Abstract
Quantum algorithms require less operations than classical algorithms. The exact reason of this has not been pinpointed until now. Our explanation is that quantum algorithms know in advance 50% of the solution of the problem they will find in the future. In fact they can be represented as the sum of all the possible histories of a respective “advanced information classical algorithm”. This algorithm, given the advanced information (50% of the bits encoding the problem solution), performs the operations (oracle’s queries) still required to identify the solution. Each history corresponds to a possible way of getting the advanced information and a possible result of computing the missing information. This explanation of the quantum speed up has an immediate practical consequence: the speed up comes from comparing two classical algorithms, with and without advanced information, with no physics involved. This simplification could open the way to a systematic exploration of the possibilities of speed up.
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Castagnoli, G. Quantum Algorithms Know in Advance 50% of the Solution They Will Find in the Future. Int J Theor Phys 48, 3383 (2009). https://doi.org/10.1007/s10773-009-0143-6
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DOI: https://doi.org/10.1007/s10773-009-0143-6