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arXiv:2407.19036 · Physical review. D/Physical review. D.

Generative flow networks in covariant loop quantum gravity

Joseph Raphael R. Bunao, Pietropaolo Frisoni, Athanasios Kogios, Jared Wogan

Published Aug 29, 2025• 0 citations
arXivHTMLPDF

Abstract

Spin foams arose as the covariant (path integral) formulation of quantum gravity depicting transition amplitudes between different quantum geometry states. As such, they provide a scheme to study the no-boundary proposal, specifically the nothing to something transition, and compute relevant observables using high-performance computing. Following recent advances, where stochastic algorithms (Markov chain Monte Carlo) were used, we employ ``generative flow networks,'' a newly developed machine-learning algorithm to compute the expectation value of the dihedral angle for a 4-simplex and compare the results with previous works.

DOI
10.1103/pvqh-3t24

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Spin foams arose as the covariant (path integral) formulation of quantum gravity depicting transition amplitudes between different quantum geometry states. As such, they provide a scheme to study the no-boundary proposal, specifically the nothing to something transition, and compute relevant observables using high-performance computing. Following recent advances, where stochastic algorithms (Markov chain Monte Carlo) were used, we employ ``generative flow networks,'' a newly developed machine-learning algorithm to compute the expectation value of the dihedral angle for a 4-simplex and compare the results with previous works.
Vertex amplitudes are elementary contributions to the transition amplitudes in the spin foam models of quantum gravity. The purpose of this article is to make the first step towards computing vertex amplitudes with the use of quantum algorithms. In our studies we are focused on a vertex amplitude of 3+1 D gravity, associated with a pentagram spin network. Furthermore, all spin labels of the spin network are assumed to be equal j = 1 / 2 , which is crucial for the introduction of the intertwiner qubits. A procedure of determining modulus squares of vertex amplitudes on universal quantum computers is proposed. Utility of the approach is tested with the use of: IBM’s ibmqx4 5-qubit quantum computer, simulator of quantum computer provided by the same company and QX quantum computer simulator. Finally, values of the vertex probability are determined employing both the QX and the IBM simulators with 20-qubit quantum register and compared with analytical predictions.
Loop quantum gravity (LQG) attempts to unify general relativity with quantum physics to offer a complete description of the universe by quantising spacetime geometry, but the numerical calculations we encounter are extraordinarily difficult. Progress has been made in the covariant formulation of LQG, but the tools do not carry over to the canonical formulation. These tools are graphical by nature, describing space with spin networks to make calculations in LQG more intuitive to the human hand. Recently, a new notation for working with spin networks has been used by arXiv:2412.20272 to offer the first accurate numerical results in canonical LQG by allowing the underlying graphs to change throughout the calculation, though they are forced to concede visual intuitiveness. In this thesis, we offer a more radical rephrasing of spin network calculations by translating them into the finite-dimensional ZX-calculus, extending previous attempts to translate into the standard (qubit) ZX-calculus (arXiv:2111.03114). Specifically, we derive the mixed-dimensional ZX-diagrams representing the generating objects of spin networks and the rules for the Penrose Spin Calculus (arXiv:2511.06012), and use these to present the ZX-form and correctness of "loop removal". We also derive the forms for several fundamental LQG objects in the finite-dimensional ZX-calculus for the first time. This gives us a high-level, intuitive graphical language that retains a flexibility to handle changing graph structures, and thus we argue positions the PSC as the new definitive language for canonical LQG. Furthermore, we investigate the possibility for a matrix-like normal form for spin networks deriving from a novel perspective of the PSC in terms of W-nodes.
Quantum computers are an increasingly hopeful means for understanding large quantum many-body systems bearing high computational complexity. Such systems exhibit complex evolutions of quantum states, and are prevailing in fundamental physics, e.g., quantum gravity. Computing the transition amplitudes between different quantum states by quantum computers is one of the promising ways to solve such computational complexity problems. In this work, we apply a 10-qubit superconducting quantum processor, where the all-to-all circuit connectivity enables a many-body entangling gate that is highly efficient for state generation, to studying the transition amplitudes in loop quantum gravity. With the device metrics such as qubit coherence, control accuracy, and integration level being continuously improved, superconducting quantum processors are expected to outperform their classical counterparts in handling many-body dynamics and may lead to a deeper understanding of quantum gravity.
Abstract In quantum theory, the expectation value of an observable can be represented as a path integral. In general, it cannot be computed analytically. There are various approximate methods of lattice calculations, for example, the Monte Carlo method. Currently, an approach to solving this problem using neural networks is being developed. In our research, we calculated path integrals in several models of relativistic quantum mechanics using the normalizing flows algorithm. For fast calculations with high accuracy, this algorithm was used in conjunction with the Markov chain generation method.
Abstract In the canonical approach of loop quantum gravity, arguably the most important outstanding problem is finding and interpreting solutions to the Hamiltonian constraint. In this work, we demonstrate that methods of machine learning are in principle applicable to this problem. We consider U(1) BF theory in three dimensions, quantised with loop quantum gravity methods. In particular, we formulate a master constraint corresponding to Hamilton and Gauß constraints using loop quantum gravity methods. To make the problem amenable for numerical simulation we fix a graph and introduce a cutoff on the kinematical degrees of freedom, effectively considering U q ( 1 ) BF theory at a root of unity. We show that the neural network quantum state ansatz can be used to numerically solve the constraints efficiently and accurately. We compute expectation values and fluctuations of certain observables and compare them with exact results or exact numerical methods where possible. We also study the dependence on the cutoff.