  The collisionless Boltzmann equation (CBE) is a fundamental equation that
governs the dynamics of a broad range of astrophysical systems from space
plasma to star clusters and galaxies. It is computationally expensive to
integrate the CBE directly in a multi-dimensional phase space, and thus the
applications to realistic astrophysical problems have been limited so far.
Recently, Todorova & Steijl (2020) proposed an efficient quantum algorithm to
solve the CBE with significantly reduced computational complexity. We extend
the algorithm to perform quantum simulations of self-gravitating systems,
incorporating the method to calculate gravity with the major Fourier modes of
the density distribution extracted from the solution-encoding quantum state.
Our method improves the dependency of time and space complexities on Nv , the
number of grid points in each velocity coordinate, compared to the classical
simulation methods. We then conduct some numerical demonstrations of our
method. We first run a 1+1 dimensional test calculation of free streaming
motion on 64*64 grids using 13 simulated qubits and validate our method. We
then perform simulations of Jeans collapse, and compare the result with
analytic and linear theory calculations. It will thus allow us to perform
large-scale CBE simulations on future quantum computers.
