  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.
