Quantum walks with sequential aperiodic jumps

Pires, Marcelo A.; Queirós, Sı́lvio M. Duarte

doi:10.1103/physreve.102.012104

Cited by 24 publications

(12 citation statements)

References 67 publications

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“…This counterintuitive result was demonstrated mathematically in 2013 [26] and experimentally in 2018 [22]. Further works have provided an analysis of the entanglement considering several protocols of disorder embedded either in the coin operator [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] or in the step operator [42][43][44]. With some exceptions, the overwhelming majority of these works focused on QW dynamics from local initial states.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Even though QWs with temporal disorder in the coin operator have been studied for a much longer time [4][5][6][7][8][9], the QWs with temporal disorder in the displacement operator exhibits an interesting phenomenology [42][43][44][46][47][48][49][50][51][52][53][54][55][56]. In some circumstances, both types of models share some similarities, for instance, the achievement of maximal asymptotic entanglement from local states [25,26,42,43].…”

Section: Literature Reviewmentioning

confidence: 99%

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Enhancing entanglement with the generalized elephant quantum walk from localized and delocalized states

Naves¹,

Pires²,

Soares-Pinto³

et al. 2022

Preprint

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Quantum walks are paradigmatic models for studies spanning from fundamental properties of quantum theory to realizations of quantum algorithms. For many years, a plethora of important results based on such models appeared in literature. Recently, a quantum walk with a nonstandard step operator was proposed and named the elephant quantum walk (EQW). With proper statistical distribution for the steps, the generalized EQW (gEQW) can be programmable to exhibit a myriad of dynamical behavior ranging from diffusion and superdiffusion to ballistic and hyperballistic spreading. Such a rich phenomenology makes the gEQW a promising model. In this work we study the influence of the statistics of the step size and the delocalization of the initial states on the entanglement entropy of the coin. Our results show that the gEQW generates maximally entangled states for almost all initial coin states and coin operators considering initially localized walkers and for the delocalized ones, taking the proper limit, the same condition is guaranteed.

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Section: Literature Reviewmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Enhancing entanglement with the generalized elephant quantum walk from localized and delocalized states

Naves¹,

Pires²,

Soares-Pinto³

et al. 2022

Preprint

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“…The key point here is that there are endless forms to set those rules and thus different routes to travel through the Hilbert space, what drives progress in assessing hard computational problems [15]. From that point of view, discrete-time quantum walks are also a powerful tool for quantum simulation of complex phenomena such as quantum phase transitions [16][17][18], nonlinear dynamics [19][20][21][22], topological phases of matter [23][24][25], localization [26][27][28][29], and many others.…”

Section: Introductionmentioning

confidence: 99%

Universal dynamical scaling laws in three-state quantum walks

Falcão,

Buarque,

Dias

et al. 2021

Preprint

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We perform a finite-time scaling analysis over the detrapping point of a three-state quantum walk on the line. The coin operator is parameterized by ρ that controls the wavepacket spreading velocity. The input state prepared at the origin is set as symmetric linear combination of two eigenstates of the coin operator with a characteristic mixing angle θ, one of them being the component that results in full spreading occurring at θc(ρ) for which no fraction of the wavepacket remains trapped near the initial position. We show that relevant quantities such as the survival probability and the participation ratio assume single parameter scaling forms at the vicinity of the detrapping angle θc. In particular, we show that the participation ratio grows linearly in time with a logarithmic correction, thus shedding light on previous reports of sublinear behavior.

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“…Topological behavior (topological invariants and topological phases) of quantum walks has also been illustrated, both theoretically [7,[42][43][44] and experimentally [45][46][47][48][49]. Quantum walks in presence of decoherence and jumps were also studied [50][51][52][53]. It has been used as a powerful tool in simulations of physical processes such as photosynthesis, breakdown of electric-field-driven systems, and so on [54][55][56].…”

Section: Introductionmentioning

confidence: 99%

Response to glassy disorder in coin on spread of quantum walker

Ghosh¹,

Sen²,

Sen³

2021

Preprint

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We analyze the response to incorporation of glassy disorder in the coin operation of a discrete-time quantum walk in one dimension. We find that the ballistic spread of the disorder-free quantum walker is inhibited by the insertion of disorder, for all the disorder distributions that we have chosen for our investigation, but remains faster than the dispersive spread of the classical random walker. While the inhibition to spread is common to all the distributions investigated, there are marked differences between the further behavior of the scalings for the different distributions. In particular, for disorder chosen from Haar-uniform and circular distributions, the response to weak disorder is weak, so that the scaling exponent falls off like a Gaussian against the disorder strength. However, for the spherical normal distribution and the two spherical Cauchy-Lorentz distributions, the response is strong even to weak disorder, and the fall-off is an exponential decay. Strong disorder universally leads to near, but faster than, the classical dispersive spread.

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Quantum walks with sequential aperiodic jumps

Cited by 24 publications

References 67 publications

Enhancing entanglement with the generalized elephant quantum walk from localized and delocalized states

Enhancing entanglement with the generalized elephant quantum walk from localized and delocalized states

Universal dynamical scaling laws in three-state quantum walks

Response to glassy disorder in coin on spread of quantum walker

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