Spin Foam Vertex Amplitudes on Quantum Computer -- Preliminary Results

TL;DR

This paper explores the use of quantum algorithms to compute vertex amplitudes in spin foam models of quantum gravity, demonstrating preliminary results on IBM and QX quantum computers with comparisons to analytical predictions.

Contribution

It introduces a novel quantum algorithm approach for calculating vertex amplitudes in 3+1D quantum gravity models using quantum computers.

Findings

Successful computation of vertex amplitude probabilities on quantum simulators.

Comparison of quantum computer results with analytical predictions shows promising accuracy.

First demonstration of quantum algorithms applied to spin foam vertex amplitudes.

Abstract

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.