We consider quantum random walks on congested lattices and contrast them to classical random walks. Congestion is modelled with lattices that contain static defects which reverse the walkers direction. We implement a dephasing process after each step
which allows us to smoothly interpolate between classical and quantum random walkers as well as study the effect of dephasing on the quantum walk. Our key results show that a quantum walker escapes a finite boundary dramatically faster than a classical walker and that this advantage remains in the presence of heavily congested lattices. Also, we observe that a quantum walker is extremely sensitive to our model of dephasing.
We use a combination of analytical and numerical techniques to calculate the noise threshold and resource requirements for a linear optical quantum computing scheme based on parity-state encoding. Parity-state encoding is used at the lowest level of
code concatenation in order to efficiently correct errors arising from the inherent nondeterminism of two-qubit linear-optical gates. When combined with teleported error-correction (using either a Steane or Golay code) at higher levels of concatenation, the parity-state scheme is found to achieve a saving of approximately three orders of magnitude in resources when compared to a previous scheme, at a cost of a somewhat reduced noise threshold.
