  We report on our non-perturbative investigations of supersymmetric Yang-Mills
quantum mechanics with 4 supercharges. We employ two independent numerical
methods. First of them is the cut Fock space method whose numerical
implementation was recently generalized to include the SU(N) gauge group. It
allowed us to calculate for the first time the spectrum of the model with SU(3)
symmetry in all fermionic sectors. Independently, we implemented the Rational
Hybrid Monte Carlo algorithm and reproduced the accessible part of the
low-energy spectrum of the model with SU(2) gauge symmetry. We argue that by
simulating at imaginary chemical potential one can get access to observables
defined in sectors of Hilbert space with a given quark number.
