We study the final stages of the evolution of a binary system consisted of a black hole and a white dwarf star. We implement the quantum hydrodynamic equations and carry out numerical simulations. As a model of a white dwarf star we consider a zero temperature droplet of attractively interacting degenerate atomic bosons and spin-polarized atomic fermions. Such mixtures are investigated experimentally nowadays. We find that the white dwarf star is stripped off its mass while passing the periastron. Due to nonlinear effects, the accretion disk originated from the white dwarf becomes fragmented and the onset of a quantum turbulence with giant quantized vortices present in the bosonic component of the accretion disk is observed. The binary system ends its life in a spectacular way, revealing quantum features underlying the white dwarf star's structure. We find a charged mass, falling onto a black hole, could be responsible for recently discovered ultraluminous X-ray bursts. The simulations show that final passage of a white dwarf near a black hole can cause a gamma-ray burst.