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arxiv: 2511.14513 · v2 · submitted 2025-11-18 · 🪐 quant-ph

Link prediction with swarms of chiral quantum walks

Gaia Forghieri , Viacheslav Dubovitskii , Matteo A. C. Rossi , Matteo G. A. Paris This is my paper

Pith reviewed 2026-05-17 20:55 UTC · model grok-4.3

classification 🪐 quant-ph
keywords link predictionchiral quantum walksswarm algorithmsprotein-protein interactionsnetwork reconstructionrobustnessevolution timequantum algorithms
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The pith

Chiral quantum walks in swarms predict links more robustly than non-chiral versions by depending less on precise evolution time.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces random phases into the generators of quantum walk Hamiltonians to create chiral versions and runs them as a swarm for link prediction on complex networks such as protein-protein interactions. This produces complementary dynamics that keep predictive accuracy high across a range of evolution times instead of requiring the single best time. A sympathetic reader would care because link prediction helps fill in incomplete biological networks used in medicine, and sensitivity to a hard-to-know hyperparameter has limited practical use of quantum methods. The authors identify phase-sampling strategies that preserve the peak accuracy of the tuned non-chiral case while adding the robustness gain. The result follows directly from the more diverse exploration enabled by chirality.

Core claim

By adding random phases to the Hamiltonian generators we create chiral quantum walks and employ swarms of them to enhance predictive power on complex networks. Compared to a non-chiral algorithm, the chiral version exhibits greater robustness, making its performance less dependent on the optimal evolution time, a critical hyperparameter of the non-chiral model. This improvement arises from complementary dynamics introduced by chirality within the swarm. By analyzing multiple phase-sampling strategies we identify configurations that achieve a practical trade-off: retaining the high predictive accuracy of the non-chiral algorithm at its optimal time while gaining the robustness typical of chir

What carries the argument

Swarms of chiral quantum walks generated by adding random phases to the Hamiltonian generators, supplying complementary dynamics that reduce dependence on exact evolution time for link prediction.

If this is right

  • The chiral swarm retains high predictive accuracy of the tuned non-chiral case while adding robustness.
  • The method supports comparisons between successive versions of evolving databases.
  • Certain phase-sampling strategies produce a practical trade-off between accuracy and reduced timing sensitivity.
  • The approach has potential to outperform classical and non-chiral quantum methods in realistic network scenarios.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same random-phase chirality trick could reduce timing sensitivity in other quantum algorithms on graphs.
  • Testing the swarm on social or technological networks would show whether the robustness gain generalizes beyond biology.
  • Lowered need for precise timing might allow shorter runs or simple averaging to cut computational cost in practice.

Load-bearing premise

The complementary dynamics from different random-phase samplings genuinely improve predictive power on realistic networks without requiring post-hoc selection of the best swarm configuration or introducing hidden fitting to the test data.

What would settle it

Apply both the non-chiral quantum walk and the chiral swarm to a protein-protein interaction network, vary the evolution time around the known optimum, and check whether the chiral swarm's accuracy remains high while the non-chiral accuracy drops sharply.

Figures

Figures reproduced from arXiv: 2511.14513 by Gaia Forghieri, Matteo A. C. Rossi, Matteo G. A. Paris, Viacheslav Dubovitskii.

Figure 1
Figure 1. Figure 1: FIG. 1. Radar chart of normalized metrics for each network from Table I. Each quantity [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Performance of link prediction at 10% link removal on the Musculus-HINT network as a function [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Evolution in time of the average AuPR on Musculus-HINT obtained through [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Average AuPR as a function of the fraction of removed links, obtained through repeated [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Average AuROC as a function of the fraction of removed links, obtained through repeated [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Convergence of the average AuROC at 10% link removal obtained from 10-fold cross-validation on [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Violin plots showing the distribution of (a) the quantum-classical distance [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
read the original abstract

Reconstructing protein-protein interaction networks is a central challenge in network medicine, often addressed using link prediction algorithms. Recent studies suggest that quantum walk-based approaches hold promise for this task. In this paper, we build on these algorithms by introducing chirality through the addition of random phases in the Hamiltonian generators. The resulting additional degrees of freedom enable a more diverse exploration of the network, which we exploit by employing a swarm of chiral quantum walks. Thus, we enhance the predictive power of quantum walks on complex networks. Indeed, compared to a non-chiral algorithm, the chiral version exhibits greater robustness, making its performance less dependent on the optimal evolution time--a critical hyperparameter of the non-chiral model. This improvement arises from complementary dynamics introduced by chirality within the swarm. By analyzing multiple phase-sampling strategies, we identify configurations that achieve a practical trade-off: retaining the high predictive accuracy of the non-chiral algorithm at its optimal time while gaining the robustness typical of chirality. Our findings highlight the versatility of chiral quantum walks and their potential to outperform both classical and non-chiral quantum methods in realistic scenarios, including comparisons between successive versions of evolving databases.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces chirality to quantum walks for link prediction on protein-protein interaction networks by adding random phases to the Hamiltonian generators. It employs swarms of such chiral walks to exploit complementary dynamics, claiming greater robustness to the evolution-time hyperparameter than non-chiral quantum walks while retaining high predictive accuracy through the identification of suitable phase-sampling strategies. The work includes comparisons on evolving databases and positions the method as potentially outperforming both classical and non-chiral quantum approaches.

Significance. If the robustness to evolution time holds without data-dependent selection of swarm configurations, the approach would address a key practical limitation of quantum-walk link prediction, reducing sensitivity to a critical hyperparameter and improving applicability to realistic, time-varying networks.

major comments (2)
  1. [Abstract] Abstract: The central robustness claim rests on the statement that 'by analyzing multiple phase-sampling strategies, we identify configurations that achieve a practical trade-off.' This post-hoc identification process is not shown to be independent of test-set performance; if the selection of favorable strategies or swarm sizes was informed by predictive scores on the target networks or held-out edges, the reported reduction in dependence on optimal t could be an artifact of selection rather than an intrinsic property of the chiral swarm's complementary dynamics.
  2. [Abstract] Abstract and results sections: The abstract reports qualitative gains in robustness and accuracy but supplies no quantitative metrics, error bars, or explicit definition of how link-prediction performance is scored (e.g., AUC, precision@K, or ranking metrics). Without these, it is impossible to evaluate whether the claimed trade-off is statistically meaningful or merely descriptive.
minor comments (2)
  1. [Methods] Clarify the precise definition of 'phase sampling strategy' and the range of random phases used; notation for the modified Hamiltonian should be introduced explicitly in the methods.
  2. [Figures] Figure captions and legends should state the number of independent runs and any error-bar conventions so that robustness claims can be visually assessed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive comments on our manuscript. We address each of the major comments below and outline the revisions we plan to make.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central robustness claim rests on the statement that 'by analyzing multiple phase-sampling strategies, we identify configurations that achieve a practical trade-off.' This post-hoc identification process is not shown to be independent of test-set performance; if the selection of favorable strategies or swarm sizes was informed by predictive scores on the target networks or held-out edges, the reported reduction in dependence on optimal t could be an artifact of selection rather than an intrinsic property of the chiral swarm's complementary dynamics.

    Authors: We appreciate the referee raising this critical issue regarding potential data-dependent selection. Upon re-examination, the phase-sampling strategies were chosen based on theoretical considerations of introducing complementary dynamics through random phases, drawing from general properties of chiral walks rather than optimizing for specific test-set performances on the protein-protein interaction networks. To strengthen this, we will add a dedicated section or subsection detailing the strategy selection process, including results from cross-validation or independent validation sets to demonstrate that the robustness is not an artifact. This will clarify that the identified configurations generalize across different network instances. revision: yes

  2. Referee: [Abstract] Abstract and results sections: The abstract reports qualitative gains in robustness and accuracy but supplies no quantitative metrics, error bars, or explicit definition of how link-prediction performance is scored (e.g., AUC, precision@K, or ranking metrics). Without these, it is impossible to evaluate whether the claimed trade-off is statistically meaningful or merely descriptive.

    Authors: We agree with the referee that including quantitative metrics would improve the clarity and impact of the abstract. In the revised manuscript, we will incorporate specific quantitative results, such as average AUC improvements with standard deviations across multiple runs, and explicitly state the evaluation metric used (AUC-ROC for link prediction). We will also ensure the results section provides error bars and statistical significance where appropriate. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical comparisons are self-contained

full rationale

The paper introduces chirality via random phases in quantum walk Hamiltonians and evaluates swarms of such walks for link prediction on networks, claiming improved robustness to evolution time through complementary dynamics. No derivation chain exists that reduces a claimed prediction or first-principles result to its own inputs by construction. The identification of phase-sampling configurations is presented as an experimental analysis step to locate practical trade-offs, not as a fitted parameter renamed as a prediction or a self-referential definition. Claims rest on direct performance metrics across strategies and networks rather than any load-bearing self-citation or ansatz smuggling. This is the common case of an algorithmic paper whose central results are externally falsifiable via replication on the same datasets.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The method builds on standard quantum-walk formalism on graphs with an added random-phase modification whose distribution is chosen by the authors; no new physical entities are postulated.

free parameters (2)
  • phase sampling strategy
    Multiple strategies are tested and some are selected for the reported trade-off performance.
  • number of walks in swarm
    Swarm size is an implicit hyperparameter whose value affects the aggregated prediction.
axioms (1)
  • standard math Quantum walks on graphs are defined by a Hamiltonian whose off-diagonal elements encode network adjacency.
    Standard construction used to introduce the chiral phases.

pith-pipeline@v0.9.0 · 5513 in / 1153 out tokens · 59938 ms · 2026-05-17T20:55:59.404420+00:00 · methodology

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Reference graph

Works this paper leans on

62 extracted references · 62 canonical work pages

  1. [1]

    We considertas a hyperparameter of our problem, on which the performance can be optimized

    Making the most of chiral complementarity We start our analysis by considering the effects of the contribution of multiple c-QW’s to our algorithm, which we refer to as aswarmof chiral walkers. We considertas a hyperparameter of our problem, on which the performance can be optimized. However, understanding the optimal value oftrequiresa prioriknowledge on...

    work page

  2. [2]

    Dependence on time As mentioned above, the problem of maximizing the AuPR requires an optimization on the hyperparametert, which defines the evolution time of the walkers. In Fig. 3 we show the depen- dency of the AuPR on time for Musculus-HINT at various link removal rates. For this analysis, we consider the second sampling method from Sec. III A 1 (suff...

    work page

  3. [3]

    Version comparison Up to now, we have evaluated the link prediction performance throughk-fold cross-validation on specific versions of network databases. That said, an additional benchmark consists of comparing different versions of the same databases, by applying link prediction to earlier versions of the networks studied in this paper. In order to do th...

    work page

  4. [4]

    Adamic and Eytan Adar

    Lada A. Adamic and Eytan Adar. Friends and neighbors on the web.Social Networks, 25(3):211–230, 2003

    work page 2003

  5. [5]

    Applications of link prediction in social networks: A review.Journal of Network and Computer Applications, 166:102716, 2020

    Nur Nasuha Daud, Siti Hafizah Ab Hamid, Muntadher Saadoon, Firdaus Sahran, and Nor Badrul Anuar. Applications of link prediction in social networks: A review.Journal of Network and Computer Applications, 166:102716, 2020. 19

    work page 2020

  6. [6]

    Supervised link prediction using structured-based feature extraction in social network.Concurrency and Computation: Practice and Experience, 34(13):e5839, 2022

    Anisha Kumari, Ranjan Kumar Behera, Kshira Sagar Sahoo, Anand Nayyar, Ashish Kumar Luhach, and Satya Prakash Sahoo. Supervised link prediction using structured-based feature extraction in social network.Concurrency and Computation: Practice and Experience, 34(13):e5839, 2022

    work page 2022

  7. [7]

    Kov´ acs, Katja Luck, Kerstin Spirohn, Yang Wang, Carl Pollis, Sadie Schlabach, Wenting Bian, Dae-Kyum Kim, Nishka Kishore, Tong Hao, Michael A

    Istv´ an A. Kov´ acs, Katja Luck, Kerstin Spirohn, Yang Wang, Carl Pollis, Sadie Schlabach, Wenting Bian, Dae-Kyum Kim, Nishka Kishore, Tong Hao, Michael A. Calderwood, Marc Vidal, and Albert- L´ aszl´ o Barab´ asi. Network-based prediction of protein interactions.Nature Communications, 10(1):1240, Mar 2019

    work page 2019

  8. [8]

    Application of network link prediction in drug discovery.BMC Bioinformatics, 22(1):187, Apr 2021

    Khushnood Abbas, Alireza Abbasi, Shi Dong, Ling Niu, Laihang Yu, Bolun Chen, Shi-Min Cai, and Qambar Hasan. Application of network link prediction in drug discovery.BMC Bioinformatics, 22(1):187, Apr 2021

    work page 2021

  9. [9]

    Normalized l3-based link prediction in protein–protein interaction networks.BMC Bioinformatics, 24(1):59, Feb 2023

    Ho Yin Yuen and Jesper Jansson. Normalized l3-based link prediction in protein–protein interaction networks.BMC Bioinformatics, 24(1):59, Feb 2023

    work page 2023

  10. [10]

    Al Musawi, Satyaki Roy, and Preetam Ghosh

    Ahmad F. Al Musawi, Satyaki Roy, and Preetam Ghosh. A review of link prediction applications in network biology.IEEE Access, 13:54997–55016, 2025

    work page 2025

  11. [11]

    Human protein reference database and human proteinpedia as resources for phosphoproteome analysis.Molecular BioSystems, 8(2):453– 463, 2012

    Renu Goel, HC Harsha, Akhilesh Pandey, and TS Keshava Prasad. Human protein reference database and human proteinpedia as resources for phosphoproteome analysis.Molecular BioSystems, 8(2):453– 463, 2012

    work page 2012

  12. [12]

    Hint: High-quality protein interactomes and their applications in under- standing human disease.BMC Systems Biology, 6(1):92, Jul 2012

    Jishnu Das and Haiyuan Yu. Hint: High-quality protein interactomes and their applications in under- standing human disease.BMC Systems Biology, 6(1):92, Jul 2012

    work page 2012

  13. [13]

    Apid database: redefining protein–protein interac- tion experimental evidences and binary interactomes.Database, 2019:baz005, 01 2019

    Diego Alonso-L´ opez, Francisco J Campos-Laborie, Miguel A Guti´ errez, Luke Lambourne, Michael A Calderwood, Marc Vidal, and Javier De Las Rivas. Apid database: redefining protein–protein interac- tion experimental evidences and binary interactomes.Database, 2019:baz005, 01 2019

    work page 2019

  14. [14]

    Begg, Wenting Bian, Ruth Brignall, Tiziana Cafarelli, Francisco J

    Katja Luck, Dae-Kyum Kim, Luke Lambourne, Kerstin Spirohn, Bridget E. Begg, Wenting Bian, Ruth Brignall, Tiziana Cafarelli, Francisco J. Campos-Laborie, Benoit Charloteaux, Dongsic Choi, Atina G. Cot´ e, Meaghan Daley, Steven Deimling, Alice Desbuleux, Am´ elie Dricot, Marinella Geb- bia, Madeleine F. Hardy, Nishka Kishore, Jennifer J. Knapp, Istv´ an A. ...

    work page 2020

  15. [15]

    The biogrid database: A comprehensive biomedical resource of curated protein, genetic, and chemical interactions.Protein Science, 30(1):187–200, 2021

    Rose Oughtred, Jennifer Rust, Christie Chang, Bobby-Joe Breitkreutz, Chris Stark, Andrew Willems, Lorrie Boucher, Genie Leung, Nadine Kolas, Frederick Zhang, Sonam Dolma, Jasmin Coulombe- Huntington, Andrew Chatr-aryamontri, Kara Dolinski, and Mike Tyers. The biogrid database: A comprehensive biomedical resource of curated protein, genetic, and chemical i...

    work page 2021

  16. [16]

    Mass spectrometry-based protein–protein interaction networks for the study of human diseases.Molecular Systems Biology, 17(1):e8792, 2021

    Alicia L Richards, Manon Eckhardt, and Nevan J Krogan. Mass spectrometry-based protein–protein interaction networks for the study of human diseases.Molecular Systems Biology, 17(1):e8792, 2021

    work page 2021

  17. [17]

    Protein-protein interaction networks as miners of biological discovery.PROTEOMICS, 22(15-16):2100190, 2022

    Steven Wang, Runxin Wu, Jiaqi Lu, Yijia Jiang, Tao Huang, and Yu-Dong Cai. Protein-protein interaction networks as miners of biological discovery.PROTEOMICS, 22(15-16):2100190, 2022

    work page 2022

  18. [18]

    Chapter twelve - protein-protein interaction network analysis for the identification of novel multi-target inhibitors and target mirnas against alzheimer’s disease

    Vinay Kumar and Kunal Roy. Chapter twelve - protein-protein interaction network analysis for the identification of novel multi-target inhibitors and target mirnas against alzheimer’s disease. In Vijay Ku- mar Prajapati, editor,Translational Bioinformatics, volume 139 ofAdvances in Protein Chemistry and Structural Biology, pages 405–467. Academic Press, 2024

    work page 2024

  19. [19]

    Molecular interaction networks and drug development: Novel approach to drug target identification and drug repositioning.The FASEB Journal, 37(1):e22660, 2023

    Joseph Loscalzo. Molecular interaction networks and drug development: Novel approach to drug target identification and drug repositioning.The FASEB Journal, 37(1):e22660, 2023. e22660 202201683R

    work page 2023

  20. [20]

    Multi-level bioinfor- matics resources support drug target discovery of protein–protein interactions.Drug Discovery Today, 29(5):103979, 2024

    Jia-Xin Liu, Xiao Zhang, Yuan-Qin Huang, Ge-Fei Hao, and Guang-Fu Yang. Multi-level bioinfor- matics resources support drug target discovery of protein–protein interactions.Drug Discovery Today, 29(5):103979, 2024

    work page 2024

  21. [21]

    Targeting protein-protein interactions in drug discovery: Modulators approved or in clinical trials for cancer treatment.Phar- macological Research, 211:107544, 2025

    Cristina Camps-Fajol, Debora Cavero, Jordi Minguill´ on, and Jordi Surrall´ es. Targeting protein-protein interactions in drug discovery: Modulators approved or in clinical trials for cancer treatment.Phar- macological Research, 211:107544, 2025

    work page 2025

  22. [22]

    Dimitrakopoulos, Maria I

    Georgios N. Dimitrakopoulos, Maria I. Klapa, and Nicholas K. Moschonas. How far are we from the completion of the human protein interactome reconstruction?Biomolecules, 12(1), 2022

    work page 2022

  23. [23]

    Structural coverage of the human interactome.Briefings in Bioinformatics, 25(1):bbad496, 01 2024

    Kayra Kosoglu, Zeynep Aydin, Nurcan Tuncbag, Attila Gursoy, and Ozlem Keskin. Structural coverage of the human interactome.Briefings in Bioinformatics, 25(1):bbad496, 01 2024

    work page 2024

  24. [24]

    A novel link predic- tion algorithm for protein-protein interaction networks by attributed graph embedding.Computers in Biology and Medicine, 137:104772, 2021

    Elahe Nasiri, Kamal Berahmand, Mehrdad Rostami, and Mohammad Dabiri. A novel link predic- tion algorithm for protein-protein interaction networks by attributed graph embedding.Computers in Biology and Medicine, 137:104772, 2021

    work page 2021

  25. [25]

    Prediction of protein–protein interaction using graph neural networks.Scientific Reports, 12(1):8360, May 2022

    Kanchan Jha, Sriparna Saha, and Hiteshi Singh. Prediction of protein–protein interaction using graph neural networks.Scientific Reports, 12(1):8360, May 2022

    work page 2022

  26. [26]

    Thafar, and Muhammad Arif

    Jun Hu, Zhe Li, Bing Rao, Maha A. Thafar, and Muhammad Arif. Improving protein-protein inter- action prediction using protein language model and protein network features.Analytical Biochemistry, 693:115550, 2024

    work page 2024

  27. [27]

    Link prediction based on local random walk.Europhysics Letters, 89(5):58007, 2010

    Weiping Liu and Linyuan L¨ u. Link prediction based on local random walk.Europhysics Letters, 89(5):58007, 2010. 21

    work page 2010

  28. [28]

    Return random walks for link prediction.Information Sciences, 510:99–107, 2020

    Manuel Curado. Return random walks for link prediction.Information Sciences, 510:99–107, 2020

    work page 2020

  29. [29]

    Random walks: A review of algorithms and applications.IEEE Transactions on Emerging Topics in Computational Intelligence, 4(2):95–107, 2020

    Feng Xia, Jiaying Liu, Hansong Nie, Yonghao Fu, Liangtian Wan, and Xiangjie Kong. Random walks: A review of algorithms and applications.IEEE Transactions on Emerging Topics in Computational Intelligence, 4(2):95–107, 2020

    work page 2020

  30. [30]

    Comparing random walks in graph embedding and link prediction.PloS one, 19(11):e0312863, 2024

    Adilson Vital Jr, Filipi Nascimento Silva, and Diego Raphael Amancio. Comparing random walks in graph embedding and link prediction.PloS one, 19(11):e0312863, 2024

    work page 2024

  31. [31]

    Iliyasu, Ahmed S

    Wen Liang, Fei Yan, Abdullah M. Iliyasu, Ahmed S. Salama, and Kaoru Hirota. A simplified quantum walk model for predicting missing links of complex networks.Entropy, 24(11), 2022

    work page 2022

  32. [32]

    Mark Goldsmith, Harto Saarinen, Guillermo Garc´ ıa-P´ erez, Joonas Malmi, Matteo A. C. Rossi, and Sabrina Maniscalco. Link prediction with continuous-time classical and quantum walks.Entropy, 25(5), 2023

    work page 2023

  33. [33]

    Moutinho, Andr´ e Melo, Bruno Coutinho, Istv´ an A

    Jo˜ ao P. Moutinho, Andr´ e Melo, Bruno Coutinho, Istv´ an A. Kov´ acs, and Yasser Omar. Quantum link prediction in complex networks.Phys. Rev. A, 107:032605, Mar 2023

    work page 2023

  34. [34]

    Aharonov, L

    Y. Aharonov, L. Davidovich, and N. Zagury. Quantum random walks.Phys. Rev. A, 48:1687–1690, Aug 1993

    work page 1993

  35. [35]

    Continuous-time quantum walks: Models for coherent transport on complex networks.Physics Reports, 502(2):37–87, 2011

    Oliver M¨ ulken and Alexander Blumen. Continuous-time quantum walks: Models for coherent transport on complex networks.Physics Reports, 502(2):37–87, 2011

    work page 2011

  36. [36]

    Joglekar, and Peng Xue

    Kunkun Wang, Yuhao Shi, Lei Xiao, Jingbo Wang, Yogesh N. Joglekar, and Peng Xue. Experimental realization of continuous-time quantum walks on directed graphs and their application in pagerank. Optica, 7(11):1524–1530, Nov 2020

    work page 2020

  37. [37]

    Quantum walk and its application domains: A systematic review.Computer Science Review, 41:100419, 2021

    Karuna Kadian, Sunita Garhwal, and Ajay Kumar. Quantum walk and its application domains: A systematic review.Computer Science Review, 41:100419, 2021

    work page 2021

  38. [38]

    Quantum walk computing: Theory, implementation, and application.Intelligent Computing, 3:0097, 2024

    Xiaogang Qiang, Shixin Ma, and Haijing Song. Quantum walk computing: Theory, implementation, and application.Intelligent Computing, 3:0097, 2024

    work page 2024

  39. [39]

    Disease gene prioritization with quantum walks.Bioinformatics, 40(8):btae513, 08 2024

    Harto Saarinen, Mark Goldsmith, Rui-Sheng Wang, Joseph Loscalzo, and Sabrina Maniscalco. Disease gene prioritization with quantum walks.Bioinformatics, 40(8):btae513, 08 2024

    work page 2024

  40. [40]

    On quantum random walks in biomolecular networks, 2025

    Viacheslav Dubovitskii, Aritra Bose, Filippo Utro, and Laxmi Pardia. On quantum random walks in biomolecular networks, 2025

    work page 2025

  41. [41]

    Biamonte, Jun Li, Hang Li, Tomi H

    Dawei Lu, Jacob D. Biamonte, Jun Li, Hang Li, Tomi H. Johnson, Ville Bergholm, Mauro Faccin, Zolt´ an Zimbor´ as, Raymond Laflamme, Jonathan Baugh, and Seth Lloyd. Chiral quantum walks.Phys. Rev. A, 93:042302, Apr 2016

    work page 2016

  42. [42]

    Massimo Frigerio, Claudia Benedetti, Stefano Olivares, and Matteo G. A. Paris. Generalized quantum- classical correspondence for random walks on graphs.Phys. Rev. A, 104:L030201, Sep 2021

    work page 2021

  43. [43]

    Massimo Frigerio, Claudia Benedetti, Stefano Olivares, and Matteo G. A. Paris. Quantum-classical distance as a tool to design optimal chiral quantum walks.Phys. Rev. A, 105:032425, Mar 2022

    work page 2022

  44. [44]

    Quadratic speedup for spatial search by continuous-time quantum walk.Phys

    Simon Apers, Shantanav Chakraborty, Leonardo Novo, and J´ er´ emie Roland. Quadratic speedup for spatial search by continuous-time quantum walk.Phys. Rev. Lett., 129:160502, Oct 2022. 22

    work page 2022

  45. [45]

    Simone Cavazzoni, Luca Razzoli, Paolo Bordone, and Matteo G. A. Paris. Perturbed graphs achieve unit transport efficiency without environmental noise.Phys. Rev. E, 106:024118, Aug 2022

    work page 2022

  46. [46]

    Massimo Frigerio and Matteo G.A. Paris. Swift chiral quantum walks.Linear Algebra and its Applica- tions, 673:28–45, 2023

    work page 2023

  47. [47]

    Emilio Annoni, Massimo Frigerio, and Matteo G. A. Paris. Enhanced quantum transport in chiral quantum walks.Quantum Information Processing, 23(4):117, Mar 2024

    work page 2024

  48. [48]

    Luilli, Giuliano Benenti, Matteo G

    Sara Finocchiaro, Giovanni O. Luilli, Giuliano Benenti, Matteo G. A. Paris, and Luca Razzoli. Optimal quantum transport on a ring via locally monitored chiral quantum walks.Phys. Rev. E, in press, 2025

    work page 2025

  49. [49]

    Controlled information transfer in continuous-time chiral quantum walks.New Journal of Physics, 23(8):083005, aug 2021

    A Khalique, A Sett, J B Wang, and J Twamley. Controlled information transfer in continuous-time chiral quantum walks.New Journal of Physics, 23(8):083005, aug 2021

    work page 2021

  50. [50]

    Alberto Bottarelli, Massimo Frigerio, and Matteo G. A. Paris. Quantum routing of information using chiral quantum walks.AVS Quantum Science, 5(2):025001, 04 2023

    work page 2023

  51. [51]

    Giovanni Ragazzi, Simone Cavazzoni, Claudia Benedetti, Paolo Bordone, and Matteo G. A. Paris. Scalable structure for chiral quantum routing.Entropy, 27(5), 2025

    work page 2025

  52. [52]

    Simone Cavazzoni, Giovanni Ragazzi, Paolo Bordone, and Matteo G. A. Paris. Perfect chiral quantum routing.Phys. Rev. A, 111:032439, Mar 2025

    work page 2025

  53. [53]

    Quantum walks in synthetic gauge fields with three-dimensional integrated photonics.Phys

    Octavi Boada, Leonardo Novo, Fabio Sciarrino, and Yasser Omar. Quantum walks in synthetic gauge fields with three-dimensional integrated photonics.Phys. Rev. A, 95:013830, Jan 2017

    work page 2017

  54. [54]

    Cedzich, T

    C. Cedzich, T. Geib, A. H. Werner, and R. F. Werner. Quantum walks in external gauge fields.Journal of Mathematical Physics, 60(1):012107, 01 2019

    work page 2019

  55. [55]

    Luca Razzoli, Luca Ghirardi, Ilaria Siloi, Paolo Bordone, and Matteo G. A. Paris. Lattice quantum magnetometry.Phys. Rev. A, 99:062330, Jun 2019

    work page 2019

  56. [56]

    Progresses and challenges in link prediction.iScience, 24(11), Nov 2021

    Tao Zhou. Progresses and challenges in link prediction.iScience, 24(11), Nov 2021

    work page 2021

  57. [57]

    The precision-recall plot is more informative than the roc plot when evaluating binary classifiers on imbalanced datasets.PloS one, 10(3):e0118432, 2015

    Takaya Saito and Marc Rehmsmeier. The precision-recall plot is more informative than the roc plot when evaluating binary classifiers on imbalanced datasets.PloS one, 10(3):e0118432, 2015

    work page 2015

  58. [58]

    Biogrid: a general repository for interaction datasets.Nucleic Acids Research, 34(suppl 1):D535– D539, 01 2006

    Chris Stark, Bobby-Joe Breitkreutz, Teresa Reguly, Lorrie Boucher, Ashton Breitkreutz, and Mike Tyers. Biogrid: a general repository for interaction datasets.Nucleic Acids Research, 34(suppl 1):D535– D539, 01 2006

    work page 2006

  59. [59]

    Human protein reference database—2009 update.Nucleic acids research, 37(suppl 1):D767–D772, 2009

    TS Keshava Prasad, Renu Goel, Kumaran Kandasamy, Shivakumar Keerthikumar, Sameer Kumar, Suresh Mathivanan, Deepthi Telikicherla, Rajesh Raju, Beema Shafreen, Abhilash Venugopal, et al. Human protein reference database—2009 update.Nucleic acids research, 37(suppl 1):D767–D772, 2009

    work page 2009

  60. [60]

    M. E. J. Newman. Clustering and preferential attachment in growing networks.Phys. Rev. E, 64:025102, Jul 2001

    work page 2001

  61. [61]

    Link prediction based on common-neighbors for dynamic social network.Procedia Computer Science, 83:82–89, 2016

    Lin Yao, Luning Wang, Lv Pan, and Kai Yao. Link prediction based on common-neighbors for dynamic social network.Procedia Computer Science, 83:82–89, 2016. The 7th International Conference on Ambient Systems, Networks and Technologies (ANT 2016) / The 6th International Conference on Sustainable Energy Information Technology (SEIT-2016) / Affiliated Workshops. 23

    work page 2016

  62. [62]

    Eugene Stanley

    Linyuan L¨ u, Liming Pan, Tao Zhou, Yi-Cheng Zhang, and H. Eugene Stanley. Toward link predictability of complex networks.Proceedings of the National Academy of Sciences, 112(8):2325–2330, 2015

    work page 2015