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.Comment: 7 pages, 3 figure
