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Linear optics with photon counting is a prominent candidate for practicalquantum computing. The protocol by Knill, Laflamme, and Milburn [Nature 409, 46(2001)] explicitly demonstrates that efficient scalable quantum computing withsingle photons, linear optical elements, and projective measurements ispossible. Subsequently, several improvements on this protocol have started tobridge the gap between theoretical scalability and practical implementation. Wereview the original theory and its improvements, and we give a few examples ofexperimental two-qubit gates. We discuss the use of realistic components, theerrors they induce in the computation, and how these errors can be corrected.Comment: 41 pages, 37 figures, many small changes, added references, and  improved discussion on error correction and fault toleranc

Linear optical quantum computing with photonic qubits