[2606.14806] Semiclassical Gravity Efficiently Solves $\mathsf{NP}$-Complete Problems

-->

General Relativity and Quantum Cosmology

arXiv:2606.14806 (gr-qc)

[Submitted on 11 Jun 2026]

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

Authors:Matthew Fox, Chaitanya Karamchedu, Sotirios Mygdalas<br>View a PDF of the paper titled Semiclassical Gravity Efficiently Solves $\mathsf{NP}$-Complete Problems, by Matthew Fox and Chaitanya Karamchedu and Sotirios Mygdalas

View PDF<br>HTML (experimental)

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.

Comments:<br>15 pages

Subjects:

General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Quantum Physics (quant-ph)

Cite as:<br>arXiv:2606.14806 [gr-qc]

(or<br>arXiv:2606.14806v1 [gr-qc] for this version)

https://doi.org/10.48550/arXiv.2606.14806

Focus to learn more

arXiv-issued DOI via DataCite (pending registration)

Submission history<br>From: Matthew Fox [view email]<br>[v1]<br>Thu, 11 Jun 2026 23:42:07 UTC (17 KB)

Full-text links:<br>Access Paper:

View a PDF of the paper titled Semiclassical Gravity Efficiently Solves $\mathsf{NP}$-Complete Problems, by Matthew Fox and Chaitanya Karamchedu and Sotirios Mygdalas<br>View PDF<br>HTML (experimental)<br>TeX Source

view license

Current browse context:

gr-qc

next >

new<br>recent<br>| 2026-06

Change to browse by:

hep-th<br>quant-ph

References & Citations

INSPIRE HEP

NASA ADS<br>Google Scholar

Semantic Scholar

export BibTeX citation<br>Loading...

BibTeX formatted citation

&times;

loading...

Data provided by:

Bookmark

Bibliographic Tools

Bibliographic and Citation Tools

Bibliographic Explorer Toggle

Bibliographic Explorer (What is the Explorer?)

Connected Papers Toggle

Connected Papers (What is Connected Papers?)

Litmaps Toggle

Litmaps (What is Litmaps?)

scite.ai Toggle

scite Smart Citations (What are Smart Citations?)

Code, Data, Media

Code, Data and Media Associated with this Article

alphaXiv Toggle

alphaXiv (What is alphaXiv?)

Links to Code Toggle

CatalyzeX Code Finder for Papers (What is CatalyzeX?)

DagsHub Toggle

DagsHub (What is DagsHub?)

GotitPub Toggle

Gotit.pub (What is GotitPub?)

Huggingface Toggle

Hugging Face (What is Huggingface?)

ScienceCast Toggle

ScienceCast (What is ScienceCast?)

Demos

Demos

Replicate Toggle

Replicate (What is Replicate?)

Spaces Toggle

Hugging Face Spaces (What is Spaces?)

Spaces Toggle

TXYZ.AI (What is TXYZ.AI?)

Related Papers

Recommenders and Search Tools

Link to Influence Flower

Influence Flower (What are Influence Flowers?)

Core recommender toggle

CORE Recommender (What is CORE?)

IArxiv recommender toggle

IArxiv Recommender<br>(What is IArxiv?)

Author

Venue

Institution

Topic

About arXivLabs

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .

Which authors of this paper are endorsers? |<br>Disable MathJax (What is MathJax?)