Spin Foam Vertex Amplitudes on Quantum Computer -- Preliminary Results
Vertex amplitudes are elementary contributions to the transition amplitudes
in the spin foam models of quantum gravity. The purpose of this article is 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 \emph{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
\emph{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.
Jakub Mielczarek