Paper Argues Semiclassical Gravity Could Enable NP-Complete Problem Solving, Suggesting Gravity Must Be Quantized
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[Submitted on 11 Jun 2026]
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Summary
This paper argues that if gravity is classical and couples to quantum fields via semiclassical Einstein field equations, then the weak-field dynamics of a massive, non-relativistic qubit could solve NP-complete problems in polynomial time. The authors attribute this computational power to the non-linear dynamics of semiclassical gravity. They conclude that these assumptions violate the Physical Extended Church-Turing Thesis, which they interpret as evidence that gravity must be quantized.
Key quotes
· 3 pulledAssuming 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 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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