considered in the context of QRWs. We found that static phase errors bring a significantly different behaviour compared to the case of phase fluctuations. Under static phase errors the algorithm retains its utility, with the average success probability displaying a damped oscillatory behaviour that asymptotically tends to a non-zero constant value.

The paper is organized as follows. In the next section we introduce the scattering quantum walk search algorithm. In section \[sec:uniform\]. we derive analytic results for the success probability of search for the case when a single coefficient describes photon losses independent of the direction. In section \[sec:non-uniform\]. we turn to direction dependent losses, and present estimations of the success probability based on analytical calculations and numerical evidence. In section \[sec:phase\].phase noise is considered and consequences for the success probability are worked out. Finally, we conclude in Sec. \[sec:conclusions\].

The scattering quantum walk search algorithm {#sec:sqrw}
============================================

The quantum walk search algorithm is based on the generalized notion of coined quantum random walk (CQRW), allowing the coin operator to be non-uniform accross the vertices. In the early literature the coin is considered as position (vertex) independent. The CQRW is defined on the product Hilbert space $\cH=\cHC \otimes \cHG$, where 