1
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Yao LH, Wald S. Coined quantum walks on the line: Disorder, entanglement, and localization. Phys Rev E 2023; 108:024139. [PMID: 37723699 DOI: 10.1103/physreve.108.024139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2023] [Accepted: 07/25/2023] [Indexed: 09/20/2023]
Abstract
Disorder in coined quantum walks generally leads to localization. We investigate the influence of the localization on the entanglement properties of coined quantum walks. Specifically, we consider quantum walks on the line and explore the effects of quenched disorder in the coin operations. After confirming that our choice of disorder localizes the walker, we study how the localization affects the properties of the coined quantum walk. We find that the mixing properties of the walk are altered nontrivially with mixing being improved at short time scales. Special focus is given to the influence of coin disorder on the properties of the quantum state and the coin-walker entanglement. We find that disorder alters the quantum state significantly even when the walker probability distribution is still close to the nondisordered case. We observe that, generically, coin disorder decreases the coin-walker entanglement and that the localization leaves distinct traces in the entanglement entropy and the entanglement negativity of the coined quantum walk.
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Affiliation(s)
- Louie Hong Yao
- Department of Physics & Center for Soft Matter and Biological Physics, MC 0435, Robeson Hall, 850 West Campus Drive, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - Sascha Wald
- Statistical Physics Group, Centre for Fluid and Complex Systems, Coventry University, United Kingdom
- 𝕃4 Collaboration & Doctoral College for the Statistical Physics of Complex Systems, Leipzig-Lorraine-Lviv-Coventry, European Union
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2
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Sokolov B, Rossi MAC, García-Pérez G, Maniscalco S. Emergent entanglement structures and self-similarity in quantum spin chains. Philos Trans A Math Phys Eng Sci 2022; 380:20200421. [PMID: 35599560 DOI: 10.1098/rsta.2020.0421] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
We introduce an experimentally accessible network representation for many-body quantum states based on entanglement between all pairs of its constituents. We illustrate the power of this representation by applying it to a paradigmatic spin chain model, the XX model, and showing that it brings to light new phenomena. The analysis of these entanglement networks reveals that the gradual establishment of quasi-long range order is accompanied by a symmetry regarding single-spin concurrence distributions, as well as by instabilities in the network topology. Moreover, we identify the existence of emergent entanglement structures, spatially localized communities enforced by the global symmetry of the system that can be revealed by model-agnostic community detection algorithms. The network representation further unveils the existence of structural classes and a cyclic self-similarity in the state, which we conjecture to be intimately linked to the community structure. Our results demonstrate that the use of tools and concepts from complex network theory enables the discovery, understanding and description of new physical phenomena even in models studied for decades. This article is part of the theme issue 'Emergent phenomena in complex physical and socio-technical systems: from cells to societies'.
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Affiliation(s)
- Boris Sokolov
- QTF Centre of Excellence, Department of Physics, Faculty of Science, University of Helsinki, Helsinki, Finland
- Algorithmiq Ltd, Kanavakatu 3C, Helsinki 00160, Finland
- InstituteQ - the Finnish Quantum Institute, University of Helsinki, Finland
| | - Matteo A C Rossi
- Algorithmiq Ltd, Kanavakatu 3C, Helsinki 00160, Finland
- QTF Centre of Excellence, Center for Quantum Engineering, Department of Applied Physics, Aalto University School of Science, Aalto 00076, Finland
- InstituteQ - the Finnish Quantum Institute, Aalto University, Finland
| | - Guillermo García-Pérez
- QTF Centre of Excellence, Department of Physics, Faculty of Science, University of Helsinki, Helsinki, Finland
- Algorithmiq Ltd, Kanavakatu 3C, Helsinki 00160, Finland
- InstituteQ - the Finnish Quantum Institute, University of Helsinki, Finland
- Complex Systems Research Group, Department of Mathematics and Statistics, University of Turku, Turun Yliopisto 20014, Finland
| | - Sabrina Maniscalco
- QTF Centre of Excellence, Department of Physics, Faculty of Science, University of Helsinki, Helsinki, Finland
- Algorithmiq Ltd, Kanavakatu 3C, Helsinki 00160, Finland
- InstituteQ - the Finnish Quantum Institute, University of Helsinki, Finland
- QTF Centre of Excellence, Center for Quantum Engineering, Department of Applied Physics, Aalto University School of Science, Aalto 00076, Finland
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3
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Abstract
We study the transport properties on honeycomb networks motivated by graphene structures by using the continuous-time quantum walk (CTQW) model. For various relevant topologies we consider the average return probability and its long-time average as measures for the transport efficiency. These quantities are fully determined by the eigenvalues and the eigenvectors of the connectivity matrix of the network. For all networks derived from graphene structures we notice a nontrivial interplay between good spreading and localization effects. Flat graphene with similar number of hexagons along both directions shows a decrease in transport efficiency compared to more one-dimensional structures. This loss can be overcome by increasing the number of layers, thus creating a graphite network, but it gets less efficient when rolling up the sheets so that a nanotube structure is considered. We found peculiar results for honeycomb networks constructed from square graphene, i.e. the same number of hexagons along both directions of the graphene sheet. For these kind of networks we encounter significant differences between networks with an even or odd number of hexagons along one of the axes.
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4
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Amoroso N, Bellantuono L, Pascazio S, Monaco A, Bellotti R. Characterization of real-world networks through quantum potentials. PLoS One 2021; 16:e0254384. [PMID: 34255791 DOI: 10.1371/journal.pone.0254384] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Accepted: 06/24/2021] [Indexed: 11/19/2022] Open
Abstract
Network connectivity has been thoroughly investigated in several domains, including physics, neuroscience, and social sciences. This work tackles the possibility of characterizing the topological properties of real-world networks from a quantum-inspired perspective. Starting from the normalized Laplacian of a network, we use a well-defined procedure, based on the dressing transformations, to derive a 1-dimensional Schrödinger-like equation characterized by the same eigenvalues. We investigate the shape and properties of the potential appearing in this equation in simulated small-world and scale-free network ensembles, using measures of fractality. Besides, we employ the proposed framework to compare real-world networks with the Erdős-Rényi, Watts-Strogatz and Barabási-Albert benchmark models. Reconstructed potentials allow to assess to which extent real-world networks approach these models, providing further insight on their formation mechanisms and connectivity properties.
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5
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Koponen IT. Systemic States of Spreading Activation in Describing Associative Knowledge Networks II: Generalisations with Fractional Graph Laplacians and q-Adjacency Kernels. Systems 2021; 9:22. [DOI: 10.3390/systems9020022] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
Associative knowledge networks are often explored by using the so-called spreading activation model to find their key items and their rankings. The spreading activation model is based on the idea of diffusion- or random walk -like spreading of activation in the network. Here, we propose a generalisation, which relaxes an assumption of simple Brownian-like random walk (or equally, ordinary diffusion process) and takes into account nonlocal jump processes, typical for superdiffusive processes, by using fractional graph Laplacian. In addition, the model allows a nonlinearity of the diffusion process. These generalizations provide a dynamic equation that is analogous to fractional porous medium diffusion equation in a continuum case. A solution of the generalized equation is obtained in the form of a recently proposed q-generalized matrix transformation, the so-called q-adjacency kernel, which can be adopted as a systemic state describing spreading activation. Based on the systemic state, a new centrality measure called activity centrality is introduced for ranking the importance of items (nodes) in spreading activation. To demonstrate the viability of analysis based on systemic states, we use empirical data from a recently reported case of a university students’ associative knowledge network about the history of science. It is shown that, while a choice of model does not alter rankings of the items with the highest rank, rankings of nodes with lower ranks depend essentially on the diffusion model.
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6
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Abstract
Random walks are fundamental models of stochastic processes with applications in various fields, including physics, biology, and computer science. We study classical and quantum random walks under the influence of stochastic resetting on arbitrary networks. Based on the mathematical formalism of quantum stochastic walks, we provide a framework of classical and quantum walks whose evolution is determined by graph Laplacians. We study the influence of quantum effects on the stationary and long-time average probability distribution by interpolating between the classical and quantum regime. We compare our analytical results on stationary and long-time average probability distributions with numerical simulations on different networks, revealing differences in the way resets affect the sampling properties of classical and quantum walks.
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Affiliation(s)
- Sascha Wald
- Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Straße 38, D-01187 Dresden, Germany
| | - Lucas Böttcher
- Department of Computational Medicine, University of California, Los Angeles, California 90024, USA.,Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland.,Center of Economic Research, ETH Zurich, 8092 Zurich, Switzerland
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7
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Cuadra L, Nieto-Borge JC. Modeling Quantum Dot Systems as Random Geometric Graphs with Probability Amplitude-Based Weighted Links. Nanomaterials (Basel) 2021; 11:375. [PMID: 33540687 PMCID: PMC7912992 DOI: 10.3390/nano11020375] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Revised: 01/18/2021] [Accepted: 01/27/2021] [Indexed: 12/28/2022]
Abstract
This paper focuses on modeling a disorder ensemble of quantum dots (QDs) as a special kind of Random Geometric Graphs (RGG) with weighted links. We compute any link weight as the overlap integral (or electron probability amplitude) between the QDs (=nodes) involved. This naturally leads to a weighted adjacency matrix, a Laplacian matrix, and a time evolution operator that have meaning in Quantum Mechanics. The model prohibits the existence of long-range links (shortcuts) between distant nodes because the electron cannot tunnel between two QDs that are too far away in the array. The spatial network generated by the proposed model captures inner properties of the QD system, which cannot be deduced from the simple interactions of their isolated components. It predicts the system quantum state, its time evolution, and the emergence of quantum transport when the network becomes connected.
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Affiliation(s)
- Lucas Cuadra
- Department of Signal Processing and Communications, University of Alcalá, 28801 Alcalá de Henares, Spain
- Department of Physics and Mathematics, University of Alcalá, 28801 Alcalá de Henares, Spain;
| | - José Carlos Nieto-Borge
- Department of Physics and Mathematics, University of Alcalá, 28801 Alcalá de Henares, Spain;
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8
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Qiang X, Wang Y, Xue S, Ge R, Chen L, Liu Y, Huang A, Fu X, Xu P, Yi T, Xu F, Deng M, Wang JB, Meinecke JDA, Matthews JCF, Cai X, Yang X, Wu J. Implementing graph-theoretic quantum algorithms on a silicon photonic quantum walk processor. Sci Adv 2021; 7:7/9/eabb8375. [PMID: 33637521 PMCID: PMC7909884 DOI: 10.1126/sciadv.abb8375] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/21/2020] [Accepted: 01/13/2021] [Indexed: 06/12/2023]
Abstract
Applications of quantum walks can depend on the number, exchange symmetry and indistinguishability of the particles involved, and the underlying graph structures where they move. Here, we show that silicon photonics, by exploiting an entanglement-driven scheme, can realize quantum walks with full control over all these properties in one device. The device we realize implements entangled two-photon quantum walks on any five-vertex graph, with continuously tunable particle exchange symmetry and indistinguishability. We show how this simulates single-particle walks on larger graphs, with size and geometry controlled by tuning the properties of the composite quantum walkers. We apply the device to quantum walk algorithms for searching vertices in graphs and testing for graph isomorphisms. In doing so, we implement up to 100 sampled time steps of quantum walk evolution on each of 292 different graphs. This opens the way to large-scale, programmable quantum walk processors for classically intractable applications.
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Affiliation(s)
- Xiaogang Qiang
- Institute for Quantum Information and State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, 410073 Changsha, China.
- National Innovation Institute of Defense Technology, AMS, 100071 Beijing, China
- Beijing Academy of Quantum Information Sciences, 100193 Beijing, China
| | - Yizhi Wang
- Institute for Quantum Information and State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, 410073 Changsha, China
| | - Shichuan Xue
- Institute for Quantum Information and State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, 410073 Changsha, China
| | - Renyou Ge
- State Key Laboratory of Optoelectronic Materials and Technologies and School of Electronics and Information Technology, Sun Yat-sen University, 510275 Guangzhou, China
| | - Lifeng Chen
- State Key Laboratory of Optoelectronic Materials and Technologies and School of Electronics and Information Technology, Sun Yat-sen University, 510275 Guangzhou, China
| | - Yingwen Liu
- Institute for Quantum Information and State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, 410073 Changsha, China
| | - Anqi Huang
- Institute for Quantum Information and State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, 410073 Changsha, China
| | - Xiang Fu
- Institute for Quantum Information and State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, 410073 Changsha, China
| | - Ping Xu
- Institute for Quantum Information and State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, 410073 Changsha, China
| | - Teng Yi
- National Innovation Institute of Defense Technology, AMS, 100071 Beijing, China
| | - Fufang Xu
- National Innovation Institute of Defense Technology, AMS, 100071 Beijing, China
- Beijing Academy of Quantum Information Sciences, 100193 Beijing, China
| | - Mingtang Deng
- Institute for Quantum Information and State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, 410073 Changsha, China
| | - Jingbo B Wang
- Department of Physics, The University of Western Australia, Perth, WA6009, Australia
| | - Jasmin D A Meinecke
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-StraBe 1, 85748 Garching, Germany
- Department für Physik, Ludwig-Maximilians-Universität, Schellingstr. 4, 80799 München, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 München, Germany
| | - Jonathan C F Matthews
- Quantum Engineering Technology Labs, H. H. Wills Physics Laboratory and Department of Electrical and Electronic Engineering, University of Bristol, BS8 1FD Bristol, UK
| | - Xinlun Cai
- State Key Laboratory of Optoelectronic Materials and Technologies and School of Electronics and Information Technology, Sun Yat-sen University, 510275 Guangzhou, China.
| | - Xuejun Yang
- Institute for Quantum Information and State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, 410073 Changsha, China
| | - Junjie Wu
- Institute for Quantum Information and State Key Laboratory of High Performance Computing, College of Computer Science and Technology, National University of Defense Technology, 410073 Changsha, China.
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9
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Tang H, Shi R, He TS, Zhu YY, Wang TY, Lee M, Jin XM. TensorFlow solver for quantum PageRank in large-scale networks. Sci Bull (Beijing) 2021; 66:120-126. [PMID: 36654218 DOI: 10.1016/j.scib.2020.09.009] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2020] [Revised: 07/24/2020] [Accepted: 08/31/2020] [Indexed: 01/20/2023]
Abstract
Google PageRank is a prevalent algorithm for ranking the significance of nodes or websites in a network, and a recent quantum counterpart for PageRank algorithm has been raised to suggest a higher accuracy of ranking comparing to Google PageRank. The quantum PageRank algorithm is essentially based on quantum stochastic walks and can be expressed using Lindblad master equation, which, however, needs to solve the Kronecker products of an O(N4) dimension and requires severely large memory and time when the number of nodes N in a network increases above 150. Here, we present an efficient solver for quantum PageRank by using the Runge-Kutta method to reduce the matrix dimension to O(N2) and employing TensorFlow to conduct GPU parallel computing. We demonstrate its performance in solving quantum stochastic walks on Erdös-Rényi graphs using an RTX 2060 GPU. The test on the graph of 6000 nodes requires a memory of 5.5 GB and time of 223 s, and that on the graph of 1000 nodes requires 226 MB and 3.6 s. Compared with QSWalk, a currently prevalent Mathematica solver, our solver for the same graph of 1000 nodes reduces the required memory and time to only 0.2% and 0.05%. We apply the solver to quantum PageRank for the USA major airline network with up to 922 nodes, and to quantum stochastic walk on a glued tree of 2186 nodes. This efficient solver for large-scale quantum PageRank and quantum stochastic walks would greatly facilitate studies of quantum information in real-life applications.
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Affiliation(s)
- Hao Tang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China; CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Ruoxi Shi
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Tian-Shen He
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Yan-Yan Zhu
- School of Physical Science, University of Chinese Academy of Sciences, Beijing 100049, China
| | - Tian-Yu Wang
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Marcus Lee
- Department of Physics, Cambridge University, Cambridge CB3 0HE, UK
| | - Xian-Min Jin
- Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China; CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China.
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10
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Busemeyer J, Zhang Q, Balakrishnan SN, Wang Z. Application of Quantum-Markov Open System Models to Human Cognition and Decision. Entropy (Basel) 2020; 22:E990. [PMID: 33286759 PMCID: PMC7597313 DOI: 10.3390/e22090990] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/16/2020] [Revised: 08/29/2020] [Accepted: 09/02/2020] [Indexed: 12/12/2022]
Abstract
Markov processes, such as random walk models, have been successfully used by cognitive and neural scientists to model human choice behavior and decision time for over 50 years. Recently, quantum walk models have been introduced as an alternative way to model the dynamics of human choice and confidence across time. Empirical evidence points to the need for both types of processes, and open system models provide a way to incorporate them both into a single process. However, some of the constraints required by open system models present challenges for achieving this goal. The purpose of this article is to address these challenges and formulate open system models that have good potential to make important advancements in cognitive science.
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Affiliation(s)
- Jerome Busemeyer
- Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN 47405, USA
| | - Qizi Zhang
- Department of Mechanical and Aerospace Engineering, Missiouri University of Science Technology, Rolla, MO 65401, USA;
| | - S. N. Balakrishnan
- Department of Mechanical Engineering, Missiouri University of Science Technology, Rolla, MO 65401, USA;
| | - Zheng Wang
- Center for Brain and Cognitive, Translational Data Analytics Institute, School of Communication, The Ohio State University, Columbus, OH 43210, USA;
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11
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Sephton B, Dudley A, Ruffato G, Romanato F, Marrucci L, Padgett M, Goyal S, Roux F, Konrad T, Forbes A. A versatile quantum walk resonator with bright classical light. PLoS One 2019; 14:e0214891. [PMID: 30964901 PMCID: PMC6456201 DOI: 10.1371/journal.pone.0214891] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/30/2019] [Accepted: 03/21/2019] [Indexed: 11/18/2022] Open
Abstract
In a Quantum Walk (QW) the "walker" follows all possible paths at once through the principle of quantum superposition, differentiating itself from classical random walks where one random path is taken at a time. This facilitates the searching of problem solution spaces faster than with classical random walks, and holds promise for advances in dynamical quantum simulation, biological process modelling and quantum computation. Here we employ a versatile and scalable resonator configuration to realise quantum walks with bright classical light. We experimentally demonstrate the versatility of our approach by implementing a variety of QWs, all with the same experimental platform, while the use of a resonator allows for an arbitrary number of steps without scaling the number of optics. This paves the way for future QW implementations with spatial modes of light in free-space that are both versatile and scalable.
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Affiliation(s)
- Bereneice Sephton
- School of Physics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa
- CSIR National Laser Centre, PO Box 395, Pretoria, South Africa
| | - Angela Dudley
- School of Physics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa
- CSIR National Laser Centre, PO Box 395, Pretoria, South Africa
| | - Gianluca Ruffato
- Department of Physics and Astronomy G. Galilei, University of Padova, Padova, Italy
| | - Filippo Romanato
- Department of Physics and Astronomy G. Galilei, University of Padova, Padova, Italy
- CNR-INFM TASC IOM National Laboratory, Trieste, Italy
| | - Lorenzo Marrucci
- Dipartimento di Fisica, University di Napoli Federico II, Complesso Universitario di Monte S. Angelo, Napoli, Italy
| | - Miles Padgett
- SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom
| | - Sandeep Goyal
- Indian Institute of Science Education and Research, Mohali, Punjab, India
| | - Filippus Roux
- School of Physics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa
- National Metrology Institute of South Africa, Pretoria, South Africa
| | - Thomas Konrad
- School of Chemistry and Physics, University of KwaZulu-Natal, Durban, South Africa
| | - Andrew Forbes
- School of Physics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa
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12
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Abstract
Quantum time evolution exhibits rich physics, attributable to the interplay between the density and phase of a wave function. However, unlike classical heat diffusion, the wave nature of quantum mechanics has not yet been extensively explored in modern data analysis. We propose that the Laplace transform of quantum transport (QT) can be used to construct an ensemble of maps from a given complex network to a circle S^{1}, such that closely related nodes on the network are grouped into sharply concentrated clusters on S^{1}. The resulting QT clustering (QTC) algorithm is as powerful as the state-of-the-art spectral clustering in discerning complex geometric patterns and more robust when clusters show strong density variations or heterogeneity in size. The observed phenomenon of QTC can be interpreted as a collective behavior of the microscopic nodes that evolve as macroscopic cluster "orbitals" in an effective tight-binding model recapitulating the network. python source code implementing the algorithm and examples are available at https://github.com/jssong-lab/QTC.
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Affiliation(s)
- Chenchao Zhao
- Department of Physics and Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Jun S Song
- Department of Physics and Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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13
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Tang H, Lin XF, Feng Z, Chen JY, Gao J, Sun K, Wang CY, Lai PC, Xu XY, Wang Y, Qiao LF, Yang AL, Jin XM. Experimental two-dimensional quantum walk on a photonic chip. Sci Adv 2018; 4:eaat3174. [PMID: 29756040 PMCID: PMC5947980 DOI: 10.1126/sciadv.aat3174] [Citation(s) in RCA: 48] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2018] [Accepted: 03/21/2018] [Indexed: 05/12/2023]
Abstract
Quantum walks, in virtue of the coherent superposition and quantum interference, have exponential superiority over their classical counterpart in applications of quantum searching and quantum simulation. The quantum-enhanced power is highly related to the state space of quantum walks, which can be expanded by enlarging the photon number and/or the dimensions of the evolution network, but the former is considerably challenging due to probabilistic generation of single photons and multiplicative loss. We demonstrate a two-dimensional continuous-time quantum walk by using the external geometry of photonic waveguide arrays, rather than the inner degree of freedoms of photons. Using femtosecond laser direct writing, we construct a large-scale three-dimensional structure that forms a two-dimensional lattice with up to 49 × 49 nodes on a photonic chip. We demonstrate spatial two-dimensional quantum walks using heralded single photons and single photon-level imaging. We analyze the quantum transport properties via observing the ballistic evolution pattern and the variance profile, which agree well with simulation results. We further reveal the transient nature that is the unique feature for quantum walks of beyond one dimension. An architecture that allows a quantum walk to freely evolve in all directions and at a large scale, combining with defect and disorder control, may bring up powerful and versatile quantum walk machines for classically intractable problems.
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Affiliation(s)
- Hao Tang
- State Key Laboratory of Advanced Optical Communication Systems and Networks, Institute of Natural Sciences and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiao-Feng Lin
- State Key Laboratory of Advanced Optical Communication Systems and Networks, Institute of Natural Sciences and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zhen Feng
- State Key Laboratory of Advanced Optical Communication Systems and Networks, Institute of Natural Sciences and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jing-Yuan Chen
- State Key Laboratory of Advanced Optical Communication Systems and Networks, Institute of Natural Sciences and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Jun Gao
- State Key Laboratory of Advanced Optical Communication Systems and Networks, Institute of Natural Sciences and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Ke Sun
- State Key Laboratory of Advanced Optical Communication Systems and Networks, Institute of Natural Sciences and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Chao-Yue Wang
- State Key Laboratory of Advanced Optical Communication Systems and Networks, Institute of Natural Sciences and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Peng-Cheng Lai
- State Key Laboratory of Advanced Optical Communication Systems and Networks, Institute of Natural Sciences and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Xiao-Yun Xu
- State Key Laboratory of Advanced Optical Communication Systems and Networks, Institute of Natural Sciences and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- State Key Laboratory of Advanced Optical Communication Systems and Networks, Institute of Natural Sciences and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Lu-Feng Qiao
- State Key Laboratory of Advanced Optical Communication Systems and Networks, Institute of Natural Sciences and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Ai-Lin Yang
- State Key Laboratory of Advanced Optical Communication Systems and Networks, Institute of Natural Sciences and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xian-Min Jin
- State Key Laboratory of Advanced Optical Communication Systems and Networks, Institute of Natural Sciences and Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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14
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Liu ZP, Zhang J, Özdemir ŞK, Peng B, Jing H, Lü XY, Li CW, Yang L, Nori F, Liu YX. Metrology with PT-Symmetric Cavities: Enhanced Sensitivity near the PT-Phase Transition. Phys Rev Lett 2016; 117:110802. [PMID: 27661674 DOI: 10.1103/physrevlett.117.110802] [Citation(s) in RCA: 69] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2015] [Indexed: 06/06/2023]
Abstract
We propose and analyze a new approach based on parity-time (PT) symmetric microcavities with balanced gain and loss to enhance the performance of cavity-assisted metrology. We identify the conditions under which PT-symmetric microcavities allow us to improve sensitivity beyond what is achievable in loss-only systems. We discuss the application of PT-symmetric microcavities to the detection of mechanical motion, and show that the sensitivity is significantly enhanced near the transition point from unbroken- to broken-PT regimes. Our results open a new direction for PT-symmetric physical systems and it may find use in ultrahigh precision metrology and sensing.
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Affiliation(s)
- Zhong-Peng Liu
- Department of Automation, Tsinghua University, Beijing 100084, China
- Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, China
| | - Jing Zhang
- Department of Automation, Tsinghua University, Beijing 100084, China
- Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, China
- Department of Electrical and Systems Engineering, Washington University, St. Louis, Missouri 63130, USA
| | - Şahin Kaya Özdemir
- Department of Electrical and Systems Engineering, Washington University, St. Louis, Missouri 63130, USA
| | - Bo Peng
- Department of Electrical and Systems Engineering, Washington University, St. Louis, Missouri 63130, USA
| | - Hui Jing
- CEMS, RIKEN, Saitama 351-0198, Japan
- Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha 410081, China
| | - Xin-You Lü
- CEMS, RIKEN, Saitama 351-0198, Japan
- School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Chun-Wen Li
- Department of Automation, Tsinghua University, Beijing 100084, China
- Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, China
| | - Lan Yang
- Department of Electrical and Systems Engineering, Washington University, St. Louis, Missouri 63130, USA
| | - Franco Nori
- CEMS, RIKEN, Saitama 351-0198, Japan
- Physics Department, The University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Yu-Xi Liu
- Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, China
- Institute of Microelectronics, Tsinghua University, Beijing 100084, China
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15
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Caruso F, Crespi A, Ciriolo AG, Sciarrino F, Osellame R. Fast escape of a quantum walker from an integrated photonic maze. Nat Commun 2016; 7:11682. [PMID: 27248707 DOI: 10.1038/ncomms11682] [Citation(s) in RCA: 56] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2015] [Accepted: 04/19/2016] [Indexed: 11/08/2022] Open
Abstract
Escaping from a complex maze, by exploring different paths with several decision-making branches in order to reach the exit, has always been a very challenging and fascinating task. Wave field and quantum objects may explore a complex structure in parallel by interference effects, but without necessarily leading to more efficient transport. Here, inspired by recent observations in biological energy transport phenomena, we demonstrate how a quantum walker can efficiently reach the output of a maze by partially suppressing the presence of interference. In particular, we show theoretically an unprecedented improvement in transport efficiency for increasing maze size with respect to purely quantum and classical approaches. In addition, we investigate experimentally these hybrid transport phenomena, by mapping the maze problem in an integrated waveguide array, probed by coherent light, hence successfully testing our theoretical results. These achievements may lead towards future bio-inspired photonics technologies for more efficient transport and computation.
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16
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Qiang X, Loke T, Montanaro A, Aungskunsiri K, Zhou X, O'Brien JL, Wang JB, Matthews JCF. Efficient quantum walk on a quantum processor. Nat Commun 2016; 7:11511. [PMID: 27146471 DOI: 10.1038/ncomms11511] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2015] [Accepted: 04/04/2016] [Indexed: 11/17/2022] Open
Abstract
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise, quantum walks have shown much potential as a framework for developing new quantum algorithms. Here we present explicit efficient quantum circuits for implementing continuous-time quantum walks on the circulant class of graphs. These circuits allow us to sample from the output probability distributions of quantum walks on circulant graphs efficiently. We also show that solving the same sampling problem for arbitrary circulant quantum circuits is intractable for a classical computer, assuming conjectures from computational complexity theory. This is a new link between continuous-time quantum walks and computational complexity theory and it indicates a family of tasks that could ultimately demonstrate quantum supremacy over classical computers. As a proof of principle, we experimentally implement the proposed quantum circuit on an example circulant graph using a two-qubit photonics quantum processor. Quantum walks are a potential framework for developing quantum algorithms, but have so far been limited to analogue quantum-simulation approaches that do not scale. Here, the authors provide a protocol for simulating exponentially large quantum walks using a polynomial number of quantum gates and qubits.
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17
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Abstract
Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce's response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process' degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making.
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Affiliation(s)
- Ismael Martínez-Martínez
- Düsseldorf Institute for Competition Economics (DICE), Heinrich Heine Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Eduardo Sánchez-Burillo
- Instituto de Ciencia de Materiales de Aragón (ICMA), CSIC-Universidad de Zaragoza and Departamento de Física de la Materia Condensada, Universidad de Zaragoza, E-50009 Zaragoza, Spain
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18
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Abstract
We study the transport efficiency of excitations on complex quantum networks with loops. For this we consider sequentially growing networks with different topologies of the sequential subgraphs. This can lead either to a universal complete breakdown of transport for complete-graph-like sequential subgraphs or to optimal transport for ringlike sequential subgraphs. The transition to optimal transport can be triggered by systematically reducing the number of loops of complete-graph-like sequential subgraphs in a small-world procedure. These effects are explained on the basis of the spectral properties of the network's Hamiltonian. Our theoretical considerations are supported by numerical Monte Carlo simulations for complex quantum networks with a scale-free size distribution of sequential subgraphs and a small-world-type transition to optimal transport.
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Affiliation(s)
- Oliver Mülken
- Physikalisches Institut, Universität Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany
| | - Maxim Dolgushev
- Physikalisches Institut, Universität Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany
| | - Mircea Galiceanu
- Departamento de Física, Universidade Federal do Amazonas, 3000 Japiim, 69077-000 Manaus-AM, Brazil.,Institut für Theoretische Physik, Technische Universtät Dresden, 01062 Dresden, Germany
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19
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Abstract
In this paper we study the quantum transport on networks with a temporal evolution governed by the fractional Schrödinger equation. We generalize the dynamics based on continuous-time quantum walks, with transitions to nearest neighbors on the network, to the fractional case that allows long-range displacements. By using the fractional Laplacian matrix of a network, we establish a formalism that combines a long-range dynamics with the quantum superposition of states; this general approach applies to any type of connected undirected networks, including regular, random, and complex networks, and can be implemented from the spectral properties of the Laplacian matrix. We study the fractional dynamics and its capacity to explore the network by means of the transition probability, the average probability of return, and global quantities that characterize the efficiency of this quantum process. As a particular case, we explore analytically these quantities for circulant networks such as rings, interacting cycles, and complete graphs.
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Affiliation(s)
- A P Riascos
- Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 México, D.F., México
| | - José L Mateos
- Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000 México, D.F., México
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20
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Abstract
We consider single-particle quantum transport on parametrized complex networks. Based on general arguments regarding the spectrum of the corresponding Hamiltonian, we derive bounds for a measure of the global transport efficiency defined by the time-averaged return probability. For treelike networks, we show analytically that a transition from efficient to inefficient transport occurs depending on the (average) functionality of the nodes of the network. In the infinite system size limit, this transition can be characterized by an exponent which is universal for all treelike networks. Our findings are corroborated by analytic results for specific deterministic networks, dendrimers and Vicsek fractals, and by Monte Carlo simulations of iteratively built scale-free trees.
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Affiliation(s)
- Nikolaj Kulvelis
- Physikalisches Institut, Universität Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany
| | - Maxim Dolgushev
- Physikalisches Institut, Universität Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany
| | - Oliver Mülken
- Physikalisches Institut, Universität Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany
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21
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Bianconi G, Rahmede C, Wu Z. Complex quantum network geometries: Evolution and phase transitions. Phys Rev E Stat Nonlin Soft Matter Phys 2015; 92:022815. [PMID: 26382462 DOI: 10.1103/physreve.92.022815] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2015] [Indexed: 06/05/2023]
Abstract
Networks are topological and geometric structures used to describe systems as different as the Internet, the brain, or the quantum structure of space-time. Here we define complex quantum network geometries, describing the underlying structure of growing simplicial 2-complexes, i.e., simplicial complexes formed by triangles. These networks are geometric networks with energies of the links that grow according to a nonequilibrium dynamics. The evolution in time of the geometric networks is a classical evolution describing a given path of a path integral defining the evolution of quantum network states. The quantum network states are characterized by quantum occupation numbers that can be mapped, respectively, to the nodes, links, and triangles incident to each link of the network. We call the geometric networks describing the evolution of quantum network states the quantum geometric networks. The quantum geometric networks have many properties common to complex networks, including small-world property, high clustering coefficient, high modularity, and scale-free degree distribution. Moreover, they can be distinguished between the Fermi-Dirac network and the Bose-Einstein network obeying, respectively, the Fermi-Dirac and Bose-Einstein statistics. We show that these networks can undergo structural phase transitions where the geometrical properties of the networks change drastically. Finally, we comment on the relation between quantum complex network geometries, spin networks, and triangulations.
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Affiliation(s)
- Ginestra Bianconi
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
| | - Christoph Rahmede
- Institute for Theoretical Physics, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
| | - Zhihao Wu
- School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China
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22
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Di Patti F, Fanelli D, Piazza F. Optimal search strategies on complex multi-linked networks. Sci Rep 2015; 5:9869. [PMID: 25950716 DOI: 10.1038/srep09869] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2015] [Accepted: 03/10/2015] [Indexed: 11/15/2022] Open
Abstract
In this paper we consider the problem of optimal search strategies on multi-linked networks, i.e. graphs whose nodes are endowed with several independent sets of links. We focus preliminarily on agents randomly hopping along the links of a graph, with the additional possibility of performing non-local hops to randomly chosen nodes with a given probability. We show that an optimal combination of the two jump rules exists that maximises the efficiency of target search, the optimum reflecting the topology of the network. We then generalize our results to multi-linked networks with an arbitrary number of mutually interfering link sets.
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23
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Bianconi G. Supersymmetric multiplex networks described by coupled Bose and Fermi statistics. Phys Rev E Stat Nonlin Soft Matter Phys 2015; 91:012810. [PMID: 25679660 DOI: 10.1103/physreve.91.012810] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2014] [Indexed: 06/04/2023]
Abstract
Until now, no simple symmetries have been detected in complex networks. Here we show that in growing multiplex networks the symmetries of multilayer structures can be exploited by their dynamical rules, forming supersymmetric multiplex networks described by coupled Bose-Einstein and Fermi-Dirac quantum statistics. The supersymmetric multiplex is formed by layers which are scale-free networks and can display a Bose-Einstein condensation of the links. To characterize the complexity of the supersymmetric multiplex using quantum information tools, we extend the definition of the network entanglement entropy to the layers of any multiplex network. Interestingly, we observe a very simple relation between the entanglement entropies of the layers of the supersymmetric multiplex network and the entropy rate of the same multiplex network. This relation therefore connects the classical nonequilibrium growing dynamics of the supersymmetric multiplex network with its quantum information static characteristics.
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Affiliation(s)
- Ginestra Bianconi
- School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom
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24
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Hermoso de Mendoza I, Pachón LA, Gómez-Gardeñes J, Zueco D. Synchronization in a semiclassical Kuramoto model. Phys Rev E Stat Nonlin Soft Matter Phys 2014; 90:052904. [PMID: 25493855 DOI: 10.1103/physreve.90.052904] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2013] [Indexed: 06/04/2023]
Abstract
Synchronization is a ubiquitous phenomenon occurring in social, biological, and technological systems when the internal rythms of their constituents are adapted to be in unison as a result of their coupling. This natural tendency towards dynamical consensus has spurred a large body of theoretical and experimental research in recent decades. The Kuramoto model constitutes the most studied and paradigmatic framework in which to study synchronization. In particular, it shows how synchronization appears as a phase transition from a dynamically disordered state at some critical value for the coupling strength between the interacting units. The critical properties of the synchronization transition of this model have been widely studied and many variants of its formulations have been considered to address different physical realizations. However, the Kuramoto model has been studied only within the domain of classical dynamics, thus neglecting its applications for the study of quantum synchronization phenomena. Based on a system-bath approach and within the Feynman path-integral formalism, we derive equations for the Kuramoto model by taking into account the first quantum fluctuations. We also analyze its critical properties, the main result being the derivation of the value for the synchronization onset. This critical coupling increases its value as quantumness increases, as a consequence of the possibility of tunneling that quantum fluctuations provide.
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Affiliation(s)
| | - Leonardo A Pachón
- Grupo de Física Atómica y Molecular, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA; Calle 70 No. 52-21, Medellín, Colombia
| | - Jesús Gómez-Gardeñes
- Departamento de Física de la Materia Condensada, Universidad de Zaragoza, E-50009 Zaragoza, Spain and Instituto de Biocomputación y Física de Sistemas Complejos, Universidad de Zaragoza, E-50018 Zaragoza, Spain
| | - David Zueco
- Departamento de Física de la Materia Condensada, Universidad de Zaragoza, E-50009 Zaragoza, Spain and Instituto de Ciencia de Materiales de Aragón, CSIC-Universidad de Zaragoza, E-50012 Zaragoza, Spain and Fundación ARAID, Paseo María Agustín 36, E-50004 Zaragoza, Spain
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25
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Abstract
We investigate the behaviour of the recently proposed Quantum PageRank algorithm, in large complex networks. We find that the algorithm is able to univocally reveal the underlying topology of the network and to identify and order the most relevant nodes. Furthermore, it is capable to clearly highlight the structure of secondary hubs and to resolve the degeneracy in importance of the low lying part of the list of rankings. The quantum algorithm displays an increased stability with respect to a variation of the damping parameter, present in the Google algorithm, and a more clearly pronounced power-law behaviour in the distribution of importance, as compared to the classical algorithm. We test the performance and confirm the listed features by applying it to real world examples from the WWW. Finally, we raise and partially address whether the increased sensitivity of the quantum algorithm persists under coordinated attacks in scale-free and random networks.
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26
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Wei ZW, Wang BH, Han XP. Renormalization and small-world model of fractal quantum repeater networks. Sci Rep 2013; 3:1222. [PMID: 23386977 DOI: 10.1038/srep01222] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2012] [Accepted: 01/15/2013] [Indexed: 11/25/2022] Open
Abstract
Quantum networks provide access to exchange of quantum information. The primary task of quantum networks is to distribute entanglement between remote nodes. Although quantum repeater protocol enables long distance entanglement distribution, it has been restricted to one-dimensional linear network. Here we develop a general framework that allows application of quantum repeater protocol to arbitrary quantum repeater networks with fractal structure. Entanglement distribution across such networks is mapped to renormalization. Furthermore, we demonstrate that logarithmical times of recursive such renormalization transformations can trigger fractal to small-world transition, where a scalable quantum small-world network is achieved. Our result provides new insight into quantum repeater theory towards realistic construction of large-scale quantum networks.
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27
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Halu A, Garnerone S, Vezzani A, Bianconi G. Phase transition of light on complex quantum networks. Phys Rev E Stat Nonlin Soft Matter Phys 2013; 87:022104. [PMID: 23496457 DOI: 10.1103/physreve.87.022104] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2012] [Indexed: 06/01/2023]
Abstract
Recent advances in quantum optics and atomic physics allow for an unprecedented level of control over light-matter interactions, which can be exploited to investigate new physical phenomena. In this work we are interested in the role played by the topology of quantum networks describing coupled optical cavities and local atomic degrees of freedom. In particular, using a mean-field approximation, we study the phase diagram of the Jaynes-Cummings-Hubbard model on complex networks topologies, and we characterize the transition between a Mott-like phase of localized polaritons and a superfluid phase. We found that, for complex topologies, the phase diagram is nontrivial and well defined in the thermodynamic limit only if the hopping coefficient scales like the inverse of the maximal eigenvalue of the adjacency matrix of the network. Furthermore we provide numerical evidences that, for some complex network topologies, this scaling implies an asymptotically vanishing hopping coefficient in the limit of large network sizes. The latter result suggests the interesting possibility of observing quantum phase transitions of light on complex quantum networks even with very small couplings between the optical cavities.
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Affiliation(s)
- Arda Halu
- Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA
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