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Sep 19, 2013
09/13
by
Martin Stefanak
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One of the key features of quantum mechanics is the interference of probability amplitudes. The reason for the appearance of interference is mathematically very simple. It is the linear structure of the Hilbert space which is used for the description of quantum systems. In terms of physics we usually talk about the superposition principle valid for individual and composed quantum objects. So, while the source of interference is understandable it leads in fact to many counter-intuitive physical...
Source: http://arxiv.org/abs/1009.0200v1
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Jun 29, 2018
06/18
by
Martin Stefanak; Stanislav Skoupy
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We consider a quantum walk with two marked vertices, sender and receiver, and analyze its application to perfect state transfer on complete bipartite graphs. First, the situation with both the sender and the receiver vertex in the same part of the graph is considered. We show that in this case the dynamics of the quantum walk is independent of the size of the second part and reduces to the one for the star graph where perfect state transfer is achieved. Second, we consider the situation where...
Topic: Quantum Physics
Source: http://arxiv.org/abs/1610.03633
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Jun 29, 2018
06/18
by
Martin Stefanak; Stanislav Skoupy
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Perfect state transfer between two marked vertices of a graph by means of discrete-time quantum walk is analyzed. We consider the quantum walk search algorithm with two marked vertices, sender and receiver. It is shown by explicit calculation that for the coined quantum walks on star graph and complete graph with self-loops perfect state transfer between the sender and receiver vertex is achieved for arbitrary number of vertices $N$ in $O(\sqrt{N})$ steps of the walk. Finally, we show that...
Topic: Quantum Physics
Source: http://arxiv.org/abs/1608.00498
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Jun 29, 2018
06/18
by
Martin Stefanak; Igor Jex
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We analyze the asymptotic scaling of persistence of unvisited sites for quantum walks on a line. In contrast to the classical random walk there is no connection between the behaviour of persistence and the scaling of variance. In particular, we find that for a two-state quantum walks persistence follows an inverse power-law where the exponent is determined solely by the coin parameter. Moreover, for a one-parameter family of three-state quantum walks containing the Grover walk the scaling of...
Topic: Quantum Physics
Source: http://arxiv.org/abs/1603.05003
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Jun 30, 2018
06/18
by
Martin Stefanak; Iva Bezdekova; Igor Jex
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Properties of the probability distribution generated by a discrete-time quantum walk, such as the number of peaks it contains, depend strongly on the choice of the initial condition. In the present paper we discuss from this point of view the model of the two-dimensional quantum walk analyzed in K. Watabe et al., Phys. Rev. A 77, 062331, (2008). We show that the limit density can be altered in such a way that it vanishes on the boundary or some line. Using this result one can suppress certain...
Topic: Quantum Physics
Source: http://arxiv.org/abs/1701.00408
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Jun 30, 2018
06/18
by
Martin Stefanak; Iva Bezdekova; Igor Jex
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We analyze two families of three-state quantum walks which show the localization effect. We focus on the role of the initial coin state and its coherence in controlling the properties of the quantum walk. In particular, we show that the description of the walk simplifies considerably when the initial coin state is decomposed in the basis formed by the eigenvectors of the coin operator. This allows us to express the limit distributions in a much more convenient form. Consequently, striking...
Topic: Quantum Physics
Source: http://arxiv.org/abs/1405.7146
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Jun 29, 2018
06/18
by
Martin Stefanak; Jaroslav Novotny; Igor Jex
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Coherent transport of excitations along chains of coupled quantum systems represents an interesting problem with a number of applications ranging from quantum optics to solar cell technology. A convenient tool for studying such processes are quantum walks. They allow to determine in a quantitative way all the process features. We study the survival probability and the transport efficiency on a simple, highly symmetric graph represented by a ring. The propagation of excitation is modeled by a...
Topic: Quantum Physics
Source: http://arxiv.org/abs/1602.04678
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Jun 28, 2018
06/18
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Iva Bezdekova; Martin Stefanak; Igor Jex
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The analysis of a physical problem simplifies considerably when one uses a suitable coordinate system. We apply this approach to the discrete-time quantum walks with coins given by $2j+1$-dimensional Wigner rotation matrices (Wigner walks), a model which was introduced in T. Miyazaki et al., Phys. Rev. A 76, 012332 (2007). First, we show that from the three parameters of the coin operator only one is physically relevant for the limit density of the Wigner walk. Next, we construct a suitable...
Topic: Quantum Physics
Source: http://arxiv.org/abs/1509.00960
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Sep 21, 2013
09/13
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Martin Stefanak; Tamas Kiss; Igor Jex
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The Polya number of a classical random walk on a regular lattice is known to depend solely on the dimension of the lattice. For one and two dimensions it equals one, meaning unit probability to return to the origin. This result is extremely sensitive to the directional symmetry, any deviation from the equal probability to travel in each direction results in a change of the character of the walk from recurrent to transient. Applying our definition of the Polya number to quantum walks on a line...
Source: http://arxiv.org/abs/0902.3600v2
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Sep 22, 2013
09/13
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Martin Stefanak; Tamas Kiss; Igor Jex
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The P\'olya number characterizes the recurrence of a random walk. We apply the generalization of this concept to quantum walks [M. \v{S}tefa\v{n}\'ak, I. Jex and T. Kiss, Phys. Rev. Lett. \textbf{100}, 020501 (2008)] which is based on a specific measurement scheme. The P\'olya 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 dimension uniquely determines it. We analyze several examples to...
Source: http://arxiv.org/abs/0805.1322v2
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Sep 23, 2013
09/13
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Peter P. Rohde; Andreas Schreiber; Martin Stefanak; Igor Jex; Christine Silberhorn
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Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more naturally to some physical implementations, such as linear optics. Numerous authors have considered walks with one or two walkers, on one dimensional graphs, and several experimental demonstrations have been performed. In this paper we discuss generalizing...
Source: http://arxiv.org/abs/1006.5556v2
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Sep 20, 2013
09/13
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Peter P. Rohde; Andreas Schreiber; Martin Stefanak; Igor Jex; Alexei Gilchrist; Christine Silberhorn
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We show that with the addition of multiple walkers, quantum walks on a line can be transformed into lattice graphs of higher dimension. Thus, multi-walker walks can simulate single-walker walks on higher dimensional graphs and vice versa. This exponential complexity opens up new applications for present-day quantum walk experiments. We discuss the applications of such higher-dimensional structures and how they relate to linear optics quantum computing. In particular we show that multi-walker...
Source: http://arxiv.org/abs/1205.1850v1
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Sep 21, 2013
09/13
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Andreas Schreiber; Aurel Gabris; Peter P. Rohde; Kaisa Laiho; Martin Stefanak; Vaclav Potocek; Craig Hamilton; Igor Jex; Christine Silberhorn
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Multi-dimensional quantum walks can exhibit highly non-trivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a 2D optical quantum walk on a lattice, demonstrating a scalable quantum walk on a non-trivial graph structure. We realized a coherent quantum walk over 12 steps and 169 positions using an optical fiber network. With our broad spectrum of quantum coins we were able to simulate the...
Source: http://arxiv.org/abs/1204.3555v1
