Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2303.01608 · Physical review. E

Discrete-time quantum walk dispersion control through long-range correlations

A. R. C. Buarque, F. S. Passos, Wandearley S. Dias, Ernesto P. Raposo

Published Jun 27, 2023• 6 citations
arXivHTMLPDF

Abstract

We investigate the evolution dynamics of inhomogeneous discrete-time one-dimensional quantum walks displaying long-range correlations in both space and time. The associated quantum coin operators of internal states are built to exhibit random inhomogeneity distribution of long-range correlations embedded in the time evolution protocol through a fractional Brownian motion with spectrum following a power-law behavior, S(k)∼1/k^{ν}. From extensive numerical simulations with averages over a large number of independent realizations of the phases of quantum coins, the power-law correlated disorder encoded in the coin phases is shown to give rise to a wide variety of spreading patterns of the qubit states, from localized to subdiffusive, diffusive, and superdiffusive (including ballistic) behavior, depending on the relative strength of the parameters driving the correlation degree. Dispersion control is possible in one-dimensional discrete-time quantum walks by tuning the long-range correlation properties assigned to the inhomogeneous quantum coin operator.

DOI
10.1103/physreve.107.064139

Related papers

On the spreading of quantum walks starting from local and delocalized states

Alexandre C. Orthey, Edgard P. M. Amorim

We investigate the ballistic spreading behavior of the one-dimensional discrete time quantum walks whose time evolution is driven by any balanced quantum coin. We obtain closed-form expressions for the long-time variance of position of quantum walks starting from any initial qubit (spin-$1/2$ particle) and position states following a delta-like (local), Gaussian and uniform probability distributions. By averaging over all spin states, we find out that the average variance of a quantum walk starting from a local state is independent of the quantum coin, while from Gaussian and uniform states it depends on the sum of relative phases between spin states given by the quantum coin, being non-dispersive for a Fourier walk and large initial dispersion. We also perform numerical simulations of the average probability distribution and variance along the time to compare them with our analytical results.

arXiv:1706.06257•Jun 20, 2017•4 citations

Characterization of anomalous diffusion in one-dimensional quantum walks

Abhaya S. Hegde, C. M. Chandrashekar

Abstract Quantum walks are known to propagate quadratically faster than their classical counterparts and are used to model dynamics in various quantum systems. The spread of the quantum walk in position space shows anomalous diffusion behavior. By controlling the action of quantum coin operation on the corresponding coin degree of freedom of the walker, one can demonstrate control over the diffusion behavior. In this work, we report different forms of coin operations on quantum walks exhibiting anomalous diffusion behavior. Homogeneous and accelerated quantum walks display superdiffusive behavior, whereas uncorrelated static and dynamic disorders in the evolution induce strong and weak localization of the particle indicating subdiffusive and normal diffusive behavior. The role played by the interference effects in the spreading of the walker has remained elusive and our aim in this work is to present the interplay between quantum coherence and mean squared displacement of the walker. We employ two reliable measures of coherence for conclusively establishing the role of quantum interference as the driving force behind the anomalous diffusive behavior in the dynamics of quantum walks.

arXiv:2112.14611•Journal of Physics A Mathematical and Theoretical•Apr 28, 2022•0 citations

Discrete-time quantum walks with energy-dependent coins

Alana Spak dos Santos, Thiago T. Tsutsui, Fabiano M. Andrade

In this work, we extend the scattering quantum walk (SQW) framework to a lattice of energy-dependent point interactions. This yields, within the coined quantum walk (CQW) formalism, a coin operator that is directly related to the scattering matrix of zero-range potentials. The model thus provides a discrete-time quantum-walk (DTQW) analog of a periodic array of point interactions of the Kronig-Penney type, where the walker's wavenumber serves as a continuous, physically transparent control parameter for the coin operation. We analyze the spectra and the dynamics of position probability and entanglement, yielding distinct results for specific energies and point interactions. We relate the spectral structure to the spatial probability distribution and explicitly characterize the long-time entanglement behavior for each point interaction. The transmission modulus determines the quasienergy gap, bandwidth, and maximum group velocity, while also controlling the long-time coin-position entanglement for the initial state considered. The four families of one-dimensional point interactions ($δ$, $δ'$, crossed and asymmetric) realize qualitatively distinct transmission profiles and span the full range of behavior, including enhanced or strongly suppressed spreading and oscillatory entanglement.

quant-pharXiv:2609.03272•Sep 4, 2026•0 citations

Driving quantum-walk spreading with the coin operator

A. Romanelli

We generalize the discrete quantum walk on the line using a time-dependent unitary coin operator. We find an analytical relation between the long-time behaviors of the standard deviation and the coin operator. Selecting the coin time sequence allows to obtain a variety of predetermined asymptotic wave-function spreadings: ballistic, sub-ballistic, diffusive, subdiffusive, and localized.

arXiv:0908.0019•Physical Review A•Oct 29, 2009•41 citations

Localization-delocalization transition in discrete-time quantum walks with long-range correlated disorder

C.V.C. Mendes, G. M. A. Almeida, M. L. Lyra +1 more

We study the effects of spatially long-range correlated phase disorder on the Hadamard quantum walk on a line. The shift operator is built to exhibit an intrinsic disorder distribution featuring long-range correlations. To impose such, we resort to fractional Brownian motion with power-law spectrum 1/k^{2α} with α≥0 being the exponent that controls the degree of correlations. We discuss the scaling behavior of the walker's wave packet and report a localization-delocalization transition controlled by α. We unveil two intermediate dynamical regimes between exponential localization and full delocalization.

Physical review. E•Feb 12, 2019•19 citations

Controlled dynamics of a multi-component discrete-time quantum walker

Vikash Mittal, Tomasz Sowiński

We investigate a discrete-time quantum walk of a three-component quantum particle on a one-dimensional lattice. As coin operators, we employ parameterized rotations generated by the Gell-Mann matrices, which enable systematic tuning of the couplings between the internal components. We analyze how these couplings influence and control the dynamics by systematically exploring the position-space probability distribution across a broad region of the parameter space. To quantify the impact of different inter-component couplings, we further examine the ratio of the mean position to the variance in each half of the lattice. Our results indicates that the system supports a rich variety of transport regimes, ranging from nearly symmetric, rapidly spreading walks to strongly anisotropic dynamics with partial localization. This framework thus provides a new avenue for engineering targeted spreading and trapping behavior in multicomponent discrete-time quantum walks.

quant-pharXiv:2608.13161•Aug 14, 2026•0 citations
We investigate the evolution dynamics of inhomogeneous discrete-time one-dimensional quantum walks displaying long-range correlations in both space and time. The associated quantum coin operators of internal states are built to exhibit random inhomogeneity distribution of long-range correlations embedded in the time evolution protocol through a fractional Brownian motion with spectrum following a power-law behavior, S(k)∼1/k^{ν}. From extensive numerical simulations with averages over a large number of independent realizations of the phases of quantum coins, the power-law correlated disorder encoded in the coin phases is shown to give rise to a wide variety of spreading patterns of the qubit states, from localized to subdiffusive, diffusive, and superdiffusive (including ballistic) behavior, depending on the relative strength of the parameters driving the correlation degree. Dispersion control is possible in one-dimensional discrete-time quantum walks by tuning the long-range correlation properties assigned to the inhomogeneous quantum coin operator.
We investigate the ballistic spreading behavior of the one-dimensional discrete time quantum walks whose time evolution is driven by any balanced quantum coin. We obtain closed-form expressions for the long-time variance of position of quantum walks starting from any initial qubit (spin-1/21/21/2 particle) and position states following a delta-like (local), Gaussian and uniform probability distributions. By averaging over all spin states, we find out that the average variance of a quantum walk starting from a local state is independent of the quantum coin, while from Gaussian and uniform states it depends on the sum of relative phases between spin states given by the quantum coin, being non-dispersive for a Fourier walk and large initial dispersion. We also perform numerical simulations of the average probability distribution and variance along the time to compare them with our analytical results.
Abstract Quantum walks are known to propagate quadratically faster than their classical counterparts and are used to model dynamics in various quantum systems. The spread of the quantum walk in position space shows anomalous diffusion behavior. By controlling the action of quantum coin operation on the corresponding coin degree of freedom of the walker, one can demonstrate control over the diffusion behavior. In this work, we report different forms of coin operations on quantum walks exhibiting anomalous diffusion behavior. Homogeneous and accelerated quantum walks display superdiffusive behavior, whereas uncorrelated static and dynamic disorders in the evolution induce strong and weak localization of the particle indicating subdiffusive and normal diffusive behavior. The role played by the interference effects in the spreading of the walker has remained elusive and our aim in this work is to present the interplay between quantum coherence and mean squared displacement of the walker. We employ two reliable measures of coherence for conclusively establishing the role of quantum interference as the driving force behind the anomalous diffusive behavior in the dynamics of quantum walks.
In this work, we extend the scattering quantum walk (SQW) framework to a lattice of energy-dependent point interactions. This yields, within the coined quantum walk (CQW) formalism, a coin operator that is directly related to the scattering matrix of zero-range potentials. The model thus provides a discrete-time quantum-walk (DTQW) analog of a periodic array of point interactions of the Kronig-Penney type, where the walker's wavenumber serves as a continuous, physically transparent control parameter for the coin operation. We analyze the spectra and the dynamics of position probability and entanglement, yielding distinct results for specific energies and point interactions. We relate the spectral structure to the spatial probability distribution and explicitly characterize the long-time entanglement behavior for each point interaction. The transmission modulus determines the quasienergy gap, bandwidth, and maximum group velocity, while also controlling the long-time coin-position entanglement for the initial state considered. The four families of one-dimensional point interactions (δδδ, δ′δ'δ′, crossed and asymmetric) realize qualitatively distinct transmission profiles and span the full range of behavior, including enhanced or strongly suppressed spreading and oscillatory entanglement.
We study the effects of spatially long-range correlated phase disorder on the Hadamard quantum walk on a line. The shift operator is built to exhibit an intrinsic disorder distribution featuring long-range correlations. To impose such, we resort to fractional Brownian motion with power-law spectrum 1/k^{2α} with α≥0 being the exponent that controls the degree of correlations. We discuss the scaling behavior of the walker's wave packet and report a localization-delocalization transition controlled by α. We unveil two intermediate dynamical regimes between exponential localization and full delocalization.
We investigate a discrete-time quantum walk of a three-component quantum particle on a one-dimensional lattice. As coin operators, we employ parameterized rotations generated by the Gell-Mann matrices, which enable systematic tuning of the couplings between the internal components. We analyze how these couplings influence and control the dynamics by systematically exploring the position-space probability distribution across a broad region of the parameter space. To quantify the impact of different inter-component couplings, we further examine the ratio of the mean position to the variance in each half of the lattice. Our results indicates that the system supports a rich variety of transport regimes, ranging from nearly symmetric, rapidly spreading walks to strongly anisotropic dynamics with partial localization. This framework thus provides a new avenue for engineering targeted spreading and trapping behavior in multicomponent discrete-time quantum walks.