  One of the central difficulties in the quantization of the gravitational
interactions is that they are described by a set of constraints. The standard
strategy for dealing with the problem is the Dirac quantization procedure,
which leads to the Wheeler-DeWitt equation. However, solutions to the equation
are known only for specific symmetry-reduced systems, including models of
quantum cosmology. Novel methods, which enable solving the equation for complex
gravitational configurations are, therefore, worth seeking.
  Here, we propose and investigate a new method of solving the Wheeler-DeWitt
equation, which employs a variational quantum computing approach, and is
possible to implement on quantum computers. For this purpose, the gravitational
system is regularized, by performing spherical compactification of the phase
space. This makes the system's Hilbert space finite-dimensional and allows to
use $SU(2)$ variables, which are easy to handle in quantum computing. The
validity of the method is examined in the case of the flat de Sitter universe.
For the purpose of testing the method, both an emulator of a quantum computer
and the IBM superconducting quantum computer have been used. The advantages and
limitations of the approach are discussed.
