  In this paper we investigate spectral stability of traveling wave solutions
to 1-$D$ quantum hydrodynamics system with nonlinear viscosity in the
$(\rho,u)$, that is, density and velocity, variables. We derive a sufficient
condition for the stability of the essential spectrum and we estimate the
maximum modulus of eigenvalues with non-negative real part. In addition, we
present numerical computations of the Evans function in sufficiently large
domain of the unstable half-plane and show numerically that its winding number
is (approximately) zero, thus giving a numerical evidence of point spectrum
stability.
