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Open AccessArticle

Spin Foam Vertex Amplitudes on Quantum Computer—Preliminary Results

1
CPT, Aix-Marseille Université, Université de Toulon, CNRS, F-13288 Marseille, France
2
Institute of Physics, Jagiellonian University, ojasiewicza 11, 30-348 Cracow, Poland
Universe 2019, 5(8), 179; https://doi.org/10.3390/universe5080179
Received: 16 April 2019 / Revised: 22 July 2019 / Accepted: 24 July 2019 / Published: 26 July 2019
(This article belongs to the Special Issue Progress in Group Field Theory and Related Quantum Gravity Formalisms)
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. View Full-Text
Keywords: Spin networks; vertex amplitudes; quantum computing Spin networks; vertex amplitudes; quantum computing
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Mielczarek, J. Spin Foam Vertex Amplitudes on Quantum Computer—Preliminary Results. Universe 2019, 5, 179.

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