Experimental demonstration of Shor's algorithm with quantum entanglement

TL;DR

This paper demonstrates a photonic implementation of Shor's quantum factoring algorithm, showcasing core quantum processes and entanglement essential for scalable quantum computing and cryptography.

Contribution

First experimental demonstration of key processes and entangled states in a compiled version of Shor's algorithm using photonic systems.

Findings

Successful demonstration of coherent control and entanglement in Shor's algorithm

Highlights the importance of characterizing quantum algorithms independently of circuit performance

Paves the way for scalable quantum computing implementations

Abstract

Shor's powerful quantum algorithm for factoring represents a major challenge in quantum computation and its full realization will have a large impact on modern cryptography. Here we implement a compiled version of Shor's algorithm in a photonic system using single photons and employing the non-linearity induced by measurement. For the first time we demonstrate the core processes, coherent control, and resultant entangled states that are required in a full-scale implementation of Shor's algorithm. Demonstration of these processes is a necessary step on the path towards a full implementation of Shor's algorithm and scalable quantum computing. Our results highlight that the performance of a quantum algorithm is not the same as performance of the underlying quantum circuit, and stress the importance of developing techniques for characterising quantum algorithms.