Quantum algorithms know in advance 50% of the solution they will find in the future

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.

The example of new quantum speed up that was just outlined in the previous version (finding the character of a permutation) is fully deployed in the present version. There are minor distributed changes to the writing

References in corpus (3)

• Most quantum states are too entangled to be useful as computational resources
• The 50% advanced information rule of the quantum algorithms
• The quantum speed up as advanced knowledge of the solution

Cited by in corpus (4)

• The quantum correlation between the selection of the problem and that of the solution sheds light on the mechanism of the quantum speed up
• Quantum computation and the physical computation level of biological information processing
• An explanation of the quantum speed up
• Discussing the explanation of the quantum speed up