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Quantum walks are an analog of classical random walks in quantum systems.Quantum walks have smaller hitting times compared to classical random walks oncertain types of graphs, leading to a quantum advantage of quantum-walks-basedalgorithms. An important feature of quantum walks is that they are accompaniedby the excitation transfer from one site to another, and a moment of hittingthe destination site is characterized by the maximum probability amplitude ofobserving the excitation on this site. It is therefore prospective to considersuch problems as candidates for quantum advantage demonstration, since gateerrors can smear out a peak in the transfer probability as a function of time,nevertheless leaving it distinguishable. We investigate the influence ofquantum 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 asingle excitation over the chain of qubits in the presence of typical noises ofa quantum processor (homogeneous and inhomogeneous Pauli noise, crosstalknoise, thermal relaxation, and dephasing noise). We find that Pauli noisemostly smears out a peak in the fidelity of excitation transfer, whilecrosstalks between qubits mostly affect the hitting time. Knowledge about thesenoise patterns allows us to propose an error mitigation procedure, which we useto refine the results of running the PST on a simulator of a noisy quantumprocessor.

The effect of quantum noise on algorithmic perfect quantum state transfer on NISQ processors