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In ordinary logic, which we learn so well that it seems inevitable, the logic of each step in sequence is independent of previous steps. For example, for any statement A, NOT(NOT A) is true if and only if A is true. It does not matter what A is or how we derived A. The only importance that the history of previous logical steps plays is bringing us to the current step. Thus, logics is like classical mechanics. The current location, mass, and forces acting in a system determine the system's future independent of the system's past. However, in a system governed by quantum mechanics, the future evolution of the system is fundamentally governed by the system's history. This is a real physical phenomenon. For example, corresponding to the classical situation, two transistors in a computer can switch on and off independently. Two adjacent quantum objects, such as two electrons, are inextricably coupled so that the future state of one electron cannot be predicted without taking into account the surrounding electrons and their history. The logic of quantum computers, i.e., of computers whose elements interact in terms of their quantum states, is fundamentally different from that of classical computers. Quantum computers, based on such properties, turn out in fact to have capacities beyond those of standard computer architecture. This superiority can be shown on a theoretical basis. If two logic gates in a quantum computer are put in sequence, the result may be different from simply one step followed by the other. NOT(NOT A) is not equivalent to A. The rules of the next logical step thus depend on the history of the object being operated upon. This is because in a quantum mechanical system an unobservable intermediate state does not have a unique value. The extraordinary power of quantum computing comes from exploiting such superposition and interference.