Quantum walks on random lattices: Diffusion, localization, and the absence of parametric quantum speedup

Duda, Rostislav; Ivaki, Moein N.; Sahlberg, Isac; Pöyhönen, Kim; Ojanen, Teemu

doi:10.1103/physrevresearch.5.023150

Cited by 3 publications

(1 citation statement)

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“…The influence of static percolation on the efficiency of the discrete-time quantum walk search was studied in [26]. 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].…”

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%