Decoherence on staggered quantum walks

Santos, Raqueline A. M.; Marquezino, Franklin de Lima

doi:10.1103/physreva.105.032452

Cited by 3 publications

(2 citation statements)

References 27 publications

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“…The effect of static percolation of the square lattice on the spreading properties of a discrete quantum walk was recently investigated in [27]. In the staggered model of the discrete time quantum walks percolation was introduced recently [28]. In the continuous time case, the influence of static percolation [29][30][31][32] and dynamical percolation [33][34][35] was also thoroughly investigated.…”

Section: Introductionmentioning

confidence: 99%

Two-particle Hadamard walk on dynamically percolated line and circle

Parýzková,

Štefaňák,

Novotný

et al. 2024

Phys. Scr.

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Asymptotic dynamics of a Hadamard walk of two non-interacting quantum particles on a dynamically percolated finite line or a circle is investigated. We construct a basis of the attractor space of the corresponding random-unitary dynamics and prove the completeness of our solution. In comparison to the one-particle case, the structure of the attractor space is much more complex, resulting in intriguing asymptotic dynamics. General results are illustrated on two examples. First, for circles of length not divisible by 4 the boundary conditions reduces the number of attractors considerably, allowing for fully analytic solution. Second, we investigate line of length 4 and determine the asymptotic cycle of reduced coin states and position distributions, focusing on the correlations between the two particles. Our results show that a random unitary evolution, which is a combination of quantum dynamics and a classical stochasticity, leads to correlations between initially uncorrelated particles. This is not possible for purely unitary evolution of non-interacting quantum particles. The shared dynamically percolated graph can thus be considered as a weak form of interaction.

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Section: Introductionmentioning

confidence: 99%

Two-particle Hadamard walk on dynamically percolated line and circle

Parýzková,

Štefaňák,

Novotný

et al. 2024

Phys. Scr.

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“…Oliveira A C et al [28] analyzed the decoherence of quantum walks in twodimensional lattices caused by broken-line-type noise. After that, decoherence based on twodimensional quantum walks has been well studied [29][30][31][32][33][34]. Dmitry Solenov and Leonid Fedichkin [35] proposed an analytical approach to decoherent continuous-time quantum walks on cycle.…”

Section: Introductionmentioning

confidence: 99%

Continuous-time quantum walk based on cycle under broken-line decoherent noise

Shi,

Tian,

Zhou

et al. 2023

Indian J Phys

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At present, decoherence continuous-time quantum walks are only based on measurement decoherence, but a new broken-line noise model for continuous-time quantum walks on the cycle is proposed. In this scheme, we first construct the Hamiltonian H according to four cases including no broken links, the link to the left of the node is broken, the link to the right of the node is broken, and both links are broken, and then the probability of a walker is reconstructed. The analysis shows that with the increase of the probability of disconnection, the oscillation of the walk gradually weakens and becomes a peak distribution, and with the continuous increase of the walk time, the probability distribution of each vertex tends to be uniform. In addition, we also analyze the mixing time of this walk model and find that a small amount of broken chain decoherence can help reduce the mixing time, thereby improving the performance of quantum walks.

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An Algebraic Model for Simulation of Percolation Decoherence on Quantum-Walk-Based Search Algorithms

Vieira,

Lopes,

Maculan

et al. 2024

Anais Do IX Encontro De Teoria Da Computação (ETC 2024)

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In this paper, we propose a linear algebra based model for percolation noise simulation in quantum-walk-based searches to analyze the impact on the success probability of the search. The model was built to allow an open and simultaneous simulation of any type of noise that represents an edge-break, which we show to be a well-behaved family of permutation matrices that maintain a particular set theory relation when acting as some system evolution operators. The simulation evolves using only linear algebra operations, opening avenues for easier analyses of unexpected observed convergence behaviour. As a use case, we investigate the simulation of a lackadaisical quantum walk with percolation noise.

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Decoherence on staggered quantum walks

Cited by 3 publications

References 27 publications

Two-particle Hadamard walk on dynamically percolated line and circle

Two-particle Hadamard walk on dynamically percolated line and circle

Continuous-time quantum walk based on cycle under broken-line decoherent noise

An Algebraic Model for Simulation of Percolation Decoherence on Quantum-Walk-Based Search Algorithms

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