Understanding Quantam Computing

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Understanding Quantam Computing Quantum Computing is something that could have been thought up a long time ago - an idea whose time has come. For any physical theory one can ask: what sort of machines will do useful computation? or, what sort of processes will count as useful computational acts? Alan Turing thought about this in 1936 with regard (implicitly) to classical mechanics, and gave the world the paradigm classical computer: the Turing machine. But even in 1936 classical mechanics was known to be false. Work is now under way - mostly theoretical, but tentatively, hesitantly groping towards the practical - in seeing what quantum mechanics means for computers and computing. In a trivial sense, everything is a quantum computer. (A pebble is a quantum computer for calculating the constant-position function - you get the idea.) And of course, today's computers exploit quantum effects (like electrons tunneling through barriers) to help do the right thing and do it fast. For that matter, both the computer and the pebble exploit a quantum effect - the "Pauli exclusion principle", which holds up ordinary matter against collapse by bringing about the kind of degeneracy we call chemistry - just to remain stable solid objects. But quantum computing is much more than that. The most exciting really new feature of quantum computing is quantum parallelism. A quantum system is in general not in one "classical state", but in a "quantum state" consisting (crudely speaking) of a superposition of many classical or classical-like states. This superposition is not just a figure of speech, covering up our ignorance of which classical-like state it's "really" in. If that was all the superposition meant, you could drop all but one of th... ... middle of paper ... ...f how this exponential improvement might be possible, we review an elementary quantum mechanical experiment that demonstrates where such power may lie hidden [5]. The two-slit experiment is prototypic for observing quantum mechanical behavior: A source emits photons, electrons or other particles that arrive at a pair of slits. These particles undergo unitary evolution and finally measurement. We see an interference pattern, with both slits open, which wholely vanishes if either slit is covered. In some sense, the particles pass through both slits in parallel. If such unitary evolution were to represent a calculation (or an operation within a calculation) then the quantum system would be performing computations in parallel. Quantum parallelism comes for free. The output of this system would be given by the constructive interference among the parallel computations.

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