2024 Recurrence and pólya number of quantum walks

Recurrence and pólya number of quantum walks

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August undefined, 2024

WebbThe recurrence probability P ≡ limT → ∞ P(T) is called Pólya number. A walk is called recurrent if the walker returns to the origin with certainty, that is, if its Pólya number equals unity ( P = 1). As shown by Pólya, unbiased random walks on a line and a … WebbRecurrences in Quantum Walks. EN. English Deutsch Français Español Português Italiano Român Nederlands Latina Dansk Svenska Norsk Magyar Bahasa Indonesia Türkçe Suomi Latvian Lithuanian česk ...

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Webb16 juni 2010 · PDF We propose a definition for the P\'olya number of continuous-time quantum walks to characterize their recurrence properties. The definition... Find, read … Webb15 juli 2012 · We review the main aspects of a recent approach to quantum walks, the CGMV method. This method proceeds by reducing the unitary evolution to canonical form, given by the so-called CMV matrices, which act as a link to the theory of orthogonal polynomials on the unit circle. This connection allows one to obtain results for quantum … dr physicians

The CGMV method for quantum walks SpringerLink

WebbRecurrence in the classical random walk is well known and described by the Pólya number. For quantum walks, recurrence is similarly understood in terms of the probability of a localized quantum walker to returntoitsorigin.Undercertaincircumstancesthequantumwalkermayalsoreturntoanarbitraryinitial … WebbRecurrence of a random walk is described by the Pólya number. For quantum walks, recurrence is understood as the return of the walker to the origin, rather than the full revival of its quantum state. Localization for two-dimensional quantum walks is known to exist in the sense of non-vanishing probability distribution in the asymptotic limit. WebbRecurrence and Pólya Number of Quantum Walks. We analyze the recurrence probability (Pólya number) for d-dimensional unbiased quantum walks. A sufficient condition for a … college internship cover letter

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Maneuvering periods of 2D quantum walks with the coin operator

Webbrandom walks. Of these walks, we are interested in the ones that return to 0. Let j= the number of steps in direction (1;0;0) k= the number of steps in the direction (0;1;0) In order to return to 0 after the 2nsteps, there must be an even number of moves in each axis direction, and an equal number in the positive and negative directions for ... Webb19 juli 2024 · The evolution of the Pólya number undergoes a rapid growth at first and a subsequent plateau before 3.875 mm, which is the same as the Pólya number for the regular case (see Supplementary Fig. 17). dr physio websiteWebb16 juni 2010 · We propose a definition for the Pólya number of continuous-time quantum walks to characterize their recurrence properties. The definition involves a series of … college internship at fbi

"Webb9 maj 2008 · The Pólya number of a quantum walk depends in general on the choice of the coin and the initial coin state, in contrast to classical random walks where the lattice … " - Recurrence and pólya number of quantum walks

Recurrence and pólya number of quantum walks

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Webb14 okt. 2009 · Štefaňák M., Jex I., Kiss T.: Recurrence and Pólya number of quantum walks. Phys. Rev. Lett. 100, 020501 (2008) Article PubMed Google Scholar Štefaňák M., Kiss T., Jex I.: Recurrence properties of unbiased coined quantum walks on infinite d -dimensional lattices. Phys. Rev. A 78, 032306 (2008) Article ADS Google Scholar Webb18 jan. 2008 · We analyze the recurrence probability (Pólya number) for d-dimensional unbiased quantum walks. A sufficient condition for a quantum walk to be recurrent is …

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WebbThe recurrence properties of random walks can be characterized by Pólya number, i.e., the probability that the walker has returned to the origin at least once. In this paper, we consider recurrence properties for a general 1D random walk on a line, in which at each time step the walker can move to the left or right with probabilities l and r, or remain at … Webb14 maj 2007 · Title: Recurrence and Pólya number of quantum walks. Authors: M. Stefanak, I. Jex, T. Kiss (Submitted on 14 May 2007 , last revised 2 Oct 2007 (this version, v2)) Abstract: We analyze the recurrence probability (P\'olya number) for d-dimensional unbiased quantum walks.

WebbRecurrence of quantum walks on lattices can be characterized by the generalized Pólya number. Its value reflects the difference between a classical and a quantum system. Webb3 sep. 2008 · The Pólya number of a quantum walk depends, in general, on the choice of the coin and the initial coin state, in contrast to classical random walks where the …

Webb19 mars 2014 · A notion of monitored recurrence for discrete-time quantum processes was recently introduced in Grünbaum et al. (Commun Math Phys (2), 320:543–569, 2013) taking the initial state as an absorbing one. We extend this notion of monitored recurrence to absorbing subspaces of arbitrary finite dimension. WebbWe analyze the recurrence probability (Pólya number) for d-dimensional unbiased quantum walks. A sufficient condition for a quantum walk to be recurrent is derived. As a by-product we find a simple criterion for localisation of quantum walks. In contrast to classical walks, where the Pólya number is characteristic for the given dimension, the recurrence …

Webb28 maj 2024 · A lattice random walk is a mathematical representation of movement through random steps on a lattice at discrete times. It is commonly referred to as Pólya’s walk when the steps occur in either of the nearest-neighbor sites.

WebbWe analyze the recurrence probability (P\\'olya number) for d-dimensional unbiased quantum walks. A sufficient condition for a quantum walk to be recurrent is... college internship interview questionsWebb1 jan. 2014 · Recurrence in the classical random walk is well known and described by the Pólya number. For quantum walks, recurrence is similarly understood in terms of the probability of a localized quantum walker to return to its origin. dr physio leg massagerWebbRecurrence in the classical random walk is well known and described by the Pólya number. For quantum walks, recurrence is similarly understood in terms of the probability of a localized quantum walker to return to its origin. drphysicsa particle physics 3Webb1 mars 2012 · The recurrence properties of random walks can be characterized by Pólya number, i.e., the probability that the walker has returned to the origin at least once.In this paper, we investigate Pólya number and first return for bursty random walk on a line, in which the walk has different step size and moving probabilities. drphysicsa particle physicsWebbWe propose a definition for the Pólya number of continuous-time quantum walks to characterize their recurrence properties. The definition involves a series of measurements on the system, each carried out on a different member from an ensemble in order to minimize the disturbance caused by it. We examine various graphs, including the ring, … college internship finderWebb14 jan. 2008 · We analyze the recurrence probability (Pólya number) for d -dimensional unbiased quantum walks. A sufficient condition for a quantum walk to be recurrent is … dr phyu lwinWebb10 jan. 2024 · quantum walk er to return to its origin is studied in Ref. [36, 37]. ... Recurrence in a classical random walk is characterized b y the Pólya number [28], which can be written as. dr physio supervolt 1029