# Simulating 0+1 Dimensional Quantum Gravity on Quantum Computers: Mini-Superspace Quantum Cosmology and the World Line Approach in Quantum Field Theory

## TL;DR

This paper explores simulating 0+1 dimensional quantum gravity and quantum cosmology using quantum computers, demonstrating classical and quantum approaches to analyze the Universe's wave function and extending to quantum field theory methods.

## Contribution

It introduces a framework for simulating mini-superspace quantum cosmology on quantum computers, including the use of variational algorithms and potential extensions to quantum field theory.

## Key findings

- Classical analysis of Friedmann-Robertson-Walker mini-superspace models.
- Implementation of quantum simulations using IBM's Qiskit and variational quantum eigensolver.
- Potential extension of the framework to quantum field theory via the world line approach.

## Abstract

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.