power to the non-linear dynamics afforded by the semiclassical Einstein field equations. Consequently, the above two assumptions entail a violation of the Physical Extended Church--Turing Thesis, which we regard as evidence for the quantization of gravity.
A qubit is a quantum bit that can be 0 and 1 at the same time. However, in this scenario, quantum speedup alone isn't enough: you need gravity to be tricky.