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

TL;DR

This paper explores the quantum properties of Schwarzschild-de Sitter black holes and Kantowski-Sachs cosmology using variational quantum algorithms on near-term quantum hardware, computing spectra with different qubit counts.

Contribution

It introduces a quantum computing approach to analyze these cosmological models, employing the Variational Quantum Eigensolver to compute operator spectra.

Findings

Highly accurate results for 4 qubits

Need for refined variational ansatz for larger qubit systems

Successful implementation on near-term quantum hardware

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 x 16, 64 x 64 and 256 x 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 represent the quantum states of a Schwarzschild-de Sitter black hole or Kantowki-Sachs cosmology accurately on a quantum computer.