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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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III.74 Quantum Computation

A quantum computer is a theoretical device that makes use of the phenomenon of “superposition” in quantum mechanics to carry out certain computations in a way that is fundamentally different from any known classical methods, and in a few important cases remarkably efficient. In classical physics, if there is some property that a particle could have, then either it has it or it does not. But according to quantum mechanics, it can exist in a sort of indeterminate state that is a linear combination of several states, in some of which it might have the property in question and in others not. The coefficients in this linear combination are called probability amplitudes: the modulus squared of the coefficient associated ...

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