Quantum Computing for Inflationary, Dark Energy and Dark Matter Cosmology

TL;DR

This paper explores the application of quantum computing to cosmology, demonstrating how quantum algorithms can simulate models of dark energy, dark matter, and inflation, with promising results and potential for scaling beyond classical methods.

Contribution

It introduces quantum computing methods, specifically VQE and EOH algorithms, to solve cosmological equations like the Wheeler-DeWitt equation, showing promising accuracy and scalability.

Findings

Quantum algorithms match classical results in cosmological models.

Quantum computing shows potential for scaling to larger, more complex problems.

Demonstrated implementation using IBM QISKit framework.

Abstract

Cosmology is in an era of rapid discovery especially in areas related to dark energy, dark matter and inflation. Quantum cosmology treats the cosmology quantum mechanically and is important when quantum effects need to be accounted for, especially in the very early Universe. Quantum computing is an emerging new method of computing which excels in simulating quantum systems. Quantum computing may have some advantages when simulating quantum cosmology, especially because the Euclidean action of gravity is unbounded from below, making the implementation of Monte Carlo simulation problematic. In this paper we present several examples of the application of quantum computing to cosmology. These include a dark energy model that is related to Kaluza-Klein theory, dark matter models where the dark sector is described by a self interacting gauge field or a conformal scalar field and an inflationary model with a slow roll potential. We implement quantum computations in the IBM QISKit software framework and show how to apply the Variational Quantum Eigensolver (VQE) and Evolution of Hamiltonian (EOH) algorithms to solve the Wheeler-DeWitt equation that can be used to describe the cosmology in the mini-superspace approximation. We find excellent agreement with classical computing results and describe the accuracy of the different quantum algorithms. Finally we discuss how these methods can be scaled to larger problems going beyond the mini-superspace approximation where the quantum computer may exceed the performance of classical computation.