Abstract In this study, we investigate the emergence of the quantum boomerang effect in discrete-time quantum walks (DTQWs) subjected to random phase disorder. Our analysis shows that this effect can arise solely from the bias induced by the coin degree of freedom of the DTQW, without requiring external bias or asymmetry. We explore the evolution of the mean position of the quantum walker, denoted as $\overline{X}(t)$ X ¯ ( t ) , under various initial conditions of the walker and quantum coin operators. The results indicate a significant dependence of the observed phenomena on the choice of initial state, enabling the selective induction of the quantum boomerang effect in both or only one portion of the wavepacket associated with specific internal states. By varying the quantum coin parameter $\theta$ θ , we find that the maximum mean position follows a power-law decay near the Pauli-Z coin, characterized by $X_{\text {Max}} \sim \theta ^{-2}$ X Max ∼ θ - 2 . Additionally, we identify a scaling behavior $X_{\text {Max}} \sim W^{-2}$ X Max ∼ W - 2 , which is consistent with the localization length observed in disordered quantum systems.Abstract In this study, we investigate the emergence of the quantum boomerang effect in discrete-time quantum walks (DTQWs) subjected to random phase disorder. Our analysis shows that this effect can arise solely from the bias induced by the coin degree of freedom of the DTQW, without requiring external bias or asymmetry. We explore the evolution of the mean position of the quantum walker, denoted as $$\overline{X}(t)$$ X ¯ ( t ) , under various initial conditions of the walker and quantum coin operators. The results indicate a significant dependence of the observed phenomena on the choice of initial state, enabling the selective induction of the quantum boomerang effect in both or only one portion of the wavepacket associated with specific internal states. By varying the quantum coin parameter $$\theta $$ θ , we find that the maximum mean position follows a power-law decay near the Pauli-Z coin, characterized by $$X_{\text {Max}} \sim \theta ^{-2}$$ X Max ∼ θ - 2 . Additionally, we identify a scaling behavior $$X_{\text {Max}} \sim W^{-2}$$ X Max ∼ W - 2 , which is consistent with the localization length observed in disordered quantum systems.

arXiv:2505.01532Quantum Information ProcessingJun 1, 20261 citation

A walk on max-plus algebra

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Discrete-time quantum walk with history dependence

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\overline{X}(t)

X ¯ ( t ) , under various initial conditions of the walker and quantum coin operators. The results indicate a significant dependence of the observed phenomena on the choice of initial state, enabling the selective induction of the quantum boomerang effect in both or only one portion of the wavepacket associated with specific internal states. By varying the quantum coin parameter

\theta

θ , we find that the maximum mean position follows a power-law decay near the Pauli-Z coin, characterized by

X_{\text {Max}} \sim \theta ^{-2}

X Max ∼ θ - 2 . Additionally, we identify a scaling behavior

X_{\text {Max}} \sim W^{-2}

X Max ∼ W - 2 , which is consistent with the localization length observed in disordered quantum systems.