Quantum Gravity Simulation: Quantum simulation with a minimum length based on the generalised uncertainty principle

Quantum Physics arXiv:2607.19602 (quant-ph) [Submitted on 21 Jul 2026] Title:Quantum Gravity Simulation: Quantum simulation with a minimum length based on the generalised uncertainty principle Authors:Jack Keable-Elliott, David J. Bacon, Andrew Burbanks, Jaewoo Joo View a PDF of the paper titled Quantum Gravity Simulation: Quantum simulation with a minimum length based on the generalised uncertainty principle, by Jack Keable-Elliott and 3 other authors View PDF HTML (experimental) Abstract:We present a recipe for simulating one-dimensional quantum systems for low and high energies with $L$ qubits within the framework of first quantisation. Assuming a minimum grid spacing $\Delta L$ in the finite-difference method, the generalised uncertainty principle (GUP) is derived analytically and shows distinct properties for low- and high-energy quantum systems. In the low-energy regime, the GUP approaches to the standard Heisenberg uncertainty principle (HUP) for $ \Delta L \ll \hbar$. However, for finite $\Delta L \neq 0$, the GUP mathematically provides three different regions dependent on the average momentum and suggests that a wavefunction can exhibit a single-point localisation at the finite momentum uncertainty due to lack of grid resolution. We then derive a new expression for the high-energy momentum and focus on two specific cases relevant to relativistic aspects. First, if the HUP is relaxed and the high-energy momentum is matched to the special-relativistic one, the resulting GUP predicts the existence of a minimum length with non-zero mass for high energy despite the continuous limit $\Delta L = 0$. Second, enforcing consistency with the HUP allows the recovery of a canonical high-energy representation with no minimum length. But this requirement brings incompatibility with the special-relativistic momentum and suggests a modified energy-momentum equation. Therefore, we believe that the proposed momentum formulation provides a novel pathway to investigate quantum gravity phenomena for high energy using quantum simulation tools. Subjects: Quantum Physics (quant-ph); General Relativity and Quantum Cosmology (gr-qc) Cite as: arXiv:2607.19602 [quant-ph] (or arXiv:2607.19602v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.19602 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jaewoo Joo [view email] [v1] Tue, 21 Jul 2026 22:05:21 UTC (369 KB) Full-text links: Access Paper: View a PDF of the paper titled Quantum Gravity Simulation: Quantum simulation with a minimum length based on the generalised uncertainty principle, by Jack Keable-Elliott and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-07 Change to browse by: gr-qc References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × 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?) 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? | Disable MathJax (What is MathJax?)