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arXiv · 2606.14806

Semiclassical Gravity Efficiently Solves $\mathsf{NP}$-Complete Problems

Matthew Fox·Chaitanya Karamchedu·Sotirios Mygdalas
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Abstract

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.

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Matthew Fox, Chaitanya Karamchedu, Sotirios Mygdalas. 2026-06-11. Semiclassical Gravity Efficiently Solves $\mathsf{NP}$-Complete Problems. https://arxiv.org/abs/2606.14806

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