  A new approach to efficient quantum computation with probabilistic gates is
proposed and analyzed in both a local and non-local setting. It combines
heralded gates previously studied for atom or atom-like qubits with logical
encoding from linear optical quantum computation in order to perform high
fidelity quantum gates across a quantum network. The error-detecting properties
of the heralded operations ensure high fidelity while the encoding makes it
possible to correct for failed attempts such that deterministic and
high-quality gates can be achieved. Importantly, this is robust to photon loss,
which is typically the main obstacle to photonic based quantum information
processing. Overall this approach opens a novel path towards quantum networks
with atomic nodes and photonic links.
