Nearly deterministic linear optical controlled-NOT gate

We show how to construct a near deterministic CNOT gate using several single photons sources, linear optics, photon number resolving quantum nondemolition detectors, and feed forward. This gate does not require the use of massively entangled states common to other implementations and is very efficient on resources with only one ancilla photon required. The key element of this gate is nondemolition detectors that use a weak cross-Kerr nonlinearity effect to conditionally generate a phase shift on a coherent probe if a photon is present in the signal mode. These potential phase shifts can then be measured using highly efficient homodyne detection.