Scaling exponent analysis and fidelity of the tunable discrete quantum walk in the noisy channel

We studied the behavior of tunable one-dimensional discrete-time quantum walk (DTQW) in the presence of decoherence, modeled as a noisy quantum channel with bit-flip, phase-flip, and general amplitude damping effects. The fidelity of the walker based on the angle parametrized coin operator is examined for different tunable conditions. DTQW with bit-flip and phase-flip or dephasing gave rise to the symmetrical probability density function profile while showing different convergence characteristics on their variance behavior. Meanwhile under decoherence with the general amplitude channel, the walker exhibits the non-symmetric profile of probability density function while retaining faster spread than a normal walk under extreme decoherence which is captured by their scaling exponent. These indicate the existence of the broad class of transport behavior of the walker. We showed that the fidelity of the walker can be optimized by adjusting the parameter of the coin rotation angle θ. This work may be useful for the optimization or better control of the quantum walk under noisy channels.