An explanation of the quantum speed up

TL;DR

This paper explains the quantum speed-up by showing that quantum algorithms effectively gain 50% of the solution information during computation, linking the speed-up to a time-symmetric information exchange.

Contribution

It explicitly models how quantum algorithms acquire partial solution information throughout the process, providing a theoretical basis for the 50% rule in quantum speed-up.

Findings

Quantum algorithms gain 50% of solution information during computation.

The 50% rule is supported by theoretical justification and multiple algorithms.

Time-symmetric information exchange underpins quantum speed-up.

Abstract

In former work, we showed that a quantum algorithm requires the number of operations (oracle's queries) of a classical algorithm that knows in advance 50% of the information that specifies the solution of the problem. We gave a preliminary theoretical justification of this "50% rule" and checked that the rule holds for a variety of quantum algorithms. Now, we make explicit the information about the solution available to the algorithm throughout the computation. The final projection on the solution becomes acquisition of the knowledge of the solution on the part of the algorithm. Backdating to before running the algorithm a time-symmetric part of this projection, feeds back to the input of the computation 50% of the information acquired by reading the solution.