Non-perturbative lattice QCD calculations at non vanishing
baryon number density are hampered by the QCD sign problem. The path
integral, that in lattice QCD is calculated numerically, becomes
highly oscillating. One possible solution is the Lefschetz thimble
approach. It requires a deformation of the original integration
domain into a manifold embedded in complex space. For properly
chosen integration manifolds (``thimbles'') the sign problem is
drastically alleviated. For some bosonic and fermionic models this
approach has been shown to work. Here we apply the thimble
disretization to (0+1)-dimensional QCD with standard staggerd
quarks and disscuss issues that may arrise in higher dimensions.