Demonstration of minisuperspace quantum cosmology using quantum computational algorithms on IBM quantum computer

Abstract

Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. Quantum computational algorithms have the potential to be an exciting new way of studying quantum cosmology. In quantum cosmology, we learn about the dynamics of the universe without constructing a complete theory of quantum gravity. Since the universal wavefunction exists in an infinite-dimensional superspace over all possible 3D metrics and modes of matter configurations, we take minisuperspaces for our work by constraining the degrees of freedom to particular 3D metrics and uniform scalar field configurations. Here, we consider a wide variety of cosmological models. We begin by analyzing an anisotropic universe with cosmological constant and classical radiation. We then study the results for higher derivatives, Kaluza–Klein theories and string dilaton in quantum cosmology. We use IBM’s Quantum Information Science Kit (QISKit) python library and the Variational Quantum Eigensolver (VQE) algorithm for studying these systems. The VQE algorithm is a hybrid algorithm that uses the variational approach and interleaves quantum and classical computations in order to find the minimum eigenvalue of the Hamiltonian for a given system. The minimum eigenvalue of the Hamiltonian obtained will serve as a boundary condition for the given wavefuntion.