Analyzing some well established facts, we give a modelindependent parameterization of black hole quantum computing in terms of a set of macro and micro quantities and their relations. These include the relations between the extraordinarily-small energy gap of black hole qubits and important time-scales of information-processing, such as, scrambling time and Page's time. We then show, confirming and extending previous results, that other systems of nature with identical quantum informatics features are attractive Bose-Einstein systems at the critical point of quantum phase transition. Here we establish a complete isomorphy between the quantum computational properties of these two systems. In particular, we show that the quantum hair of a critical condensate is strikingly similar to the quantum hair of a black hole. Irrespectively whether one takes the similarity between the two systems as a remarkable coincidence or as a sign of a deeper underlying connection, the following is evident. Black holes are not unique in their way of quantum information processing and we can manufacture black hole based quantum computers in labs by taking advantage of quantum criticality. Fortschritte der Physik Progress of Physics G. Dvali and M. Panchenko: Black hole based quantum computing in labs and in the sky der Physik Progress of Physics G. Dvali and M. Panchenko: Black hole based quantum computing in labs and in the sky Extending the results of [6] we have designed examples of computational sequences.

Recent ideas about understanding physics of black hole informationprocessing 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 weaklyinteracting 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.

In a series of papers [1] it was proposed that black holes can be understood as Bose-Einstein condensates at the critical point of a quantum phase transition. Therefore other bosonic systems with quantum criticalities, such as the Lieb-Liniger model with attractive interactions, could possibly be used as toy models for black holes. Even such simple models are hard to analyse, as mean field theory usually breaks down at the critical point. Very few analytic results are known. In this paper we present a method of studying such systems at quantum critical points analytically. We will be able to find explicit expressions for the low energy spectrum of the Lieb-Liniger model and thereby to confirm the expected black hole like properties of such systems. This opens up an exciting possibility of constructing and studying black hole like systems in the laboratory.