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

TL;DR

Quantum algorithms are explained as having prior knowledge of 50% of the solution, which accounts for their efficiency, by representing them as sums over all possible histories of a classical algorithm with advanced information.

Contribution

This paper introduces a novel explanation for quantum speed-up, showing it as classical algorithms with 50% of the solution known in advance, simplifying the understanding of quantum advantage.

Findings

Quantum algorithms effectively know 50% of the solution beforehand.

Quantum speed-up can be explained through classical algorithms with advanced information.

This approach allows systematic exploration of quantum speed-up without quantum physics.

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.