Log in

Relevant bibliographies by topics / Topological Computing / Journal articles

To see the other types of publications on this topic, follow the link: Topological Computing.

Journal articles on the topic 'Topological Computing'

Author: Grafiati

Published: 5 June 2025

Last updated: 24 June 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Topological Computing.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

CHEON, Sangmo. "In Search of Majorana Fermions: Topological Superconductors and Quantum Computing." Physics and High Technology 34, no. 5 (2025): 17–25. https://doi.org/10.3938/phit.34.015.

Full text

Abstract:

The combination of topology and superconductivity has led to the discovery of topological superconductors—quantum phases that host Majorana zero modes (MZMs), exotic quasiparticles with non-Abelian statistics. These modes offer a pathway to fault-tolerant quantum computation, in which quantum information is stored nonlocally and manipulated via topologically protected operations. We review the theoretical foundations of Majorana fermions, the Kitaev chain, and the mathematical structure of topological superconductors. We highlight their potential realization in semiconductor nanowires and also examine iron-based superconductors, particularly FeTe1-xSex, which uniquely combines topology, correlation, and superconductivity. We also discuss the architecture of topological quantum computation, including braiding-based Clifford gates, magic state distillation for universality, and measurement-based schemes. Furthermore, we highlight how external parameters‒pressure, strain, magnetic field, and temperature‒can be used to control or induce topological superconductivity. As research advances, the search for Majorana states is reshaping our understanding of quantum matter and what it can compute.

APA, Harvard, Vancouver, ISO, and other styles

2

Scappucci, G., P. J. Taylor, J. R. Williams, T. Ginley, and S. Law. "Crystalline materials for quantum computing: Semiconductor heterostructures and topological insulators exemplars." MRS Bulletin 46, no. 7 (2021): 596–606. http://dx.doi.org/10.1557/s43577-021-00147-8.

Full text

Abstract:

AbstractHigh-purity crystalline solid-state materials play an essential role in various technologies for quantum information processing, from qubits based on spins to topological states. New and improved crystalline materials emerge each year and continue to drive new results in experimental quantum science. This article summarizes the opportunities for a selected class of crystalline materials for qubit technologies based on spins and topological states and the challenges associated with their fabrication. We start by describing semiconductor heterostructures for spin qubits in gate-defined quantum dots and benchmark GaAs, Si, and Ge, the three platforms that demonstrated two-qubit logic. We then examine novel topologically nontrivial materials and structures that might be incorporated into superconducting devices to create topological qubits. We review topological insulator thin films and move onto topological crystalline materials, such as PbSnTe, and its integration with Josephson junctions. We discuss advances in novel and specialized fabrication and characterization techniques to enable these. We conclude by identifying the most promising directions where advances in these material systems will enable progress in qubit technology.

APA, Harvard, Vancouver, ISO, and other styles

3

LEE, Hyun-Jung, and Mahn-Soo CHOI. "Applications of Topological Insulators and Topological Quantum Computing." Physics and High Technology 20, no. 3 (2011): 30. http://dx.doi.org/10.3938/phit.20.011.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Vidya S Umadi. "Computing Topological Indices of Certain Networks." Communications on Applied Nonlinear Analysis 31, no. 2 (2024): 416–29. http://dx.doi.org/10.52783/cana.v31.611.

Full text

Abstract:

In mathematical chemistry, topological indices are molecular descriptors that are calculated on the molecular graph of a chemical compound. The molecular graph is a graph which is obtained from some chemical structures. The degree of every molecular graph cannot exceeds 4. Topological indices are numerical quantities of a graph that describe its topology. An atom represents a vertex and a bond between two atoms represents an edge in a molecular graph. Mainly there are three types of topological indices viz., degree-based, distance based and eigenvalue-based topological indices. The first degree-based topological indices are the first and second Zagreb indices. The first Zagreb index M_1 is defined as the sum of squares of degrees of each vertex in a graph G and the second Zagreb index M_2 is the product of degree of every adjacent vertices. In this case the summation goes on the set of edges of a graph G. The most studied topological indices are degree-based topological indices. Motivated by these topological indices in this paper, we introduce five new degree-based topological indices based on the neighborhood degree of a vertex. Further, we compute the values of various nanostructures like hexagonal parallelogram P(m,n) nanotube, triangular benzenoid G_n,zigzag-edge coronoid fused with starphene nanotubes ZCS(k,l,m), dominating derived networks D_1,D_2,D_3, Porphyrin Dendrimer, Zinc-Porphyrin Dendrimer, Propyl Ether Imine Dendrimer, Poly(Ethylene amido amine Dendrimer, PAMAM dendrimers(????????1,????????2,????????1), linear polyomino chain L_n,Z_n,B_n^1 (n≥3),B_n^2 (n≥3) and triangular, hourglass, and jagged-rectangle benzenoid systems of these indices. The standard computational techniques are used for the computation of topological indices of nanostructures. For the edge partition of the nanostructures the algebraic techniques are used. Using these techniques computation of topological indices became easy and also helped to get the more accurate results.

APA, Harvard, Vancouver, ISO, and other styles

5

Fowler, A. G., and K. Goyal. "Topological cluster state quantum computing." Quantum Information and Computation 9, no. 9&10 (2009): 721–38. http://dx.doi.org/10.26421/qic9.9-10-1.

Full text

Abstract:

The quantum computing scheme described by Raussendorf et. al (2007), when viewed as a cluster state computation, features a 3-D cluster state, novel adjustable strength error correction capable of correcting general errors through the correction of Z errors only, a threshold error rate approaching 1% and low overhead arbitrarily long-range logical gates. In this work, we review the scheme in detail framing the discussion solely in terms of the required 3-D cluster state and its stabilizers.

APA, Harvard, Vancouver, ISO, and other styles

6

Rowell, Eric C., and Zhenghan Wang. "Mathematics of topological quantum computing." Bulletin of the American Mathematical Society 55, no. 2 (2018): 183–238. http://dx.doi.org/10.1090/bull/1605.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Palacio-Morales, Alexandra, Eric Mascot, Sagen Cocklin, et al. "Atomic-scale interface engineering of Majorana edge modes in a 2D magnet-superconductor hybrid system." Science Advances 5, no. 7 (2019): eaav6600. http://dx.doi.org/10.1126/sciadv.aav6600.

Full text

Abstract:

Topological superconductors are predicted to harbor exotic boundary states—Majorana zero-energy modes—whose non-Abelian braiding statistics present a new paradigm for the realization of topological quantum computing. Using low-temperature scanning tunneling spectroscopy, here, we report on the direct real-space visualization of chiral Majorana edge states in a monolayer topological superconductor, a prototypical magnet-superconductor hybrid system composed of nanoscale Fe islands of monoatomic height on a Re(0001)-O(2 × 1) surface. In particular, we demonstrate that interface engineering by an atomically thin oxide layer is crucial for driving the hybrid system into a topologically nontrivial state as confirmed by theoretical calculations of the topological invariant, the Chern number.

APA, Harvard, Vancouver, ISO, and other styles

8

Wang, Michelle, Cooper Doyle, Bryn Bell, et al. "Topologically protected entangled photonic states." Nanophotonics 8, no. 8 (2019): 1327–35. http://dx.doi.org/10.1515/nanoph-2019-0058.

Full text

Abstract:

AbstractEntangled multiphoton states lie at the heart of quantum information, computing, and communications. In recent years, topology has risen as a new avenue to robustly transport quantum states in the presence of fabrication defects, disorder, and other noise sources. Whereas topological protection of single photons and correlated photons has been recently demonstrated experimentally, the observation of topologically protected entangled states has thus far remained elusive. Here, we experimentally demonstrate the topological protection of spatially entangled biphoton states. We observe robustness in crucial features of the topological biphoton correlation map in the presence of deliberately introduced disorder in the silicon nanophotonic structure, in contrast with the lack of robustness in non-topological structures. The topological protection is shown to ensure the coherent propagation of the entangled topological modes, which may lead to robust propagation of quantum information in disordered systems.

APA, Harvard, Vancouver, ISO, and other styles

9

Banerjee, Sourav. "Tuneable phononic crystals and topological acoustics." Open Access Government 42, no. 1 (2024): 252–53. http://dx.doi.org/10.56367/oag-042-11436.

Full text

Abstract:

Tuneable phononic crystals and topological acoustics Sourav Banerjee, Professor from the University of South Carolina, navigates the field of tuneable phononic crystals and topological acoustics. Acoustics, an age-old field of study, has recently revealed new physics with new degrees of freedom of wave propagation. These new findings are invaluable for information processing using acoustic modality. Information processing using acoustics is called acoustic computing. Computing Boolean algebra, which has already been demonstrated, could pave the pathways even for quantum computing using acoustics. Not in the very distant future, the recently discovered quantum and topological behavior of acoustics could be an integral part of computing modalities.

APA, Harvard, Vancouver, ISO, and other styles

10

Jahn, M. W., and P. E. Bradley. "COMPUTING WATERTIGHT VOLUMETRIC MODELS FROM BOUNDARY REPRESENTATIONS TO ENSURE CONSISTENT TOPOLOGICAL OPERATIONS." ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences VIII-4/W2-2021 (October 7, 2021): 21–28. http://dx.doi.org/10.5194/isprs-annals-viii-4-w2-2021-21-2021.

Full text

Abstract:

Abstract. To simulate environmental processes, noise, flooding in cities as well as the behaviour of buildings and infrastructure, ‘watertight’ volumetric models are a measuring prerequisite. They ensure topologically consistent 3D models and allow the definition of proper topological operations. However, in many existing city or other geo-information models, topologically unchecked boundary representations are used to store spatial entities. In order to obtain consistent topological models, including their ‘fillings’, in this paper, a triangulation combined with overlay and path-finding methods is presented by climbing up the dimension, beginning with the wireframe model. The algorithms developed for this task are presented, whereby using the philosophy of graph databases and the Property Graph Model. Examples to illustrate the algorithms are given, and experiments are performed on a data-set from Erfurt, Thuringia (Germany), providing complex geometries of buildings. The heavy influence of double precision arithmetic on the results, in particular the positional and angular precision, is discussed in the end.

APA, Harvard, Vancouver, ISO, and other styles

11

Jordan, S. P. "Permutational quantum computing." Quantum Information and Computation 10, no. 5&6 (2010): 470–97. http://dx.doi.org/10.26421/qic10.5-6-7.

Full text

Abstract:

In topological quantum computation the geometric details of a particle trajectory are irrelevant; only the topology matters. Taking this one step further, we consider a model of computation that disregards even the topology of the particle trajectory, and computes by permuting particles. Whereas topological quantum computation requires anyons, permutational quantum computation can be performed with ordinary spin-1/2 particles, using a variant of the spin-network scheme of Marzuoli and Rasetti. We do not know whether permutational computation is universal. It may represent a new complexity class within BQP. Nevertheless, permutational quantum computers can in polynomial time approximate matrix elements of certain irreducible representations of the symmetric group and approximate certain transition amplitudes from the Ponzano-Regge spin foam model of quantum gravity. No polynomial time classical algorithms for these problems are known.

APA, Harvard, Vancouver, ISO, and other styles

12

Yang, Hong, Chi Zhang, and Lan Zhuo. "Research on Quantum State Implementation Based on Topological Insulators." Journal of Physics: Conference Series 2843, no. 1 (2024): 012019. http://dx.doi.org/10.1088/1742-6596/2843/1/012019.

Full text

Abstract:

Abstract This paper first introduces the mainstream technology route of quantum computing. The analysis provides the role and advantages of topological insulators in quantum computing, such as providing stable quantum bits, enhancing the coherence and non-locality of quantum bits, and enabling the transmission of quantum information and entanglement allocation. This paper then proposes a quantum state implementation scheme based on Bi2Se3, based on the characteristics and advantages of the quantum Hall effect of topological insulators. It includes calculating the eigenstates of the Hamiltonian of topological insulators, obtaining the spatial distribution of wave functions, and generating a quantum bit platform based on topological insulators. A quantum state implementation system based on topological insulator (Bi2Se3) was constructed, and the system framework and reference configuration were provided. The solution presented in this article is an important research achievement in topological quantum computing, providing more possibilities for the implementation of feasible fault-tolerant quantum computer prototypes.

APA, Harvard, Vancouver, ISO, and other styles

13

Zhao, Weidong, M. C. Shanmukha, A. Usha, Mohammad Reza Farahani, and K. C. Shilpa. "Computing SS Index of Certain Dendrimers." Journal of Mathematics 2021 (September 24, 2021): 1–14. http://dx.doi.org/10.1155/2021/7483508.

Full text

Abstract:

The numerical descriptor gathers the data from the molecular graphs and helps to know the characteristics of the chemical structure known as topological index. The QSAR/QSPR/QSTR studies are benefited with the significant role played by topological indices in the drug design. Topological indices provide the information about the physical/chemical/biological properties of chemical compounds. The Zagreb indices are widely studied because of their extensive usage in chemical graph theory. Inspired by the earlier work on inverse sum indeg index (ISI index), novel topological index known as SS index is introduced and computed for four dendrimer structures. Also, the strong correlation coefficient between SS index and 5 physico-chemical characteristics such as boiling point (bp), molar volume (mv), molar refraction (mr), heats of vaporization (hv), and critical pressure (cp) of 67 alkane isomers have been determined. It is found that newly introduced index has shown good correlation in comparison with three most popular existing indices (ISI index and first and second Zagreb indices). In the last part, the mathematical properties of SS index are discussed.

APA, Harvard, Vancouver, ISO, and other styles

14

Asselmeyer-Maluga, Torsten. "Topological Quantum Computing and 3-Manifolds." Quantum Reports 3, no. 1 (2021): 153–65. http://dx.doi.org/10.3390/quantum3010009.

Full text

Abstract:

In this paper, we will present some ideas to use 3D topology for quantum computing. Topological quantum computing in the usual sense works with an encoding of information as knotted quantum states of topological phases of matter, thus being locked into topology to prevent decay. Today, the basic structure is a 2D system to realize anyons with braiding operations. From the topological point of view, we have to deal with surface topology. However, usual materials are 3D objects. Possible topologies for these objects can be more complex than surfaces. From the topological point of view, Thurston’s geometrization theorem gives the main description of 3-dimensional manifolds. Here, complements of knots do play a prominent role and are in principle the main parts to understand 3-manifold topology. For that purpose, we will construct a quantum system on the complements of a knot in the 3-sphere. The whole system depends strongly on the topology of this complement, which is determined by non-contractible, closed curves. Every curve gives a contribution to the quantum states by a phase (Berry phase). Therefore, the quantum states can be manipulated by using the knot group (fundamental group of the knot complement). The universality of these operations was already showed by M. Planat et al.

APA, Harvard, Vancouver, ISO, and other styles

15

Zhang, Jinying, Yulin Si, Yexiaotong Zhang, Bingnan Wang, and Xinye Wang. "Dual-Band High-Throughput and High-Contrast All-Optical Topology Logic Gates." Micromachines 15, no. 12 (2024): 1492. https://doi.org/10.3390/mi15121492.

Full text

Abstract:

Optical computing offers advantages such as high bandwidth and low loss, playing a crucial role in signal processing, communication, and sensing applications. Traditional optical logic gates, based on nonlinear fibers and optical amplifiers, suffer from poor robustness and large footprints, hindering their on-chip integration. All-optical logic gates based on topological photonic crystals have emerged as a promising approach for developing robust and monolithic optical computing systems. Expanding topological photonic crystal logic gates from a single operating band to dual bands can achieve high throughput, significantly enhancing parallel computing capabilities. This study integrates the topological protection offered by valley photonic crystals with linear interference effects to design and implement seven optical computing logic gates on a silicon substrate. These gates, based on dual-band valley photonic crystal topological protection, include OR, XOR, NOT, NAND, NOR, and AND. The robustness of the implemented OR logic gates was verified in the presence of boundary defects. The results demonstrate that multi-band parallel computing all-optical logic gates can be achieved using topological photonic crystals, and these gates exhibit high robustness. The all-optical logic gates designed in this study hold significant potential for future applications in optical signal processing, optical communication, optical sensing, and other related areas.

APA, Harvard, Vancouver, ISO, and other styles

16

Brennen, Gavin K., and Jiannis K. Pachos. "Why should anyone care about computing with anyons?" Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2089 (2007): 1–24. http://dx.doi.org/10.1098/rspa.2007.0026.

Full text

Abstract:

In this article we present a pedagogical introduction of the main ideas and recent advances in the area of topological quantum computation. We give an overview of the concept of anyons and their exotic statistics, present various models that exhibit topological behaviour and establish their relation to quantum computation. Possible directions for the physical realization of topological systems and the detection of anyonic behaviour are elaborated.

APA, Harvard, Vancouver, ISO, and other styles

17

RASHID, Muhammad Aamer, Sarfraz AHMAD, Muhammad Kamran SIDDIQUI, and Muhammad NAEEM. "Computing topological indices of crystallographic structures." Revue Roumaine de Chimie 65, no. 5 (2020): 447–59. http://dx.doi.org/10.33224/rrch.2020.65.5.04.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Aguado, Ramón, and Leo P. Kouwenhoven. "Majorana qubits for topological quantum computing." Physics Today 73, no. 6 (2020): 44–50. http://dx.doi.org/10.1063/pt.3.4499.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Bonelli, Giulio, Alessandro Tanzini, and Maxim Zabzine. "Computing amplitudes in topological M-theory." Journal of High Energy Physics 2007, no. 03 (2007): 023. http://dx.doi.org/10.1088/1126-6708/2007/03/023.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Pollner, Péter, and Gábor Vattay. "New Method for Computing Topological Pressure." Physical Review Letters 76, no. 22 (1996): 4155–58. http://dx.doi.org/10.1103/physrevlett.76.4155.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Ahmed, Faisal, and Zhipei Sun. "Empowering neuromorphic computing with topological states." Journal of Semiconductors 45, no. 11 (2024): 110401. http://dx.doi.org/10.1088/1674-4926/24080029.

Full text

APA, Harvard, Vancouver, ISO, and other styles

22

Giavitto, Jean-Louis, and Olivier Michel. "The Topological Structures of Membrane Computing." Fundamenta Informaticae 49, no. 1-3 (2002): 123–45. https://doi.org/10.3233/fun-2002-491-310.

Full text

Abstract:

In its initial presentation, the P system formalism describes the topology of the membranes as a set of nested regions. In this paper, we present an algebraic structure developped in combinatorial topology that can be used to describe finer adjacency relationships between membranes. Using an appropriate abstract setting, this technical device enables us to reformulate also the computation within a membrane and proposes a unified view on several computational mechanisms initially inspired by biological processes. These theoretical tools are instantiated in MGS, an experimental programming language handling various types of membrane structures in a homogeneous and uniform syntax.

APA, Harvard, Vancouver, ISO, and other styles

23

Petre, Luigia, Kaisa Sere, and Marina Waldén. "A Topological Approach to Distributed Computing." Electronic Notes in Theoretical Computer Science 28 (2000): 59–80. http://dx.doi.org/10.1016/s1571-0661(05)80630-9.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Yokoyama, Misako. "Computing topological degree using noisy information." Journal of Complexity 6, no. 4 (1990): 379–88. http://dx.doi.org/10.1016/0885-064x(90)90029-d.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Assenov, Yassen, Fidel Ramírez, Sven-Eric Schelhorn, Thomas Lengauer, and Mario Albrecht. "Computing topological parameters of biological networks." Bioinformatics 24, no. 2 (2007): 282–84. http://dx.doi.org/10.1093/bioinformatics/btm554.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Melent'ev, Victor Aleksandrovich. "ABOUT TOPOLOGICAL COMPACTNESS OF COMPUTING SYSTEMS." Theoretical & Applied Science 19, no. 11 (2014): 59–65. http://dx.doi.org/10.15863/tas.2014.11.19.12.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Gao, Wei, Muhammad Imran, Abdul Qudair Baig, Haidar Ali, and Mohammad Reza Farahani. "Computing topological indices of Sudoku graphs." Journal of Applied Mathematics and Computing 55, no. 1-2 (2016): 99–117. http://dx.doi.org/10.1007/s12190-016-1027-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

28

Spandl, Christoph. "Computing the topological entropy of shifts." MLQ 53, no. 4-5 (2007): 493–510. http://dx.doi.org/10.1002/malq.200710014.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Spandl, Christoph. "Computing the Topological Entropy of Shifts." Electronic Notes in Theoretical Computer Science 167 (January 2007): 131–55. http://dx.doi.org/10.1016/j.entcs.2006.08.011.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

S Shenbaga Devi. "Computing topological indices of Porous Graphene." Advances in Nonlinear Variational Inequalities 28, no. 6s (2025): 827–35. https://doi.org/10.52783/anvi.v28.4429.

Full text

Abstract:

Topological indices in chemical graph theory helps to quantify the molecular structure and to analyse the correlation of the structures using physical, chemical, and biological properties. In this paper, we have discussed several degree-based topological indices like first hyper zagreb, second hyper zagreb, reduced second Zagreb, forgotten, harmonic, sombor, arithmetic geometric, reduced reciprocal randic and SS indices for porous graphene. This will be useful for determining the relationship between the mathematical qualities and the characteristics of a specific chemical compound. This study is beneficial for the fields of chemical sensors, energy storage, and DNA sequencing.

APA, Harvard, Vancouver, ISO, and other styles

31

Amaral, Marcelo, David Chester, Fang Fang, and Klee Irwin. "Exploiting Anyonic Behavior of Quasicrystals for Topological Quantum Computing." Symmetry 14, no. 9 (2022): 1780. http://dx.doi.org/10.3390/sym14091780.

Full text

Abstract:

The concrete realization of topological quantum computing using low-dimensional quasiparticles, known as anyons, remains one of the important challenges of quantum computing. A topological quantum computing platform promises to deliver more robust qubits with additional hardware-level protection against errors that could lead to the desired large-scale quantum computation. We propose quasicrystal materials as such a natural platform and show that they exhibit anyonic behavior that can be used for topological quantum computing. Different from anyons, quasicrystals are already implemented in laboratories. In particular, we study the correspondence between the fusion Hilbert spaces of the simplest non-abelian anyon, the Fibonacci anyons, and the tiling spaces of the one-dimensional Fibonacci chain and the two-dimensional Penrose tiling quasicrystals. A concrete encoding on these tiling spaces of topological quantum information processing is also presented by making use of inflation and deflation of such tiling spaces. While we outline the theoretical basis for such a platform, details on the physical implementation remain open.

APA, Harvard, Vancouver, ISO, and other styles

32

Edwards, Chris. "Tales of Topological Qubits." Communications of the ACM 66, no. 12 (2023): 8–10. http://dx.doi.org/10.1145/3624436.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Gu, Lili, Shamaila Yousaf, Akhlaq Ahmad Bhatti, Peng Xu, and Adnan Aslam. "Computing Some Degree-Based Topological Indices of Honeycomb Networks." Complexity 2022 (January 4, 2022): 1–13. http://dx.doi.org/10.1155/2022/2771059.

Full text

Abstract:

A topological index is a numeric quantity related with the chemical composition claiming to correlate the chemical structure with different chemical properties. Topological indices serve to predict physicochemical properties of chemical substance. Among different topological indices, degree-based topological indices would be helpful in investigating the anti-inflammatory activities of certain chemical networks. In the current study, we determine the neighborhood second Zagreb index and the first extended first-order connectivity index for oxide network O X n , silicate network S L n , chain silicate network C S n , and hexagonal network H X n . Also, we determine the neighborhood second Zagreb index and the first extended first-order connectivity index for honeycomb network H C n .

APA, Harvard, Vancouver, ISO, and other styles

34

Zhang, Xiujun, Nazeran Idrees, Salma Kanwal, Muhammad Jawwad Saif, and Fatima Saeed. "Computing Topological Invariants of Deep Neural Networks." Computational Intelligence and Neuroscience 2022 (October 7, 2022): 1–11. http://dx.doi.org/10.1155/2022/9051908.

Full text

Abstract:

A deep neural network has multiple layers to learn more complex patterns and is built to simulate the activity of the human brain. Currently, it provides the best solutions to many problems in image recognition, speech recognition, and natural language processing. The present study deals with the topological properties of deep neural networks. The topological index is a numeric quantity associated to the connectivity of the network and is correlated to the efficiency and accuracy of the output of the network. Different degree-related topological indices such as Zagreb index, Randic index, atom-bond connectivity index, geometric-arithmetic index, forgotten index, multiple Zagreb indices, and hyper-Zagreb index of deep neural network with a finite number of hidden layers are computed in this study.

APA, Harvard, Vancouver, ISO, and other styles

35

Ehrhardt, Max, Christoph Dittel, Matthias Heinrich, and Alexander Szameit. "Topological Hong-Ou-Mandel interference." Science 384, no. 6702 (2024): 1340–44. http://dx.doi.org/10.1126/science.ado8192.

Full text

Abstract:

The interplay of topology and optics provides a route to pursue robust photonic devices, with the application to photonic quantum computation in its infancy. However, the possibilities of harnessing topological structures to process quantum information with linear optics, through the quantum interference of photons, remain largely uncharted. Here, we present a Hong-Ou-Mandel interference effect of topological origin. We show that this interference of photon pairs—ranging from constructive to destructive—is solely determined by a synthetic magnetic flux, rendering it resilient to errors on a fundamental level. Our implementation establishes a quantized flux that facilitates exclusively destructive quantum interference. Our findings pave the way toward the development of next-generation photonic quantum circuitry and scalable quantum computing protected by virtue of topologically robust quantum gates.

APA, Harvard, Vancouver, ISO, and other styles

36

Kotlyar, Victor V., Alexey A. Kovalev, Elena S. Kozlova, and Alexandra A. Savelyeva. "Tailoring the Topological Charge of a Superposition of Identical Parallel Laguerre–Gaussian Beams." Micromachines 13, no. 12 (2022): 2227. http://dx.doi.org/10.3390/mi13122227.

Full text

Abstract:

In optical computing machines, data can be transmitted by optical vortices, and the information can be encoded by their topological charges. Thus, some optical mechanisms are needed for performing simple arithmetic operations with the topological charges. Here, a superposition of several parallel identical Laguerre–Gaussian beams with single rings is studied. It is analytically and numerically shown that if the weighting coefficients of the superposition are real, then the total topological charge of the superposition is equal to the topological charge of each component in the initial plane and in the far field. We prove that the total topological charge of the superposition can be changed by the phase delay between the beams. In the numerical simulation, we demonstrate the incrementing and decrementing the topological charge. Potential application areas are in optical computing machines and optical data transmission.

APA, Harvard, Vancouver, ISO, and other styles

37

Kaiser, Uwe. "A short survey of quantum computing." Journal of Knot Theory and Its Ramifications 26, no. 03 (2017): 1741004. http://dx.doi.org/10.1142/s0218216517410048.

Full text

Abstract:

Quantum computing is closely related to [Formula: see text]-dimensional topological quantum field theory through its approach in topological quantum computation. The following are notes based on lectures given by the author at the Mathematics Department of George Washington University. The idea is to give a brief introduction and survey of a few basic facts of quantum computing to an audience of non-experts interested in taking a quick look at some of the most important concepts of quantum computing. The author is a topologist with strong interest in the general ideas of quantum computing. The notes touch on how quantum topology enters the field but emphasizes the general ideas of quantum computing in the first place.

APA, Harvard, Vancouver, ISO, and other styles

38

Chu, Chun-Guang, An-Qi Wang, and Zhi-Min Liao. "Josephson effect in topological semimetal-superconductor heterojunctions." Acta Physica Sinica 72, no. 8 (2023): 087401. http://dx.doi.org/10.7498/aps.72.20230397.

Full text

Abstract:

Topological semimetals are exotic phases of quantum matter with gapless electronic excitation protected by symmetry. Benefitting from its unique relativistic band dispersion, topological semimetals host abundant quantum states and quantum effects, esuch as Fermi-arc surface states and chiral anomaly. In recent years, due to the potential application in topological quantum computing, the hybrid system of topology and superconductivity has aroused wide interest in the community. Recent experimental progress of topological semimetal-superconductor heterojunctions is reviewed in two aspects: 1) Josephson current as a mode filter of different topological quantum states; 2) detection and manipulation of topological superconductivity and Majorana zero modes. For the former, utilizing Josephson interference, ballistic transport of Fermi-arc surface states is revealed, higher-order topological phases are discovered, and finite-momentum Cooper pairing and superconducting diode effect are realized. For the latter, by detecting a.c. Josephson effect in Dirac semimetal, the 4π-periodic supercurrent is discovered. By all-electric gate control, the topological transition of superconductivity is obtained. Outlooks of future research on topological semimetal-superconductor heterojunctions and their application in Majorana braiding and topological quantum computing are discussed.

APA, Harvard, Vancouver, ISO, and other styles

39

Idrees, Nazeran, Raghisa Khalid, Fozia Bashir Farooq, and Sumiya Nasir. "Computing Topological Invariants of Triangular Chandelier Lattice." Computers, Materials & Continua 63, no. 3 (2020): 1119–32. http://dx.doi.org/10.32604/cmc.2020.08166.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

V Patil, Prashant, and Rahul Munavalli V. "Computing topological indices of certain windmill graphs." Journal of Computational Mathematica 6, no. 1 (2022): 001–14. http://dx.doi.org/10.26524/cm117.

Full text

Abstract:

Let V (G), be the vertex set of graph G, we define Vd = {v ∈ V (G) : SG(u) = d} in which SG(u) = ∑v∈NG(u) dG(v) and NG(u) = {v ∈ V(G) : uv ∈ E(G)}. In this paper we express the explicit formula for Sanskruti index S(G), fth M1 and M2 Zagreb indices, fifth M1 and M2 multiplicative Zagreb indices for Dutch windmill graph, Kulli cyclic windmill graph, Kulli path windmill graph and French windmill graph.

APA, Harvard, Vancouver, ISO, and other styles

41

Horsman, Clare. "Quantum picturalism for topological cluster-state computing." New Journal of Physics 13, no. 9 (2011): 095011. http://dx.doi.org/10.1088/1367-2630/13/9/095011.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Ebrahimi, Mahmood, and Mehdi Alaeiyan. "New Method for Computing Some Topological Indices." Journal of Computational and Theoretical Nanoscience 12, no. 10 (2015): 3527–30. http://dx.doi.org/10.1166/jctn.2015.4233.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Imran, Muhammad, Abdul Qudair Baig, Shafiq Ur Rehman, Haidar Ali, and Roslan Hasni. "Computing topological polynomials of mesh-derived networks." Discrete Mathematics, Algorithms and Applications 10, no. 06 (2018): 1850077. http://dx.doi.org/10.1142/s1793830918500775.

Full text

Abstract:

Topological descriptors are numerical parameters of a molecular graph which characterize its molecular topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randić, atom-bond connectivity [Formula: see text] and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. The counting polynomials are those polynomials having at exponent the extent of a property partition and coefficients the multiplicity/occurrence of the corresponding partition. All of the studied interconnection mesh networks in this paper are motivated by the molecular structure of a Sodium chloride NaCl. In this paper, Omega, Sadhana and PI polynomials are computed for mesh-derived networks. These polynomials were proposed on the ground of quasi-orthogonal cut edge strips in polycyclic graphs. These polynomials count equidistant and non-equidistant edges in graphs. Moreover, the analytical closed formulas of these polynomials for mesh-derived networks are computed for the first time.

APA, Harvard, Vancouver, ISO, and other styles

44

DILÃO, RUI, and JOSÉ AMIGÓ. "COMPUTING THE TOPOLOGICAL ENTROPY OF UNIMODAL MAPS." International Journal of Bifurcation and Chaos 22, no. 06 (2012): 1250152. http://dx.doi.org/10.1142/s0218127412501520.

Full text

Abstract:

We derive an algorithm to determine recursively the lap number (minimal number of monotone pieces) of the iterates of unimodal maps of an interval with free end-points. For this family of maps, the kneading sequence does not determine the lap numbers. The algorithm is obtained by the sign analysis of the itineraries of the critical point and of the boundary points of the interval map. We apply this algorithm to the estimation of the growth number and the topological entropy of maps with direct and reverse bifurcations.

APA, Harvard, Vancouver, ISO, and other styles

45

Burton, P. J., and M. D. Gould. "Unitary R-matrices for topological quantum computing." Reports on Mathematical Physics 57, no. 1 (2006): 89–96. http://dx.doi.org/10.1016/s0034-4877(06)80010-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

Sakkalis, Takis, and Zenon Ligatsikas. "Computing the topological degree of polynomial maps." Bulletin of the Australian Mathematical Society 56, no. 1 (1997): 87–94. http://dx.doi.org/10.1017/s0004972700030768.

Full text

Abstract:

Let C be a cube in Rn+1 and let F = (f1, …, fn+1) be a polynomial vector field. In this note we propose a recursive algorithm for the computation of the degree of F on C. The main idea of the algorithm is that the degree of F is equal to the algebraic sum of the degrees of the map (f1, f2, …, fi−1, fi, fi+1, …, fn+1) over all sides of C, thereby reducing an (n + 1)–dimensional problem to an n–dimensional one.

APA, Harvard, Vancouver, ISO, and other styles

47

Liu, Jia-Bao, Wei Gao, Muhammad Kamran Siddiqui, and Muhammad Reza Farahani. "Computing three topological indices for Titania nanotubes." AKCE International Journal of Graphs and Combinatorics 13, no. 3 (2016): 255–60. http://dx.doi.org/10.1016/j.akcej.2016.07.001.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

Block, Louis, James Keesling, Shihai Li, and Kevin Peterson. "An improved algorithm for computing topological entropy." Journal of Statistical Physics 55, no. 5-6 (1989): 929–39. http://dx.doi.org/10.1007/bf01041072.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

Webster, Paul. "Topological Quantum Computing in Multiple Surface Codes." Quantum Views 4 (April 6, 2020): 34. http://dx.doi.org/10.22331/qv-2020-04-06-34.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

Paoluzzi, Alberto, Vadim Shapiro, Antonio Dicarlo, Francesco Furiani, Giulio Martella, and Giorgio Scorzelli. "Topological Computing of Arrangements with (Co)Chains." ACM Transactions on Spatial Algorithms and Systems 7, no. 1 (2021): 1–29. http://dx.doi.org/10.1145/3401988.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!