Demonstration of Shor's quantum factoring algorithm using photonic qubits

We report an experimental demonstration of a complied version of Shor's algorithm using four photonic qubits. We choose the simplest instance of this algorithm, that is, factorization of N=15 in the case that the period $r=2$ and exploit a simplified linear optical network to coherently implement the quantum circuits of the modular exponential execution and semi-classical quantum Fourier transformation. During this computation, genuine multiparticle entanglement is observed which well supports its quantum nature. This experiment represents a step toward full realization of Shor's algorithm and scalable linear optics quantum computation.