Experimental realisation of Shor's quantum factoring algorithm using qubit recycling

TL;DR

This paper demonstrates a scalable implementation of Shor's quantum factoring algorithm using qubit recycling, significantly reducing resource requirements and successfully factoring N=21 with distinguishable output.

Contribution

It introduces a resource-efficient version of Shor's algorithm with qubit recycling, enabling larger-scale quantum factoring with fewer qubits.

Findings

Successfully factored N=21 with a recycled qubit approach

Reduced qubit count to one third of standard protocol

Distinguishable algorithmic output from noise

Abstract

Quantum computational algorithms exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms. Shor's quantum algorithm for fast number factoring is a key example and the prime motivator in the international effort to realise a quantum computer. However, due to the substantial resource requirement, to date, there have been only four small-scale demonstrations. Here we address this resource demand and demonstrate a scalable version of Shor's algorithm in which the n qubit control register is replaced by a single qubit that is recycled n times: the total number of qubits is one third of that required in the standard protocol. Encoding the work register in higher-dimensional states, we implement a two-photon compiled algorithm to factor N=21. The algorithmic output is distinguishable from noise, in contrast to previous demonstrations. These results point to larger-scale implementations of Shor's algorithm by harnessing scalable resource reductions applicable to all physical architectures.