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Condensed Matter
Special Issues
Quantum Cellular Automata and Quantum Walks
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Quantum Cellular Automata and Quantum Walks

A special issue of Condensed Matter (ISSN 2410-3896).

Deadline for manuscript submissions: closed (28 February 2019) | Viewed by 16224

Special Issue Editors

Prof. Dr. Giacomo D'Ariano

E-Mail Website
Guest Editor
Quit Group, Dipartimento di Fisica, Università degli studi di Pavia, via Bassi 6, 27100 Pavia, Italy
Interests: quantum information; quantum mechanics and foundations of quantum theory
Special Issues, Collections and Topics in MDPI journals
Dr. Alessandro Bisio

E-Mail Website
Guest Editor
Department of Physics, University of Pavia, via Bassi 6, 27100 Pavia, Italy
Interests: quantum information; foundations of quantum mechanics; quantum optics; quantum computing physics
Dr. Alessandro Tosini

E-Mail Website
Guest Editor
QUIT Group, Physics Department, Pavia University, INFN Sezione di Pavia, Via Bassi 6, 27100 Pavia, Italy
Interests: quantum field theory; quantum information; foundations of quantum theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Quantum Cellular Automata (QCAs) and Quantum Walks (QWs) are a versatile platform for various scopes. On one hand, they have been used for empowering quantum algorithms, such as database searches, or graph isomorphisms. On the other hand, QCAs and QWs are among the most promising quantum simulators, with possible realizations in a variety of physical systems, such as nuclear magnetic resonance, trapped ions, integrated photonics, and bulk optics. From a fundamental standpoint, QCAs and QWs are outstanding candidates to understand quantum dynamics from an information-theoretic perspective. In particular, they are the ideal framework for studying the principles of locality and causality of the physical laws. A distinctive feature of the research activity in Quantum Cellular Automata and Quantum Walks is its multidisciplinary nature, linking quantum mechanics, many body physics, particle physics, computer science and discrete mathematics. The goal of this Special Issue is to collect state-of-the-art results on subjects from experiments, theory and simulations and to reveal the role of QCAs and QWs in other related fields.

Regards,

Prof. Giacomo D'Ariano
Dr. Alessandro Bisio
Dr. Alessandro Tosini
Guest Editors

Manuscript Submission Information

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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. Condensed Matter is an international peer-reviewed open access quarterly 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 1600 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 cellular automata
  • quantum walks
  • quantum simulations
  • quantum information
  • quantum algorithms
  • quantum computing
  • quantum optics
  • many body physics

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Published Papers (5 papers)

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Research

18 pages, 307 KiB  
Article
Operational Algorithms for Separable Qubit X States
by Demosthenes Ellinas
Condens. Matter 2019, 4(3), 64; https://doi.org/10.3390/condmat4030064 - 2 Jul 2019
Viewed by 2778
Abstract
This work motivates and applies operational methodology to simulation of quantum statistics of separable qubit X states. Three operational algorithms for evaluating separability probability distributions are put forward. Building on previous findings, the volume function characterizing the separability distribution is determined via quantum [...] Read more.
This work motivates and applies operational methodology to simulation of quantum statistics of separable qubit X states. Three operational algorithms for evaluating separability probability distributions are put forward. Building on previous findings, the volume function characterizing the separability distribution is determined via quantum measurements of multi-qubit observables. Three measuring states, one for each algorithm are generated via (i) a multi-qubit channel map, (ii) a unitary operator generated by a Hamiltonian describing a non-uniform hypergraph configuration of interactions among 12 qubits, and (iii) a quantum walk CP map in a extended state space. Higher order CZ gates are the only tools of the algorithms hence the work associates itself computationally with the Instantaneous Quantum Polynomial-time Circuits (IQP), while wrt possible implementation the work relates to the Lechner-Hauke-Zoller (LHZ) architecture of higher order coupling. Finally some uncertainty aspects of the quantum measurement observables are discussed together with possible extensions to non-qubit separable bipartite systems. Full article
(This article belongs to the Special Issue Quantum Cellular Automata and Quantum Walks)
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16 pages, 473 KiB  
Article
On Quantum Extensions of Hydrodynamic Lattice Gas Automata
by Peter Love
Condens. Matter 2019, 4(2), 48; https://doi.org/10.3390/condmat4020048 - 11 May 2019
Cited by 2 | Viewed by 2930
Abstract
We consider quantum extensions of classical hydrodynamic lattice gas models. We find that the existence of local conserved quantities strongly constrains such extensions. We find the only extensions that retain local conserved quantities correspond to changing the local encoding of a subset of [...] Read more.
We consider quantum extensions of classical hydrodynamic lattice gas models. We find that the existence of local conserved quantities strongly constrains such extensions. We find the only extensions that retain local conserved quantities correspond to changing the local encoding of a subset of the bits. These models maintain separability of the state throughout the evolution and are thus efficiently classically simulable. We then consider evolution of these models in the case where any of the bits can be encoded and measured in one of two local bases. In the case that either encoding is allowed, the models are efficiently classically simulable. In the case that both encoding and measurement is allowed in either basis, we argue that efficient classical simulation is unlikely. In particular, for classical models that are computationally universal such quantum extensions can encode Simon’s algorithm, thus presenting an obstacle to efficient classical simulation. Full article
(This article belongs to the Special Issue Quantum Cellular Automata and Quantum Walks)
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Figure 1

16 pages, 301 KiB  
Article
Discrete Geometry from Quantum Walks
by Fabrice Debbasch
Condens. Matter 2019, 4(2), 40; https://doi.org/10.3390/condmat4020040 - 11 Apr 2019
Cited by 11 | Viewed by 2764
Abstract
A particular family of Discrete Time Quantum Walks (DTQWs) simulating fermion propagation in 2D curved space-time is revisited. Usual continuous covariant derivatives and spin-connections are generalized into discrete covariant derivatives along the lattice coordinates and discrete connections. The concepts of metrics and 2-beins [...] Read more.
A particular family of Discrete Time Quantum Walks (DTQWs) simulating fermion propagation in 2D curved space-time is revisited. Usual continuous covariant derivatives and spin-connections are generalized into discrete covariant derivatives along the lattice coordinates and discrete connections. The concepts of metrics and 2-beins are also extended to the discrete realm. Two slightly different Riemann curvatures are then defined on the space-time lattice as the curvatures of the discrete spin connection. These two curvatures are closely related and one of them tends at the continuous limit towards the usual, continuous Riemann curvature. A simple example is also worked out in full. Full article
(This article belongs to the Special Issue Quantum Cellular Automata and Quantum Walks)
12 pages, 341 KiB  
Article
Quantized Alternate Current on Curved Graphene
by Kyriakos Flouris, Sauro Succi and Hans J. Herrmann
Condens. Matter 2019, 4(2), 39; https://doi.org/10.3390/condmat4020039 - 9 Apr 2019
Cited by 3 | Viewed by 3207
Abstract
Based on the numerical solution of the Quantum Lattice Boltzmann Method in curved space, we predicted the onset of a quantized alternating current on curved graphene sheets. This numerical prediction was verified analytically via a set of semi-classical equations that related the Berry [...] Read more.
Based on the numerical solution of the Quantum Lattice Boltzmann Method in curved space, we predicted the onset of a quantized alternating current on curved graphene sheets. This numerical prediction was verified analytically via a set of semi-classical equations that related the Berry curvature to real space curvature. The proposed quantized oscillating current on curved graphene could form the basis for the implementation of quantum information-processing algorithms. Full article
(This article belongs to the Special Issue Quantum Cellular Automata and Quantum Walks)
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Figure 1

9 pages, 8604 KiB  
Article
A Novel Bulk-Optics Scheme for Quantum Walk with High Phase Stability
by Andrea Geraldi, Luís Diego Bonavena, Carlo Liorni, Paolo Mataloni and Álvaro Cuevas
Condens. Matter 2019, 4(1), 14; https://doi.org/10.3390/condmat4010014 - 18 Jan 2019
Cited by 3 | Viewed by 3674
Abstract
A novel bulk optics scheme for quantum walks is presented. It consists of a one-dimensional lattice built on two concatenated displaced Sagnac interferometers that make it possible to reproduce all the possible trajectories of an optical quantum walk. Because of the closed loop [...] Read more.
A novel bulk optics scheme for quantum walks is presented. It consists of a one-dimensional lattice built on two concatenated displaced Sagnac interferometers that make it possible to reproduce all the possible trajectories of an optical quantum walk. Because of the closed loop configuration, the interferometric structure is intrinsically stable in phase. Moreover, the lattice structure is highly configurable, as any phase component perceived by the walker is accessible, and finally, all output modes can be measured at any step of the quantum walk evolution. We report here on the experimental implementation of ordered and disordered quantum walks. Full article
(This article belongs to the Special Issue Quantum Cellular Automata and Quantum Walks)
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