1. A method for high fidelity quantum teleportation, comprising the steps of: receiving an input photon representing a particular quantum superposition state for logical values 0 and 1; generating a plurality of ancilla photons in a particular ancilla quantum state chosen to reduce a rate of error for obtaining a teleported photon below a threshold error rate; combining the plurality of ancilla photons with the input photon using one or more linear optical elements to populate a plurality of output channels; measuring a number of photons representing logical value 1 in a subset of the plurality of output channels; determining a particular output channel of the plurality of output channels based on the number of photons from said measuring step; and obtaining a teleported photon at the particular output channel in the quantum superposition state of the input photon with an error rate below the threshold error rate.