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Related papers: Quantum Tutte Embeddings

200 papers

Tutte's celebrated barycentric embedding theorem describes a natural way to build straight-line embeddings (crossing-free drawings) of a (3-connected) planar graph: map the vertices of the outer face to the vertices of a convex polygon, and…

Computational Geometry · Computer Science 2026-03-10 Éric Colin de Verdière , Vincent Despré , Loïc Dubois

In this paper, we initiate the study of quantum algorithms in the Graph Drawing research area. We focus on two foundational drawing standards: 2-level drawings and book layouts. Concerning $2$-level drawings, we consider the problems of…

Data Structures and Algorithms · Computer Science 2023-07-18 Susanna Caroppo , Giordano Da Lozzo , Giuseppe Di Battista

This work shows that minimizing the depth of a quantum circuit composed of commuting operations reduces to a vertex coloring problem on an appropriately constructed graph, where gates correspond to vertices and edges encode…

Quantum Physics · Physics 2026-02-11 Hochang Lee , Kyung Chul Jeong , Panjin Kim

Quantum computing is captured in the formalism of the monoidal subcategory of $\textbf{Vect}_{\mathbb C}$ generated by $\mathbb C^2$ -- in particular, quantum circuits are diagrams in $\textbf{Vect}_{\mathbb C}$ -- while topological quantum…

Quantum Physics · Physics 2024-06-04 Mahmud Azam , Steven Rayan

Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…

Machine Learning · Statistics 2014-01-20 Brian Baingana , Georgios B. Giannakis

Quantum computation is a promising emerging technology which, compared to conventional computation, allows for substantial speed-ups e.g. for integer factorization or database search. However, since physical realizations of quantum…

Quantum Physics · Physics 2018-06-07 Alwin Zulehner , Robert Wille

The key obstacle to the realization of a scalable quantum computer is overcoming environmental and control errors. Topological quantum computation has attracted great attention because it has emerged as one of the most promising approaches…

Mesoscale and Nanoscale Physics · Physics 2023-09-12 Deyuan Zou , Naiqiao Pan , Tian Chen , Houjun Sun , Xiangdong Zhang

This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…

Quantum Physics · Physics 2015-06-19 Louis H. Kauffman , Samuel J. Lomonaco

This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…

Quantum Physics · Physics 2024-07-17 Boxuan Ai

We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality…

Quantum Physics · Physics 2020-02-12 E. O. Kiktenko , A. S. Nikolaeva , Peng Xu , G. V. Shlyapnikov , A. K. Fedorov

We introduce the concept of embedding quantum simulators, a paradigm allowing the efficient quantum computation of a class of bipartite and multipartite entanglement monotones. It consists in the suitable encoding of a simulated quantum…

Quantum Physics · Physics 2015-06-16 R. Di Candia , B. Mejia , H. Castillo , J. S. Pedernales , J. Casanova , E. Solano

Graphical models are useful tools for describing structured high-dimensional probability distributions. Development of efficient algorithms for generating unbiased and independent samples from graphical models remains an active research…

Quantum Physics · Physics 2026-04-02 Nico Piatkowski , Christa Zoufal

Tensor networks have been successfully applied in simulation of quantum physical systems for decades. Recently, they have also been employed in classical simulation of quantum computing, in particular, random quantum circuits. This paper…

Quantum Physics · Physics 2025-07-08 Xin Hong , Xiangzhen Zhou , Sanjiang Li , Yuan Feng , Mingsheng Ying

Quantum computers hold promise to improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties more complex than tractable at present on classical architectures. Here, we discuss…

Quantum Physics · Physics 2022-05-03 Christian Vorwerk , Nan Sheng , Marco Govoni , Benchen Huang , Giulia Galli

The connection between certain entangled states and graphs has been heavily studied in the context of measurement-based quantum computation as a tool for understanding entanglement. Here we show that this correspondence can be harnessed in…

Quantum Physics · Physics 2016-03-23 Liming Zhao , Carlos A. Pérez-Delgado , Joseph F. Fitzsimons

We investigate quantum circuits for graph representation learning, and propose equivariant quantum graph circuits (EQGCs), as a class of parameterized quantum circuits with strong relational inductive bias for learning over graph-structured…

Machine Learning · Computer Science 2022-06-15 Péter Mernyei , Konstantinos Meichanetzidis , İsmail İlkan Ceylan

Node embedding is a key technique for representing graph nodes as vectors while preserving structural and relational properties, which enables machine learning tasks like feature extraction, clustering, and classification. While classical…

Quantum Physics · Physics 2025-03-11 Hristo N. Djidjev

Topological quantum computation is a promising technique to achieve large-scale, error-corrected computation. Quantum hardware is used to create a large, 3-dimensional lattice of entangled qubits while performing computation requires…

Quantum Physics · Physics 2014-04-04 Alexandru Paler , Simon J. Devitt , Kae Nemoto , Ilia Polian

Distributed quantum computing is motivated by the difficulty in building large-scale, individual quantum computers. To solve that problem, a large quantum circuit is partitioned and distributed to small quantum computers for execution.…

Quantum Physics · Physics 2023-10-09 Marc Grau Davis , Joaquin Chung , Dirk Englund , Rajkumar Kettimuthu

Quantum state tomography is a key process in most quantum experiments. In this work, we employ quantum machine learning for state tomography. Given an unknown quantum state, it can be learned by maximizing the fidelity between the output of…