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1. Experimental simulation of loop quantum gravity on a photonic chip

   https://doi.org/10.1038/s41534-023-00702-y  

   van der Meer, Reinier; Huang, Zichang; Anguita, Malaquias Correa; Qu, Dongxue; Hooijschuur, Peter; Liu, Hongguang; Han, Muxin; Renema, Jelmer J.; Cohen, Lior (December 2023, npj Quantum Information)

   Abstract The unification of general relativity and quantum theory is one of the fascinating problems of modern physics. One leading solution is Loop Quantum Gravity (LQG). Simulating LQG may be important for providing predictions which can then be tested experimentally. However, such complex quantum simulations cannot run efficiently on classical computers, and quantum computers or simulators are needed. Here, we experimentally demonstrate quantum simulations of spinfoam amplitudes of LQG on an integrated photonics quantum processor. We simulate a basic transition of LQG and show that the derived spinfoam vertex amplitude falls within 4% error with respect to the theoretical prediction, despite experimental imperfections. We also discuss how to generalize the simulation for more complex transitions, in realistic experimental conditions, which will eventually lead to a quantum advantage demonstration as well as expand the toolbox to investigate LQG. 

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2. Key Issues Review: A short review of loop quantum gravity

   https://doi.org/https://doi.org/10.1088/1361-6633/abed91  

   Ashtekar, A; Bianchi, E. (January 2021, Reports on progress in physics)

   An outstanding open issue in our quest for physics beyond Einstein is the unification of general relativity (GR) and quantum physics. Loop quantum gravity (LQG) is a leading approach toward this goal. At its heart is the central lesson of GR: gravity is a manifestation of spacetime geometry. Thus, the approach emphasizes the quantum nature of geometry and focuses on its implications in extreme regimes—near the big bang and inside black holes—where Einstein’s smooth continuum breaks down.We present a brief overview of the main ideas underlying LQG and highlight a few recent advances. This report is addressed to non-experts. 

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3. Harmonic balls in Liouville quantum gravity

   https://doi.org/10.1112/plms.70018  

   Bou‐Rabee, Ahmed; Gwynne, Ewain (January 2025, Proceedings of the London Mathematical Society)

   Abstract Harmonic balls are domains that satisfy the mean‐value property for harmonic functions. We establish the existence and uniqueness of harmonic balls on Liouville quantum gravity (LQG) surfaces using the obstacle problem formulation of Hele–Shaw flow. We show that LQG harmonic balls are neither Lipschitz domains nor LQG metric balls, and that the boundaries of their complementary connected components are Jordan curves. We conjecture that LQG harmonic balls are the scaling limit of internal diffusion limited aggregation on random planar maps. In a companion paper, we prove this in the special case of mated‐CRT maps. 

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4. Integrability of SLE via conformal welding of random surfaces

   https://doi.org/10.1002/cpa.22180  

   Ang, Morris; Holden, Nina; Sun, Xin (May 2024, Communications on Pure and Applied Mathematics)

   Abstract We demonstrate how to obtain integrability results for the Schramm‐Loewner evolution (SLE) from Liouville conformal field theory (LCFT) and the mating‐of‐trees framework for Liouville quantum gravity (LQG). In particular, we prove an exact formula for the law of a conformal derivative of a classical variant of SLE called . Our proof is built on two connections between SLE, LCFT, and mating‐of‐trees. Firstly, LCFT and mating‐of‐trees provide equivalent but complementary methods to describe natural random surfaces in LQG. Using a novel tool that we call theuniform embeddingof an LQG surface, we extend earlier equivalence results by allowing fewer marked points and more generic singularities. Secondly, the conformal welding of these random surfaces produces SLE curves as their interfaces. In particular, we rely on the conformal welding results proved in our companion paper Ang, Holden and Sun (2023). Our paper is an essential part of a program proving integrability results for SLE, LCFT, and mating‐of‐trees based on these two connections. 

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5. Gaussian curvature on random planar maps and Liouville quantum gravity

   https://doi.org/10.1007/s00440-025-01430-4  

   Hip, Andres_A Contreras; Gwynne, Ewain (April 2026, Probability Theory and Related Fields)

   Abstract We investigate the notion of curvature in the context of Liouville quantum gravity (LQG) surfaces. We define the Gaussian curvature for LQG, which we conjecture is the scaling limit of discrete curvature on random planar maps. Motivated by this, we study asymptotics for the discrete curvature of$$\epsilon $$ $ϵ$ -mated CRT maps. More precisely, we prove that the discrete curvature integrated against a$$C_c^2$$ $C_c^2$ test function is of order$$\epsilon ^{o(1)},$$ ${ϵ}^{o\left(1\right)},$ which is consistent with our scaling limit conjecture. On the other hand, we prove the total discrete curvature on a fixed space-filling SLE segment scaled by$$\epsilon ^{\frac{1}{4}}$$ ${ϵ}^{\frac{1}{4}}$ converges in distribution to an explicit random variable. 

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