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The recent Google's claim on breakthrough in quantum computing is a gongsignal for further analysis of foundational roots of (possible) superiority ofsome quantum algorithms over the corresponding classical algorithms. This noteis a step in this direction. We start with critical analysis of rather commonreference to entanglement and quantum nonlocality as the basic sources ofquantum superiority. We elevate the role of the Bohr's {\it principle ofcomplementarity}\footnote{} (PCOM) by interpreting the Bell-experiments asstatistical tests of this principle. (Our analysis also includes comparison ofclassical vs genuine quantum entanglements.) After a brief presentation of PCOMand endowing it with the information interpretation, we analyze itscomputational counterpart. The main implication of PCOM is that by using thequantum representation of probability, one need not compute the jointprobability distribution (jpd) for observables involved in the process ofcomputation. Jpd's calculation is exponentially time consuming. Consequently,classical probabilistic algorithms involving calculation of jpd for $n$ randomvariables can be over-performed by quantum algorithms (for big values of $n).$Quantum algorithms are based on quantum probability calculus. It is crucialthat the latter modifies the classical formula of total probability (FTP).Probability inference based on the quantum version of FTP leads to constructiveinterference of probabilities increasing probabilities of some events. We alsostress the role the basic feature of the genuine quantum superpositioncomparing with the classical wave superposition: generation of discrete eventsin measurements on superposition states. Finally, the problem of superiority ofquantum computations is coupled with the quantum measurement problem andlinearity of dynamics of the quantum state update.

Echoing the recent Google success: Foundational Roots of Quantum Supremacy