  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.
