  Error-detection and correction are necessary prerequisites for any scalable
quantum computing architecture. Given the inevitability of unwanted physical
noise in quantum systems and the propensity for errors to spread as
computations proceed, computational outcomes can become substantially
corrupted. This observation applies regardless of the choice of physical
implementation. In the context of photonic quantum information processing,
there has recently been much interest in passive linear optics quantum
computing, which includes boson-sampling, as this model eliminates the
highly-challenging requirements for feed-forward via fast, active control. That
is, these systems are passive by definition. In usual scenarios, error
detection and correction techniques are inherently active, making them
incompatible with this model, arousing suspicion that physical error processes
may be an insurmountable obstacle. Here we explore a photonic error-detection
technique, based on W-state encoding of photonic qubits, which is entirely
passive, based on post-selection, and compatible with these near-term photonic
architectures of interest. We show that this W-state redundant encoding
techniques enables the suppression of dephasing noise on photonic qubits via
simple fan-out style operations, implemented by optical Fourier transform
networks, which can be readily realised today. The protocol effectively maps
dephasing noise into heralding failures, with zero failure probability in the
ideal no-noise limit. We present our scheme in the context of a single photonic
qubit passing through a noisy communication or quantum memory channel, which
has not been generalised to the more general context of full quantum
computation.
