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Entropy
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Quantum Walks and Related Issues
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Quantum Walks and Related Issues

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (15 December 2019) | Viewed by 20779

Special Issue Editors

Prof. Dr. Gregg Jaeger

E-Mail Website
Guest Editor
Quantum Communication and Measurement Laboratory, Department of Electrical and Computer Engineering and Division of Natural Science and Mathematics, Boston University, Boston, MA 02215, USA
Interests: quantum information; foundations of quantum mechanics; quantum cryptography; quantum metrology; history and philosophy of science; quantum optics; stochastic processes; genetics
Special Issues, Collections and Topics in MDPI journals
Dr. David S. Simon

E-Mail Website
Guest Editor
1 Department of Physics and Astronomy, Stonehill College, Easton, MA 02357, USA
2 Department of Electrical and Computer Engineering and Photonics Center, Boston University, Boston, MA 02215, USA
Interests: quantum optics; quantum mechanics; quantum field theory; theoretical physics; optical engineering
Prof. Alexander V. Sergienko

E-Mail Website
Guest Editor
Department of Electrical and Computer Engineering and Physics, Boston University, Boston, MA 02215, USA
Interests: quantum information; quantum communication and cryptography; quantum networking; quantum imaging; linear-optical quantum computing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleague,

Quantum walks have been systematically studied for over 20 years and display many distinct features that distinguish them from classical random walks. They have become of increasing interest over time due to their potential use in quantum information science, for example, in implementation of quantum algorithms and in conducting quantum simulations of other systems. In particular, multi-particle quantum walks have been shown to be capable of universal quantum computation.

Quantum walks have been implemented in many types of physical systems, ranging from nuclear magnetic resonance and trapped atoms to linear optics. Recent research has explored walks in higher dimensions, in complex networks, and with multiple walkers, including entangled walkers. Beyond walks in position space, quantum walks in more exotic variables such as optical orbital angular momentum have been implemented.

As quantum walks grow to touch on more areas of research, a fresh perspective on the current state of the field and of research in related areas is timely. The goal of this Special Issue is to provide a guide to the field and a sampling of recent developments. This issue covers all aspects of quantum walks and their applications with special emphasis on recent work on photonic walks.

Prof. Gregg Jaeger
Dr. David S. Simon
Prof. Alexander Sergienko
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • quantum walks, photonic walks
  • linear optical systems
  • quantum information processing
  • quantum simulation
  • random walks
  • quantum algorithms

Published Papers (5 papers)

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Research

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13 pages, 4382 KiB  
Article
Eigenvalues of Two-State Quantum Walks Induced by the Hadamard Walk
by Shimpei Endo, Takako Endo, Takashi Komatsu and Norio Konno
Entropy 2020, 22(1), 127; https://0-doi-org.brum.beds.ac.uk/10.3390/e22010127 - 20 Jan 2020
Cited by 7 | Viewed by 3681
Abstract
Existence of the eigenvalues of the discrete-time quantum walks is deeply related to localization of the walks. We revealed, for the first time, the distributions of the eigenvalues given by the splitted generating function method (the SGF method) of the space-inhomogeneous quantum walks [...] Read more.
Existence of the eigenvalues of the discrete-time quantum walks is deeply related to localization of the walks. We revealed, for the first time, the distributions of the eigenvalues given by the splitted generating function method (the SGF method) of the space-inhomogeneous quantum walks in one dimension we had treated in our previous studies. Especially, we clarified the characteristic parameter dependence for the distributions of the eigenvalues with the aid of numerical simulation. Full article
(This article belongs to the Special Issue Quantum Walks and Related Issues)
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17 pages, 372 KiB  
Article
Can a Quantum Walk Tell Which Is Which?A Study of Quantum Walk-Based Graph Similarity
by Giorgia Minello, Luca Rossi and Andrea Torsello
Entropy 2019, 21(3), 328; https://0-doi-org.brum.beds.ac.uk/10.3390/e21030328 - 26 Mar 2019
Cited by 11 | Viewed by 4004
Abstract
We consider the problem of measuring the similarity between two graphs using continuous-time quantum walks and comparing their time-evolution by means of the quantum Jensen-Shannon divergence. Contrary to previous works that focused solely on undirected graphs, here we consider the case of both [...] Read more.
We consider the problem of measuring the similarity between two graphs using continuous-time quantum walks and comparing their time-evolution by means of the quantum Jensen-Shannon divergence. Contrary to previous works that focused solely on undirected graphs, here we consider the case of both directed and undirected graphs. We also consider the use of alternative Hamiltonians as well as the possibility of integrating additional node-level topological information into the proposed framework. We set up a graph classification task and we provide empirical evidence that: (1) our similarity measure can effectively incorporate the edge directionality information, leading to a significant improvement in classification accuracy; (2) the choice of the quantum walk Hamiltonian does not have a significant effect on the classification accuracy; (3) the addition of node-level topological information improves the classification accuracy in some but not all cases. We also theoretically prove that under certain constraints, the proposed similarity measure is positive definite and thus a valid kernel measure. Finally, we describe a fully quantum procedure to compute the kernel. Full article
(This article belongs to the Special Issue Quantum Walks and Related Issues)
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19 pages, 2139 KiB  
Article
Quantum-Inspired Evolutionary Approach for the Quadratic Assignment Problem
by Wojciech Chmiel and Joanna Kwiecień
Entropy 2018, 20(10), 781; https://0-doi-org.brum.beds.ac.uk/10.3390/e20100781 - 12 Oct 2018
Cited by 15 | Viewed by 4388
Abstract
The paper focuses on the opportunity of the application of the quantum-inspired evolutionary algorithm for determining minimal costs of the assignment in the quadratic assignment problem. The idea behind the paper is to present how the algorithm has to be adapted to this [...] Read more.
The paper focuses on the opportunity of the application of the quantum-inspired evolutionary algorithm for determining minimal costs of the assignment in the quadratic assignment problem. The idea behind the paper is to present how the algorithm has to be adapted to this problem, including crossover and mutation operators and introducing quantum principles in particular procedures. The results have shown that the performance of our approach in terms of converging to the best solutions is satisfactory. Moreover, we have presented the results of the selected parameters of the approach on the quality of the obtained solutions. Full article
(This article belongs to the Special Issue Quantum Walks and Related Issues)
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Review

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32 pages, 3579 KiB  
Review
Directionally-Unbiased Unitary Optical Devices in Discrete-Time Quantum Walks
by Shuto Osawa, David S. Simon and Alexander V. Sergienko
Entropy 2019, 21(9), 853; https://0-doi-org.brum.beds.ac.uk/10.3390/e21090853 - 31 Aug 2019
Cited by 6 | Viewed by 3215
Abstract
The optical beam splitter is a widely-used device in photonics-based quantum information processing. Specifically, linear optical networks demand large numbers of beam splitters for unitary matrix realization. This requirement comes from the beam splitter property that a photon cannot go back out of [...] Read more.
The optical beam splitter is a widely-used device in photonics-based quantum information processing. Specifically, linear optical networks demand large numbers of beam splitters for unitary matrix realization. This requirement comes from the beam splitter property that a photon cannot go back out of the input ports, which we call “directionally-biased”. Because of this property, higher dimensional information processing tasks suffer from rapid device resource growth when beam splitters are used in a feed-forward manner. Directionally-unbiased linear-optical devices have been introduced recently to eliminate the directional bias, greatly reducing the numbers of required beam splitters when implementing complicated tasks. Analysis of some originally directional optical devices and basic principles of their conversion into directionally-unbiased systems form the base of this paper. Photonic quantum walk implementations are investigated as a main application of the use of directionally-unbiased systems. Several quantum walk procedures executed on graph networks constructed using directionally-unbiased nodes are discussed. A significant savings in hardware and other required resources when compared with traditional directionally-biased beam-splitter-based optical networks is demonstrated. Full article
(This article belongs to the Special Issue Quantum Walks and Related Issues)
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17 pages, 653 KiB  
Review
Photonic Discrete-time Quantum Walks and Applications
by Leonardo Neves and Graciana Puentes
Entropy 2018, 20(10), 731; https://0-doi-org.brum.beds.ac.uk/10.3390/e20100731 - 24 Sep 2018
Cited by 16 | Viewed by 4550
Abstract
We present a review of photonic implementations of discrete-time quantum walks (DTQW) in the spatial and temporal domains, based on spatial- and time-multiplexing techniques, respectively. Additionally, we propose a detailed novel scheme for photonic DTQW, using transverse spatial modes of single photons and [...] Read more.
We present a review of photonic implementations of discrete-time quantum walks (DTQW) in the spatial and temporal domains, based on spatial- and time-multiplexing techniques, respectively. Additionally, we propose a detailed novel scheme for photonic DTQW, using transverse spatial modes of single photons and programmable spatial light modulators (SLM) to manipulate them. Unlike all previous mode-multiplexed implementations, this scheme enables simulation of an arbitrary step of the walker, only limited, in principle, by the SLM resolution. We discuss current applications of such photonic DTQW architectures in quantum simulation of topological effects and the use of non-local coin operations based on two-photon hybrid entanglement. Full article
(This article belongs to the Special Issue Quantum Walks and Related Issues)
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