Completing the physical representation of quantum algorithms provides a retrocausal explanation of their speedup

TL;DR

This paper offers a retrocausal explanation for quantum speedup by completing the physical representation of quantum algorithms, linking it to the known optimal classical histories with future knowledge, and justifies retrocausality as a complete physical description.

Contribution

It provides a fundamental justification for retrocausal explanations of quantum algorithms by completing their physical representation, addressing controversy over retrocausality.

Findings

Retrocausality explains quantum speedup via classical histories with future knowledge.

Completing the physical representation justifies retrocausality as a complete description.

The approach predicts the number of oracle queries needed for optimal quantum solutions.

Abstract

In previous works, we showed that an optimal quantum algorithm can always be seen as a sum over classical histories in each of which the problem solver knows in advance one of the possible halves of the solution she will read in the future and performs the computation steps (oracle queries) still needed to reach it. Given an oracle problem, this retrocausal explanation of the speedup yields the order of magnitude of the number of oracle queries needed to solve it in an optimal quantum way. Presently, we provide a fundamental justification for the explanation in question and show that it comes out by just completing the physical representation of quantum algorithms. Since the use of retrocausality in quantum mechanics is controversial, showing that it answers the well accepted requirement of the completeness of the physical description should be an important pass.