  Recent ideas about understanding physics of black hole information-processing
in terms of quantum criticality allow us to implement black hole mechanisms of
quantum computing within critical Bose-Einstein systems. The generic feature,
uncovered both by analytic and numeric studies, is the emergence at the
critical point of gapless weakly-interacting modes, which act as qubits for
information-storage at a very low energy cost. These modes can be effectively
described in terms of either Bogoliubov or Goldstone degrees of freedom. The
ground-state at the critical point is maximally entangled and far from being
classical. We confirm this near-critical behavior by a new analytic method. We
compute growth of entanglement and show its consistency with black hole type
behavior. On the other hand, in the over-critical regime the system develops a
Lyapunov exponent and scrambles quantum information very fast. By, manipulating
the system parameters externally, we can put it in and out of various regimes
and in this way control the sequence of information storage and processing. By
using gapless Bogoliubov modes as control qubits we design some simple logic
gates.
