Quantum Computing of Schwarzschild-de Sitter Black Holes and Kantowski-Sachs Cosmology

Abstract

The quantum mechanics of Schwarzschild-de Sitter black holes is of great recent interest because of their peculiar thermodynamic properties as well as their realization in modern dark energy cosmology which indicates the presence of a small positive cosmological constant. We study Schwarzschild-de Sitter black holes and also the Kantowki-Sachs Cosmology using quantum computing. In these cases in addition to the Hamiltonian there is a Mass operator which plays an important role in describing the quantum states of the black hole and Kantowski-Sachs cosmology. We compute the spectrum of these operators using classical and quantum computing. For quantum computing we use the Variational Quantum Eigensolver which is hybrid classical-quantum algorithm that runs on near term quantum hardware. We perform our calculations using 4, 6 and 8 qubits in a harmonic oscillator basis, realizing the quantum operators of the Schwarzschild-de Sitter black hole and Kantowski-Sachs cosmology in terms of 16 × 16, 64 × 64 and 256 × 256 matrices respectively. For the 4 qubit case we find highly accurate results but for the other cases we find a more refined variational ansatz will be necessary to accurately represent the quantum states of a Schwarzschild-de Sitter black hole or Kantowki-Sachs cosmology accurately on a quantum computer.