Shor's Algorithm from the Mindset of Quantum Oracles

TL;DR

This paper proposes a new deterministic approach to quantum computing based on a conceptual foundation involving quantum oracles and state selection, aiming to replicate Shor's algorithm's results with similar resource efficiency.

Contribution

It introduces a novel theoretical framework for quantum computing using quantum oracles and state selection, providing a new perspective on implementing Shor's algorithm deterministically.

Findings

Demonstrates a relativized process achieving Shor's factorization results

Introduces the concept of quantum state selection via POVM

Proposes a prototype quantum oracle system

Abstract

The aim of this work is to show a brand-new way of making deterministic Quantum Computing (short QC), in the sense of Theory of Calculability, by meaning of unitary evolution. We start from the original Shor's Algorithm to explain how the newest one works, at least compared to theory. We will give a new conceptual foundation of QC, resulting from a set of conventional and well known results of Calculability and Quantum Mechanics. In the practice, if that can be used in its general sense, we will show an inaccessible relativized process which let us able to obtain same results with the same outlay in the time resource as the Shor's one for factorizing a given number n. Then the QO-system will be a prototype way giving to the relativized calculus the possibility to put in to practice an oracle, kind of object having till now abstract nature. The basic physical tool of our theorization, we call Quantum State Selection, consists in the twin-combined measurement process through positive valued measure operator (POVM), needed to provide the quantum oracle's answer.