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Entropy
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Quantum Walks: Applications and Fundamentals
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Quantum Walks: Applications and Fundamentals

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

Deadline for manuscript submissions: closed (31 March 2022) | Viewed by 6726

Special Issue Editor

Dr. Giuseppe Di Molfetta

E-Mail Website
Guest Editor
CNRS, LIS, Aix-Marseille Université, 13000 Marseille, France
Interests: natural computing; discrete dynamical system; quantum simulation; quantum algorithms

Special Issue Information

Dear Colleagues,

Quantum walks (QWs), and their generalizations, the multiparticle quantum lattice gas automata (QLGA), and the quantum cellular automata (QCA), underlie simulations of physics, many a search algorithm, and are participants in aspects of quantum machine learning (QML). The emergence of quantum devices presents opportunities to extend the reach of classical computing through quantum algorithms. Often, techniques developed to simulate fundamental physics, among them QW and QCA, find applications in quantum/hybrid algorithms and accelerate optimizations. In the current noisy intermediate-scale quantum (NISQ) regime of quantum devices, competing criteria of noise and decoherence and the availability of limited resources must be considered in simulations, and QWs are no exception. Circuits for QWs will avail quantum error correction (QEC)-based schemes for fault tolerance in the future, when a higher number of qubits, error-corrected, are available.

Considering the recent advances achieved in the field of QW, this Special Issue will collect new ideas and describe promising methods arising from the field of QW-based quantum computation and quantum simulation.

This Special Issue will accept unpublished original papers and comprehensive reviews focused on (but not restricted to) the following research areas, where QW and QCA play a main role:

  • QW- or (QCA-) based quantum simulation;
  • QW-based quantum algorithmics with and without QEC;
  • Fault-tolerant quantum cellular automata;
  • QW and their application to quantum machine learning;
  • QW and their application to quantum communication and cryptography.

Dr. Giuseppe Di Molfetta
Guest Editor

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
  • quantum cellular automata
  • quantum simulation
  • quantum algorithmics

Published Papers (3 papers)

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Research

12 pages, 278 KiB  
Article
Return Probability of Quantum and Correlated Random Walks
by Chusei Kiumi, Norio Konno and Shunya Tamura
Entropy 2022, 24(5), 584; https://doi.org/10.3390/e24050584 - 21 Apr 2022
Cited by 3 | Viewed by 1512
Abstract
The analysis of the return probability is one of the most essential and fundamental topics in the study of classical random walks. In this paper, we study the return probability of quantum and correlated random walks in the one-dimensional integer lattice by the [...] Read more.
The analysis of the return probability is one of the most essential and fundamental topics in the study of classical random walks. In this paper, we study the return probability of quantum and correlated random walks in the one-dimensional integer lattice by the path counting method. We show that the return probability of both quantum and correlated random walks can be expressed in terms of the Legendre polynomial. Moreover, the generating function of the return probability can be written in terms of elliptic integrals of the first and second kinds for the quantum walk. Full article
(This article belongs to the Special Issue Quantum Walks: Applications and Fundamentals)
11 pages, 3216 KiB  
Article
Dirac Spatial Search with Electric Fields
by Julien Zylberman and Fabrice Debbasch
Entropy 2021, 23(11), 1441; https://doi.org/10.3390/e23111441 - 31 Oct 2021
Cited by 3 | Viewed by 1937
Abstract
Electric Dirac quantum walks, which are a discretisation of the Dirac equation for a spinor coupled to an electric field, are revisited in order to perform spatial searches. The Coulomb electric field of a point charge is used as a non local oracle [...] Read more.
Electric Dirac quantum walks, which are a discretisation of the Dirac equation for a spinor coupled to an electric field, are revisited in order to perform spatial searches. The Coulomb electric field of a point charge is used as a non local oracle to perform a spatial search on a 2D grid of N points. As other quantum walks proposed for spatial search, these walks localise partially on the charge after a finite period of time. However, contrary to other walks, this localisation time scales as N for small values of N and tends asymptotically to a constant for larger Ns, thus offering a speed-up over conventional methods. Full article
(This article belongs to the Special Issue Quantum Walks: Applications and Fundamentals)
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13 pages, 761 KiB  
Article
Quantum Walk on the Generalized Birkhoff Polytope Graph
by Rafael Cação, Lucas Cortez, Ismael de Farias, Ernee Kozyreff, Jalil Khatibi Moqadam and Renato Portugal
Entropy 2021, 23(10), 1239; https://doi.org/10.3390/e23101239 - 23 Sep 2021
Viewed by 2060
Abstract
We study discrete-time quantum walks on generalized Birkhoff polytope graphs (GBPGs), which arise in the solution-set to certain transportation linear programming problems (TLPs). It is known that quantum walks mix at most quadratically faster than random walks on cycles, two-dimensional lattices, hypercubes, and [...] Read more.
We study discrete-time quantum walks on generalized Birkhoff polytope graphs (GBPGs), which arise in the solution-set to certain transportation linear programming problems (TLPs). It is known that quantum walks mix at most quadratically faster than random walks on cycles, two-dimensional lattices, hypercubes, and bounded-degree graphs. In contrast, our numerical results show that it is possible to achieve a greater than quadratic quantum speedup for the mixing time on a subclass of GBPG (TLP with two consumers and m suppliers). We analyze two types of initial states. If the walker starts on a single node, the quantum mixing time does not depend on m, even though the graph diameter increases with it. To the best of our knowledge, this is the first example of its kind. If the walker is initially spread over a maximal clique, the quantum mixing time is O(m/ϵ), where ϵ is the threshold used in the mixing times. This result is better than the classical mixing time, which is O(m1.5/ϵ). Full article
(This article belongs to the Special Issue Quantum Walks: Applications and Fundamentals)
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