  We propose a practical, scalable, and efficient scheme for quantum
computation using spatially separated matter qubits and single photon
interference effects. The qubit systems can be NV-centers in diamond,
Pauli-blockade quantum dots with an excess electron or trapped ions with
optical transitions, which are each placed in a cavity and subsequently
entangled using a double-heralded single-photon detection scheme. The fidelity
of the resulting entanglement is extremely robust against the most important
errors such as detector loss, spontaneous emission, and mismatch of cavity
parameters. We demonstrate how this entangling operation can be used to
efficiently generate cluster states of many qubits, which, together with single
qubit operations and readout, can be used to implement universal quantum
computation. Existing experimental parameters indicate that high fidelity
clusters can be generated with a moderate constant overhead.
