  It was recently shown by Motes, Gilchrist, Dowling & Rohde [PRL 113, 120501
(2014)] that a time-bin encoded fiber-loop architecture can implement an
arbitrary passive linear optics transformation. This was shown in the case of
an ideal scheme whereby the architecture has no sources of error. In any
realistic implementation, however, physical errors are present, which corrupt
the output of the transformation. We investigate the dominant sources of error
in this architecture --- loss and mode-mismatch --- and consider how it affects
the BosonSampling protocol, a key application for passive linear optics. For
our loss analysis we consider two major components that contribute to loss ---
fiber and switches --- and calculate how this affects the success probability
and fidelity of the device. Interestingly, we find that errors due to loss are
not uniform (unique to time-bin encoding), which asymmetrically biases the
implemented unitary. Thus, loss necessarily limits the class of unitaries that
may be implemented, and therefore future implementations must prioritise
minimising loss rates if arbitrary unitaries are to be implemented. Our
formalism for mode-mismatch is generlized to account for various phenomenon
that may cause mode-mismatch, but we focus on two --- errors in fiber-loop
lengths, and time-jitter of the photon source. These results provide a
guideline for how well future experimental implementations might perform in
light of these error mechanisms.

Quantum Physics