On Optimizing Quantum Cosmological Simulations of Self-Gravitating Dark Matter
By David Cao, Ronit Kapur, Rishabh Prabhu
Today, visible matter makes up less than 5% of the total mass in the universe. The rest of the mass can be largely attributed to an invisible matter known as dark matter. Although dark matter is invisible, it is integral to the structure of the universe, as galaxies, clusters, and other deep sky objects are primarily composed of dark matter. Because dark matter is so important to understanding the inner workings of the universe, it is essential to be able to model it. Traditional classical simulations struggle to do this, as modeling dark matter requires extensive computational time and space—it requires approximating solutions to the nonlinear differential equations that describe dark matter dynamics. These differential equations—the Vlasov-Poisson (VP) equations—have been formulated to approximate the time evolution of self-gravitating dark matter.. Previous studies find that, in the cases of cold dark matter and general self-gravitating dark matter respectively, the VP equations can be approximated by the Schrödinger-Poisson (SP) equations. Not only are the SP equations more applicable to quantum simulations—as they directly evolve a wave function—but they also exhibit smoother solutions without discontinuities or singularities. We apply a hybrid classical-quantum algorithm, specifically variational quantum computing (VQC), an approach analogous to machine learning. In doing so, one addresses the computing limitations of purely classically simulating dark matter. We build on previous work by simulating cosmological dark matter in 2D space and account for the exponential build-up of error over compounding time intervals.