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.
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