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Entropy
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Quantum Walks for Quantum Technologies
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Quantum Walks for Quantum Technologies

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

Deadline for manuscript submissions: 10 April 2025 | Viewed by 6688

Special Issue Editors

Dr. Luca Razzoli

E-Mail Website
Guest Editor
1. Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell’Insubria, via Valleggio 11, 22100 Como, Italy
2. Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria 16, 20133 Milano, Italy
Interests: quantum walks; quantum thermodynamics; quantum metrology
Dr. Paolo Bordone

E-Mail Website
Guest Editor
1. Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università degli Studi di Modena e Reggio Emilia, via Campi 213/A, 41125 Modena, Italy
2. Centro S3, CNR-Istituto di Nanoscienze, via Campi 213/A, 41125 Modena, Italy
Interests: coherent and noisy quantum dynamics; quantum walks; quantum transport; electron quantum optics; complex quantum systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The first quantum revolution—the understanding of the physical laws in the microscopic, quantum realm—created all the core technologies of our modern society. Nowadays, the possibility of manipulating individual quantum systems has paved the way for the second quantum revolution, which aims to fully harness quantum phenomena to develop radically new quantum technologies.

Quantum walks (QWs)—the quantum counterpart of classical random walks—are a concept as simple as they are powerful: They describe the propagation of a quantum particle over a discrete space subject to given constraints. A rich plethora of different QWs have stemmed from such a seminal idea, such as continuous or discrete time, chiral, lackadaisical, stochastic, topological, etc., denoting an increasing interest in the topic from several research areas and a diversification of possible applications.

Their versatility and peculiar quantum features have made them paradigmatic models in quantum technologies. In recent years, QWs have been widely used in modelling the transport of excitation and information across networks, and they have proven to be a universal model for quantum computation and to provide speed-up in quantum algorithms, for e.g., spatial search. Proposals of quantum communication protocols and public-key cryptographic systems based on QWs have been put forward, in addition to their use as quantum probes and as quantum simulation schemes having been foreseen.

In this spirit, the present Special Issue is devoted to presenting the current theoretical and experimental state of the art surrounding the role of QWs in the four leading areas of quantum technologies. Original unpublished research articles and review articles are therefore invited on these topics:

(i) Quantum communication;

(ii) Quantum computation;

(iii) Quantum simulation;

(iv) Quantum metrology, sensing, and imaging;

(v) Quantum control;

(vi) Quantum software and theory;

topics (v) and (vi) have been included as they are both important areas of research that cut across all four leading areas (i–iv).

Dr. Luca Razzoli
Dr. Paolo Bordone
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
  • multiparticle quantum walks
  • quantum algorithms
  • quantum estimation
  • quantum cryptography
  • quantum networks
  • quantum transport
  • quantum information
  • quantum optics
  • entanglement

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Published Papers (3 papers)

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Research

28 pages, 9040 KiB  
Article
First Hitting Times on a Quantum Computer: Tracking vs. Local Monitoring, Topological Effects, and Dark States
by Qingyuan Wang, Silin Ren, Ruoyu Yin, Klaus Ziegler, Eli Barkai and Sabine Tornow
Entropy 2024, 26(10), 869; https://doi.org/10.3390/e26100869 - 16 Oct 2024
Cited by 4 | Viewed by 1359
Abstract
We investigate a quantum walk on a ring represented by a directed triangle graph with complex edge weights and monitored at a constant rate until the quantum walker is detected. To this end, the first hitting time statistics are recorded using unitary dynamics [...] Read more.
We investigate a quantum walk on a ring represented by a directed triangle graph with complex edge weights and monitored at a constant rate until the quantum walker is detected. To this end, the first hitting time statistics are recorded using unitary dynamics interspersed stroboscopically by measurements, which are implemented on IBM quantum computers with a midcircuit readout option. Unlike classical hitting times, the statistical aspect of the problem depends on the way we construct the measured path, an effect that we quantify experimentally. First, we experimentally verify the theoretical prediction that the mean return time to a target state is quantized, with abrupt discontinuities found for specific sampling times and other control parameters, which has a well-known topological interpretation. Second, depending on the initial state, system parameters, and measurement protocol, the detection probability can be less than one or even zero, which is related to dark-state physics. Both return-time quantization and the appearance of the dark states are related to degeneracies in the eigenvalues of the unitary time evolution operator. We conclude that, for the IBM quantum computer under study, the first hitting times of monitored quantum walks are resilient to noise. However, a finite number of measurements leads to broadening effects, which modify the topological quantization and chiral effects of the asymptotic theory with an infinite number of measurements. Full article
(This article belongs to the Special Issue Quantum Walks for Quantum Technologies)
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20 pages, 1986 KiB  
Article
Continuous-Time Quantum Walk in Glued Trees: Localized State-Mediated Almost Perfect Quantum-State Transfer
by Vincent Pouthier, Lucie Pepe and Saad Yalouz
Entropy 2024, 26(6), 490; https://doi.org/10.3390/e26060490 - 2 Jun 2024
Viewed by 1001
Abstract
In this work, the dynamics of a quantum walker on glued trees is revisited to understand the influence of the architecture of the graph on the efficiency of the transfer between the two roots. Instead of considering regular binary trees, we focus our [...] Read more.
In this work, the dynamics of a quantum walker on glued trees is revisited to understand the influence of the architecture of the graph on the efficiency of the transfer between the two roots. Instead of considering regular binary trees, we focus our attention on leafier structures where each parent node could give rise to a larger number of children. Through extensive numerical simulations, we uncover a significant dependence of the transfer on the underlying graph architecture, particularly influenced by the branching rate (M) relative to the root degree (N). Our study reveals that the behavior of the walker is isomorphic to that of a particle moving on a finite-size chain. This chain exhibits defects that originate in the specific nature of both the roots and the leaves. Therefore, the energy spectrum of the chain showcases rich features, which lead to diverse regimes for the quantum-state transfer. Notably, the formation of quasi-degenerate localized states due to significant disparities between M and N triggers a localization process on the roots. Through analytical development, we demonstrate that these states play a crucial role in facilitating almost perfect quantum beats between the roots, thereby enhancing the transfer efficiency. Our findings offer valuable insights into the mechanisms governing quantum-state transfer on trees, with potential applications for the transfer of quantum information. Full article
(This article belongs to the Special Issue Quantum Walks for Quantum Technologies)
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24 pages, 1352 KiB  
Article
Efficient Implementation of Discrete-Time Quantum Walks on Quantum Computers
by Luca Razzoli, Gabriele Cenedese, Maria Bondani and Giuliano Benenti
Entropy 2024, 26(4), 313; https://doi.org/10.3390/e26040313 - 2 Apr 2024
Cited by 3 | Viewed by 2697
Abstract
Quantum walks have proven to be a universal model for quantum computation and to provide speed-up in certain quantum algorithms. The discrete-time quantum walk (DTQW) model, among others, is one of the most suitable candidates for circuit implementation due to its discrete nature. [...] Read more.
Quantum walks have proven to be a universal model for quantum computation and to provide speed-up in certain quantum algorithms. The discrete-time quantum walk (DTQW) model, among others, is one of the most suitable candidates for circuit implementation due to its discrete nature. Current implementations, however, are usually characterized by quantum circuits of large size and depth, which leads to a higher computational cost and severely limits the number of time steps that can be reliably implemented on current quantum computers. In this work, we propose an efficient and scalable quantum circuit implementing the DTQW on the 2n-cycle based on the diagonalization of the conditional shift operator. For t time steps of the DTQW, the proposed circuit requires only O(n2+nt) two-qubit gates compared to the O(n2t) of the current most efficient implementation based on quantum Fourier transforms. We test the proposed circuit on an IBM quantum device for a Hadamard DTQW on the 4-cycle and 8-cycle characterized by periodic dynamics and by recurrent generation of maximally entangled single-particle states. Experimental results are meaningful well beyond the regime of few time steps, paving the way for reliable implementation and use on quantum computers. Full article
(This article belongs to the Special Issue Quantum Walks for Quantum Technologies)
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