Abstract

Quantum algorithms are computational routines that exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms. Shor’s quantum factoring algorithm [1] is a key example and the prime motivator in the international effort to realise a quantum computer. However, due to the large number of resources required, to date, there have been only four small scale demonstrations [2-5]. 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 [6]. Encoding the work register in higher-dimensional states, we implement a two-photon compiled algorithm to factor N = 21 [7]. Significantly, the algorithmic output exhibits structure that is distinguishable from noise, in contrast to previous demonstrations.

© 2013 IEEE