Emergent nonlinear phenomena in discrete-time quantum walks

Mendonça, João Pedro; Moura, F. A. B. F. de; Lyra, M. L.; Almeida, G. M. A.

doi:10.1103/physreva.101.062335

Cited by 15 publications

(2 citation statements)

References 62 publications

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“…In [61] the work in [60] was generalized by using mathematical techniques appropriate to Floquet systems, which allowed for the finding of new bifurcations. Another alternative is that of Mendonça et al [62], who propose a nonlinear displacement operator of the form…”

Section: Nonlinear Dqwmentioning

confidence: 99%

Bright and dark solitons in a photonic nonlinear quantum walk: lessons from the continuum

Anglés-Castillo,

Pérez,

Roldán

2024

New J. Phys.

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We propose a nonlinear quantum walk model inspired in a photonic implementation in which thepolarization state of the light field plays the role of the coin-qubit. In particular, we take profit of thenonlinear polarization rotation occurring in optical media with Kerr nonlinearity, which allows toimplement a nonlinear coin operator, one that depends on the state of the coin-qubit. We considerthe space-time continuum limit of the evolution equation, which takes the form of a nonlinear Diracequation. The analysis of this continuum limit allows us to gain some insight into the existenceof different solitonic structures, such as bright and dark solitons. We illustrate several propertiesof these solitons with numerical calculations, including the effect on them of an additional phasesimulating an external electric field.

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Section: Nonlinear Dqwmentioning

confidence: 99%

Bright and dark solitons in a photonic nonlinear quantum walk: lessons from the continuum

Anglés-Castillo,

Pérez,

Roldán

2024

New J. Phys.

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“…It is basically a cellular automaton [25] whose updating rules are run by a preset sequence of quantum gates. Given recent experimental advances in the field [26][27][28] as well as their wide range of applications, from quantum algorithms [29] to simulation of involved phenomena in condensed matter physics [15,[30][31][32][33][34], DTQWs make for a suitable starting point.…”

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confidence: 99%

Rogue waves in discrete-time quantum walks

Buarque,

Dias,

de Moura

et al. 2022

Preprint

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Rogue waves are rapid and unpredictable events of exceptional amplitude reported in various fields, such as oceanography and optics, with much of the interest being targeted towards their physical origins and likelihood of occurrence. Here, we use the all-round framework of discrete-time quantum walks to study the onset of those events due to a random phase modulation, unveiling its long-tailed statistics, distribution profile, and dependence upon the degree of randomness. We find that those rogue waves belong the Gumbel family of extreme value distributions.

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Nonlinearity‐Induced Enhancement of Entanglement in Quantum Walk

Ye,

Fei

2024

Adv Quantum Tech

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The quantum entanglement between the coin state and the position in nonlinear quantum walks is investigated. This study reveals that the nonlinearity of the quantum walk has a significant impact on the enhancement of quantum entanglement in an initially separable bipartite system. It is demonstrated that by selecting appropriate nonlinear parameters the initial separable states may turn to be entangled, and even approach to maximal entangled states.

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Emergent nonlinear phenomena in discrete-time quantum walks

Cited by 15 publications

References 62 publications

Bright and dark solitons in a photonic nonlinear quantum walk: lessons from the continuum

Bright and dark solitons in a photonic nonlinear quantum walk: lessons from the continuum

Rogue waves in discrete-time quantum walks

Nonlinearity‐Induced Enhancement of Entanglement in Quantum Walk

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