Simulating Self-Gravitating Dark Matter with Variational Quantum Computing
By Abhinav Angirekula, Dhruv Anurag, Rohan Kompella
Galaxies have far too little observable matter for them to be gravitationally bound. Thus, there must be a theoretical, unobservable from of matter that makes up this missing mass: dark matter. Dark matter does not interact with light and we can only see its effects through gravitational lensing. The current leading candidates for dark matter are weakly interacting massive particles (WIMPs), primordial black holes, and axions. Accurate dark matter simulations are vital for researching their true nature, as scientists can compare simulations to their observations. If there are discrepancies between the two, there might be an undiscovered property or interaction that dark matter has. While dark matter simulation appears to be incredibly complicated, it really just boils down to time evolving a system using differential equations. In our case, the Schrödinger-Poisson equations are a system of non-linear differential equations that govern the evolution of several types of dark matter models: from fuzzy dark matter to standard cold dark matter. Mocz and Szasz were able to solve the Schrödinger-Poisson equations using a classical spectral method, and used a variational quantum algorithm outlined by Lubasch et. al. and were able to successfully model dark matter. However, instead of running their quantum algorithm on a quantum computer, they ran it on a simulation of a quantum computer on a classical machine. For our project, we want to replicate the results of Mocz and Szasz and implement both their classical and quantum algorithms. We want to run their quantum algorithm on an actual quantum computer (e.g. IBM), and the number of qubits used in it is under the maximum limit of quantum computers we could use so that we can compare the efficiency of each algorithm.
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