  Quantum walks are an analog of classical random walks in quantum systems.
Quantum walks have smaller hitting times compared to classical random walks on
certain types of graphs, leading to a quantum advantage of quantum-walks-based
algorithms. An important feature of quantum walks is that they are accompanied
by the excitation transfer from one site to another, and a moment of hitting
the destination site is characterized by the maximum probability amplitude of
observing the excitation on this site. It is therefore prospective to consider
such problems as candidates for quantum advantage demonstration, since gate
errors can smear out a peak in the transfer probability as a function of time,
nevertheless leaving it distinguishable. We investigate the influence of
quantum noise on hitting time and fidelity of a typical quantum walk problem -
a perfect state transfer (PST) over a qubit chain. We simulate dynamics of a
single excitation over the chain of qubits in the presence of typical noises of
a quantum processor (homogeneous and inhomogeneous Pauli noise, crosstalk
noise, thermal relaxation, and dephasing noise). We find that Pauli noise
mostly smears out a peak in the fidelity of excitation transfer, while
crosstalks between qubits mostly affect the hitting time. Knowledge about these
noise patterns allows us to propose an error mitigation procedure, which we use
to refine the results of running the PST on a simulator of a noisy quantum
processor.
