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arXiv:2207.00557 · npj Quantum Information

Experimental simulation of loop quantum gravity on a photonic chip

Reinier van der Meer, Zichang Huang, Malaquias Correa Anguita, Dongxue Qu, Peter Hooijschuur, Hongguang Liu, Muxin Han, Jelmer J. Renema, Lior Cohen

Published Apr 4, 2023• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/s41534-023-00702-y

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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.
The problem of simulating complex quantum processes on classical computers gave rise to the field of quantum simulations. Quantum simulators solve problems, such as Boson sampling, where classical counterparts fail. In another field of physics, the unification of general relativity and quantum theory is one of the greatest challenges of our time. One leading approach is Loop Quantum Gravity (LQG). Here, we connect these two fields and design a linear-optical simulator such that the evolution of the optical quantum gates simulates the spinfoam amplitudes of LQG. It has been shown that computing transition amplitudes in simple quantum field theories falls into the class BQP -- which strongly suggests that computing transition amplitudes of LQG are classically intractable. Therefore, these amplitudes are efficiently computable with universal quantum computers which are, alas, possibly decades away. We propose here an alternative special-purpose linear-optical quantum computer, which can be implemented using current technologies. This machine is capable of efficiently computing these quantities. This work opens a new way to relate quantum gravity to quantum information and will expand our understanding of the theory.
The problem of simulating complex quantum processes on classical computers gave rise to the field of quantum simulations. Quantum simulators solve problems, such as boson sampling, where classical counterparts fail. In another field of physics, the unification of general relativity and quantum theory is one of the greatest challenges of our time. One leading approach is loop quantum gravity (LQG). Here, we connect these two fields and design a linear-optical simulator such that the evolution of the optical quantum gates simulates the spin-foam amplitudes of LQG. It has been shown that computing transition amplitudes in simple quantum field theories falls into the bounded-error quantum polynomial time class, which strongly suggests that computing transition amplitudes of LQG are classically intractable. Therefore, these amplitudes are efficiently computable with universal quantum computers, which are, alas, possibly decades away. We propose here an alternative special-purpose linear-optical quantum computer that can be implemented using current technologies. This machine is capable of efficiently computing these quantities. This work opens a new way to relate quantum gravity to quantum information and will expand our understanding of the theory.
Abstract Quantum simulation has shown its irreplaceable role in many fields, where it is difficult for classical computers to do much. On a four-qubit Nuclear Magnetic Resonance (NMR) quantum simulator, we experimentally simulate the spin-network states by simulating quantum spacetime tetrahedra. The fidelities of our experimentally prepared quantum tetrahedra are all above 95%. We then use the quantum tetradedra prepared by the Nuclear Magnetic Resonance to simulate a spinfoam vertex amplitude, which displays the local dynamics of quantum spacetime. By measuring the geometric properties on the corresponding quantum tetrahedra and simulating their interaction, our experiment serves as a basic module that represents the Feynman diagram vertex in the spinfoam formulation of Loop Quantum Gravity(LQG). This is an initial attempt to study LQG by quantum information processing.
Loop Quantum Gravity (LQG) is one of the leading approaches to unify quantum physics and General Relativity (GR). The Hilbert space of LQG is spanned by spin-networks which describe the local geometry of quantum space-time. Simulation of LQG spin-network states and their dynamics is classically intractable and is widely believed to fall in the Bounded Quantum Polynomial (BQP) time complexity class. There have been many recent attempts to simulate these states using novel and off the shelf quantum computing technologies. In this article, we review three such efforts which utilize superconducting qubits, linear optical qubits and Nuclear Magnetic Resonance (NMR) qubits respectively. The articles chosen for this review represent state of the art in quantum simulations of LQG.
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.