  Quantum computers are a promising candidate to radically expand computational
science through increased computing power and more effective algorithms. In
particular quantum computing could have a tremendous impact in the field of
quantum cosmology. The goal of quantum cosmology is to describe the evolution
of the Universe through the Wheeler-DeWitt equation or path integral methods
without having to first formulate a full theory of quantum gravity. The quantum
computer provides an advantage in this endeavor because it can perform path
integrals in Lorentzian space and does not require constructing contour
integrations in Euclidean gravity. Also quantum computers can provide
advantages in systems with fermions which are difficult to analyze on classical
computers. In this study, we first employed classical computational methods to
analyze a Friedmann-Robertson-Walker mini-superspace with a scalar field and
visualize the calculated wave function of the Universe for a variety of
different values of the spatial curvature and cosmological constant. We them
used IBM's Quantum Information Science Kit Python library and the variational
quantum eigensolver to study the same systems on a quantum computer. The
framework can also be extended to the world line approach to quantum field
theory.
