Quantum Cosmology on Quantum Computer

With physical quantum computers becoming increasingly accessible, research on their applications across various fields has advanced rapidly. In this paper, we present the first study of quantum cosmology conducted on physical quantum computers, employing a newly proposed Hybrid Quantum-Classical (HQC) algorithm rather than the commonly used Variational Quantum Eigensolver (VQE). Specifically, we solve a constrained Hamiltonian equation derived by quantizing the Friedmann equation in cosmology. To solve this constraint equation, H |psi> = 0, where H is a Hamiltonian operator and |psi> = |psi(theta)> is the wave function of phase angle theta describing the cosmic quantum state, we iteratively use the quantum computer to compute the eigenvalues of <psi | H | psi>, while a classical computer manages the underlying probability density function within the Probabilistic Bisection Algorithm (PBA) to update theta until the solution of <psi | H | psi> = 0 is achieved to a desired accuracy. Executing our algorithm on IBM's quantum computers, we attain a high-precision solution for theta, achieving approximately 1 percent error.