Researcher Matthew Fox argues that semiclassical gravity could solve NP-complete problems in polynomial time. The theory assumes a classical gravitational field coupling to quantum fields through semiclassical Einstein field equations. This setup allows a massive, non-relativistic qubit to perform calculations that are typically impossible for standard computers.

Computational power comes from the non-linear dynamics found in these field equations. This theoretical ability to solve complex problems quickly directly violates the Physical Extended Church-Turing Thesis. Most physicists believe this thesis holds true for any physical system, making this theoretical discovery a contradiction of established computational laws.

Fox uses this contradiction to argue that gravity must be quantized. Since the semiclassical model leads to an unrealistic computational efficiency, the initial assumptions about a classical gravitational field are likely wrong. This finding suggests that quantization of gravity is the only way to avoid these impossible computational shortcuts.