Realization of a scalable Shor algorithm

TL;DR

This paper demonstrates a fully scalable implementation of Shor's quantum factoring algorithm using an ion-trap quantum computer, successfully factoring the number fifteen with high success probability, marking a significant step toward practical quantum computing.

Contribution

It presents the first realization of a scalable Shor algorithm as proposed by Kitaev, employing seven qubits and modular multipliers on an ion-trap platform.

Findings

Successfully factored the number fifteen.

Achieved success probabilities over 90%.

Demonstrated control of generalized arithmetic operations.

Abstract

Quantum computers are able to outperform classical algorithms. This was long recognized by the visionary Richard Feynman who pointed out in the 1980s that quantum mechanical problems were better solved with quantum machines. It was only in 1994 that Peter Shor came up with an algorithm that is able to calculate the prime factors of a large number vastly more efficiently than known possible with a classical computer. This paradigmatic algorithm stimulated the flourishing research in quantum information processing and the quest for an actual implementation of a quantum computer. Over the last fifteen years, using skillful optimizations, several instances of a Shor algorithm have been implemented on various platforms and clearly proved the feasibility of quantum factoring. For general scalability, though, a different approach has to be pursued. Here, we report the realization of a fully scalable Shor algorithm as proposed by Kitaev. For this, we demonstrate factoring the number fifteen by effectively employing and controlling seven qubits and four "cache-qubits", together with the implementation of generalized arithmetic operations, known as modular multipliers. The scalable algorithm has been realized with an ion-trap quantum computer exhibiting success probabilities in excess of 90%.