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Astrophysics

Semiclassical Gravity Efficiently Solves -Complete Problems

Matthew Fox, Chaitanya Karamchedu, Sotirios Mygdalas

Featured June 17, 2026

Original Paper

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Simply

Semiclassical gravity's special non-linear effects could let a quantum particle solve super-hard computer problems super fast, which suggests gravity itself must be quantum to avoid this paradox.

In depth
The paper demonstrates that if gravity is described by semiclassical Einstein field equations, its weak-field dynamics introduce non-linearities into quantum mechanics. These non-linear dynamics can be exploited to efficiently solve NP-complete problems in polynomial time, a feat believed impossible for any physical system, thereby violating the Physical Extended Church–Turing Thesis and suggesting gravity must be quantum.

Key Takeaways

  • 1
    The weak-field limit of semiclassical gravity, described by the Schrödinger-Newton equation, introduces non-linear dynamics for massive quantum particles due to gravitational self-interaction.
  • 2
    This non-linearity enables an exponential 'stretching' of distances between quantum states on the manifold of pure states, allowing for efficient state discrimination between exponentially close states.
  • 3
    By iteratively applying this non-linear evolution, the authors show that NP-complete problems can be solved in polynomial time, which challenges the Physical Extended Church–Turing Thesis and provides an argument for the quantization of gravity.

Conceptual Flow

HIGH LEVEL
1
Methodology: How Semiclassical Gravity Solves Hard Problems

The paper shows how the non-linear nature of gravity, when treated semiclassically, can be used to quickly separate very similar quantum states, which helps solve difficult computational problems.

Hard Problem
Encode as Qubit State
Semiclassical Gravity Dynamics
States Magnified
Problem Solved
2
Results: Implication for Quantum Gravity

Because semiclassical gravity can solve problems thought to be impossible for physical systems, the authors argue this means gravity must actually be quantum, not classical.

Semiclassical Gravity
Solves NP-Complete Problems
Violates Physical Limits
Gravity Must Be Quantum