Shors 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 Shors 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 Shors algorithm. Demonstration of these processes is a necessary step on the path towards a full implementation of Shors 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.
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