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arXiv:2003.13124 · Physical review. D/Physical review. D.

Quantum simulations of a qubit of space

Grzegorz Czelusta, Jakub Mielczarek A B

Published Feb 2, 2021• 17 citations
arXivHTMLPDF

Abstract

In loop quantum gravity approach to Planck scale physics, quantum geometry is represented by superposition of the so-called spin network states. In the recent literature, a class of spin networks promising from the perspective of quantum simulations of quantum gravitational systems has been studied. In this case, the spin network states are represented by graphs with four-valent nodes, and two dimensional intertwiner Hilbert spaces (qubits of space) attached to them. In this article, construction of quantum circuits for a general intertwiner qubit is presented. The obtained circuits are simulated on 5-qubit (Yorktown) and 15-qubit (Melbourne) IBM superconducting quantum computers, giving satisfactory fidelities. The circuits provide building blocks for quantum simulations of complex spin networks in the future. Furthermore, a class of maximally entangled states of spin networks is introduced. As an example of application, attempts to determine transition amplitudes for a monopole and a dipole spin network with the use of superconducting quantum processor are made.

DOI
10.1103/physrevd.103.046001

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In loop quantum gravity approach to Planck scale physics, quantum geometry is represented by superposition of the so-called spin network states. In the recent literature, a class of spin networks promising from the perspective of quantum simulations of quantum gravitational systems has been studied. In this case, the spin network states are represented by graphs with four-valent nodes, and two dimensional intertwiner Hilbert spaces (qubits of space) attached to them. In this article, construction of quantum circuits for a general intertwiner qubit is presented. The obtained circuits are simulated on 5-qubit (Yorktown) and 15-qubit (Melbourne) IBM superconducting quantum computers, giving satisfactory fidelities. The circuits provide building blocks for quantum simulations of complex spin networks in the future. Furthermore, a class of maximally entangled states of spin networks is introduced. As an example of application, attempts to determine transition amplitudes for a monopole and a dipole spin network with the use of superconducting quantum processor are made.
Spin network states are a powerful tool for constructing the SU(2)SU(2)SU(2) gauge theories on a graph. In loop quantum gravity (LQG), they have yielded many promising predictions, although progress has been limited by the computational challenge of dealing with high-dimensional Hilbert spaces. To explore more general configurations, quantum computing methods can be applied by representing spin network states as quantum circuits. In this article, we introduce an improved method for constructing quantum circuits for 4-valent Ising spin networks, which utilizes a smaller number of qubits than previous approaches. This has practical implications for the implementation of quantum circuits. We also demonstrate the procedure with various examples, including the construction of a 10-node Ising spin network state. The key ingredient of the method is the variational transfer of partial states, which we illustrate through numerous examples. Our improved construction provides a promising avenue for further exploring the potential of quantum computing methods in quantum gravity research.
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.
The article addresses the possibility of implementing spin network states, used in the loop quantum gravity approach to Planck scale physics on an adiabatic quantum computer. The discussion focuses on applying currently available technologies and analyzes a concrete example of a D-Wave machine. It is introduced a class of simple spin network states which can be implemented on the Chimera graph architecture of the D-Wave quantum processor. However, extension beyond the currently available quantum processor topologies is required to simulate more sophisticated spin network states. This may inspire new generations of adiabatic quantum computers. A possibility of simulating loop quantum gravity is discussed, and a method of solving a graph non-changing scalar (Hamiltonian) constraint with the use of adiabatic quantum computations is proposed. The presented results establish a basis for the future simulations of Planck scale physics, specifically quantum cosmological configurations, on quantum annealers.
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 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.