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About 10,000 papers for “Quantum graph”

Quantum graph walks II: Quantum walks on graph coverings

Higuchi Yusuke, Konno Norio, Sato Iwao et al. · Yokohama National University Repository (Yokohama National University) · 2013

Cited by 0

Quantum Graph Analysis

Peter Maunz, Jonathan David Sterk, Daniel Lobser et al. · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2016

In recent years, advanced network analytics have become increasingly important to na- tional security with applications ranging from cyber security to detection and disruption of ter- rorist networks. While classical computing solutions have received considerable investment, the development of quantum algorithms to address problems, such as data mining of attributed relational graphs, is a largely unexplored space. Recent theoretical work has shown that quan- tum algorithms for graph analysis can be more efficient than their classical counterparts. Here, we have implemented a trapped-ion-based two-qubit quantum information proces- sor to address these goals. Building on Sandia's microfabricated silicon surface ion traps, we have designed, realized and characterized a quantum information processor using the hyperfine qubits encoded in two 171 Yb + ions. We have implemented single qubit gates using resonant microwave radiation and have employed Gate set tomography (GST) to characterize the quan- tum process. For the first time, we were able to prove that the quantum process surpasses the fault tolerance thresholds of some quantum codes by demonstrating a diamond norm distance of less than 1 . 9 x 10 [?] 4 . We used Raman transitions in order to manipulate the trapped ions' motion and realize two-qubit gates. We characterized the implemented motion sensitive and insensitive single qubit processes and achieved a maximal process infidelity of 6 . 5 x 10 [?] 5 . We implemented the two-qubit gate proposed by Molmer and Sorensen and achieved a fidelity of more than 97 . 7%.

Cited by 0Open access

Quantum Graph Parameters

Darbari Kozekanan, Parisa · Journal of International Crisis and Risk Communication Research · 2022

This dissertation considers some of the advantages, and limits, of applying quantum computing to solve two important graph problems. The first is estimating a graph's quantum chromatic number. The quantum chromatic number is the minimum number of colors necessary in a two-player game where the players cannot communicate but share an entangled state and must convince a referee with probability one that they have a proper vertex coloring. We establish several spectral lower bounds for the quantum chromatic number. These lower bounds extend the well-known Hoffman lower bound for the classical chromatic number. The second is the Pattern Matching on Labeled Graphs Problem (PMLG). Here the objective is to match a string (called a pattern) P to a walk in an edge labeled graph G = (V, E). In addition to providing a new quantum algorithm for PMLG, this work establishes conditional lower bounds on the time complexity of any quantum algorithm for PMLG. These include a conditional lower bound based on the recently proposed NC-QSETH and a reduction from the Longest Common Subsequence Problem (LCS). For PMLG where substitutions are allowed to the pattern, our results demonstrate that (i) a quantum algorithm running in time O(|E|m1-ε + |E|1-εm) for any constant ε > 0 would provide an algorithm for LCS on two strings X and Y running in time Õ(|X||Y|1-ε + |X|1-ε|Y|), which is better than any known quantum algorithm for LCS, and (ii) a quantum algorithm running in time O(|E|m½-ε + |E|½-εm) would violate NC-QSETH. Results (i) and (ii) hold even when restricted to binary alphabets for P and the edge labels in G. Our quantum algorithm is for all versions of PMLG (exact, only substitutions, and substitutions/insertions/deletions) and runs in time Õ(√|V||E|· m), making it an improvement over the classical O(|E|m) time algorithm when the graph is non-sparse.

Cited by 0Open access

From Quantum Graph Computing to Quantum Graph Learning: A Survey

Yehui Tang, Junchi Yan, Edwin R. Hancock · arXiv (Cornell University) · 2022

Quantum computing (QC) is a new computational paradigm whose foundations relate to quantum physics. Notable progress has been made, driving the birth of a series of quantum-based algorithms that take advantage of quantum computational power. In this paper, we provide a targeted survey of the development of QC for graph-related tasks. We first elaborate the correlations between quantum mechanics and graph theory to show that quantum computers are able to generate useful solutions that can not be produced by classical systems efficiently for some problems related to graphs. For its practicability and wide-applicability, we give a brief review of typical graph learning techniques designed for various tasks. Inspired by these powerful methods, we note that advanced quantum algorithms have been proposed for characterizing the graph structures. We give a snapshot of quantum graph learning where expectations serve as a catalyst for subsequent research. We further discuss the challenges of using quantum algorithms in graph learning, and future directions towards more flexible and versatile quantum graph learning solvers.

Cited by 3Open access

Quantum Graph Attention Networks: Trainable Quantum Encoders for Inductive Graph Learning

Arthur M. Faria, Mehdi Djellabi, Igor O. Sokolov et al. · ArXiv.org · 2025

We introduce Quantum Graph Attention Networks (QGATs) as trainable quantum encoders for inductive learning on graphs, extending the Quantum Graph Neural Networks (QGNN) framework. QGATs leverage parameterized quantum circuits to encode node features and neighborhood structures, with quantum attention mechanisms modulating the contribution of each neighbor via dynamically learned unitaries. This allows for expressive, locality-aware quantum representations that can generalize across unseen graph instances. We evaluate our approach on the QM9 dataset, targeting the prediction of various chemical properties. Our experiments compare classical and quantum graph neural networks-with and without attention layers-demonstrating that attention consistently improves performance in both paradigms. Notably, we observe that quantum attention yields increasing benefits as graph size grows, with QGATs significantly outperforming their non-attentive quantum counterparts on larger molecular graphs. Furthermore, for smaller graphs, QGATs achieve predictive accuracy comparable to classical GAT models, highlighting their viability as expressive quantum encoders. These results show the potential of quantum attention mechanisms to enhance the inductive capacity of QGNN in chemistry and beyond.

Cited by 0Open access

New Quantum Graph Theory

Materov, Sergej · Figshare · 2025

A Testable Quantum Graph Theory of Spacetime: Predictions for Cryogenic Qubits and Colliders. The theory provides explicit falsifiability criteria. Universe as finite directed graph.

Cited by 0Open access

VLSI Quantum Graph Photonics

Zuntao Fu, Jie Bao, Tanumoy Pramanik et al. · 2023

We report a graph-based very-large-scale-integrated silicon-photonic quantum chip. Having the correspondence between quantum chip and graph theory, we demonstrate the generation of multiphoton multidimensional entanglement and determination of modulussquared Hafnian (Permanent) of graph’s adjacency matrices.

Cited by 0

Quantum Causal Graph Dynamics

Pablo Arrighi, Simon Martiel · HAL (Le Centre pour la Communication Scientifique Directe) · 2016

Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded speed, with respect to the distance given by the graph. Suppose, moreover, that the graph itself is subject to the evolution, and may be driven to be in a quantum superposition of graphs---in accordance to the superposition principle. We show that these unitary causal operators must decompose as a finite-depth circuit of local unitary gates. This unifies a result on Quantum Cellular Automata with another on Reversible Causal Graph Dynamics. Along the way we formalize a notion of causality which is valid in the context of quantum superpositions of time-varying graphs, and has a number of good properties. Keywords: Quantum Lattice Gas Automata, Block-representation, Curtis-Hedlund-Lyndon, No-signalling, Localizability, Quantum Gravity, Quantum Graphity, Causal Dynamical Triangulations, Spin Networks, Dynamical networks, Graph Rewriting.

Cited by 0Open access

Quantum graph walks I:

2016

Cited by 0

Quantum Information . . . Graph States

Dirk-michael Schlingemann · 2005

Eigenschaften durch einen Graphen beschrieben werden. Jeder Knoten des Graphen entspricht einem einzelnen System oder Teilchen. Eine Kante kann als Quantenkorrelation (Verschränkung) zwischen den verbundenen Teilchen angesehen werden. Die hier dargestellte Theorie der Graphenzustände ist einerseits aus dem Modell des Einweg-Quantencomputers und andererseits aus dem Konzept der Graphencodes entstanden, nachdem sich die enge Beziehung beider Begriffe herausgestellt hatte. Der Einweg-Quantencomputer ist ein neues Modell zur Realisierung von

Cited by 0

New Quantum Graph Theory

Materov, Sergej · Figshare · 2025

In the previous version, the Hamiltonian was not explicitly derived, which confined the theoretical predictions to highly complex and currently inaccessible experimental regimes. This work reports an explicitly falsifiable (already today) discrete–quantum‐graph model of spacetime and noise in quantum processors. Continuum limits and recovery of field equations (ℓp→0) remain open for future work; our focus is on delivering real, quantitative falsifiability now.

Cited by 0Open access

New Quantum Graph Theory

Materov, Sergej · Figshare · 2025

Cited by 0Open access

Approximation of Quantum Graph . . .

Pavel Exner, Olaf Post · 2008

Cited by 0

Time-dependent quantum graph

D. U. Matrasulov, Jambul Yusupov, K.K. Sabirov et al. · arXiv (Cornell University) · 2012

In this paper we study quantum star graphs with time-dependent bond lengths. Quantum dynamics is treated by solving Schrodinger equation with time-dependent boundary conditions given on graphs. Time-dependence of the average kinetic energy is analyzed. Space-time evolution of the Gaussian wave packet is treated for harmonically breathing star graph.

Cited by 0Open access

New Quantum Graph Theory

Materov, Sergej · Figshare · 2025

Cited by 0Open access

New Quantum Graph Theory

Materov, Sergej · Figshare · 2025

A Testable Quantum Graph Theory of Spacetime: Predictions for Cryogenic Qubits and Colliders. The theory provides explicit falsifiability criteria. Universe as finite directed graph.

Cited by 0Open access

Quantum graph as a quantum spectral filter

Turek, Ondřej, Cheon, Taksu · arXiv (Cornell University) · 2012

We study the transmission of a quantum particle along a straight input--output line to which a graph $Γ$ is attached at a point. In the point of contact we impose a singularity represented by a certain properly chosen scale-invariant coupling with a coupling parameter $α$. We show that the probability of transmission along the line as a function of the particle energy tends to the indicator function of the energy spectrum of $Γ$ as $α\to\infty$. This effect can be used for a spectral analysis of the given graph $Γ$. Its applications include a control of a transmission along the line and spectral filtering. The result is illustrated with an example where $Γ$ is a loop exposed to a magnetic field. Two more quantum devices are designed using other special scale-invariant vertex couplings. They can serve as a band-stop filter and as a spectral separator, respectively.

Cited by 0Open access

Quantum secret sharing with quantum graph states

Liang Jian-Wu, Cheng Zi, Jinjing Shi et al. · Acta Physica Sinica · 2016

Quantum secret sharing is an important way to achieve secure communications, which has critical applications in the field of information security for its physical properties. According to the perspective of the practical applications, improving the confidentiality and integrity of secret sharing schemes is a good method to increase the security and reliability of communications. In this paper, we propose a quantum secret sharing scheme based on generator matrix segmentation and the structural features of quantum graph states. The security of the secure secret sharing scheme is guaranteed by the pattern of transferring information by stabilizers, scalability of the information and new recovery strategy provided by the entanglement of the related graph states. It puts forward an effective solution to the problem of matrix cycle period, where some numbers without the primitive element cannot construct the generation matrix. First of all, the physical properties of quantum bits (qubits), such as uncertainty principle, no-cloning theorem and indistinguishability, not only optimize the classical schemes but also ensure the absolute safety of communication. Secondly, the application of matrix segmentation makes secret information has better scalability. It improves the coding diversity and the difficulty in deciphering. Thirdly, the favorable entanglement properties and mature experiment preparation techniques of graph states provide an approach to the practical applications. The superiority of the yielded graph states is described in graphical fashion with an elegant stabilizer. Fourthly, the shuffling operation can ensure the independence of the message among participants. Therefore, Eve can not obtain any useful information by measuring randomly. Two group-recovery protocols are proposed to show the secret recovering processing through rebuilding sub-secrets among legal cooperative participants. In the scheme design, the dealer extracts the classical secret information according to the corresponding principle between the classical and quantum information, and divides the classical secret through generated matrix which is produced with the primitive elements in finite domain satisfying the linear independence for any k column vectors. Then the dealer encodes information into graph states and distributes particles to the legal participants with unitary operations. Subsequently, the credible center obtains sub-secrets by the theory of graph states and the group recovery protocol. He can achieve the initial classical secret via the inverse algorithm of matrix segmentation. After getting the classical secret, he recovers quantum secret according to the relationship between classical information and quantum information. Theoretical analysis shows that this scheme can provide better security and scalability of the information. It is appropriate to realize the secret sharing in the quantum network communication to protect secrets from eavesdropping. Also, it can provide an approach to designing diverse and scalable quantum secure communication schemes based on quantum graph states, the algorithm of matrix segmentation, and group-recovery protocol.

Cited by 5Open access

Guided graph compression for quantum graph neural networks

Casals, Mikel, Belis, Vasilis, Combarro, Elias F. et al. · Repository for Publications and Research Data (ETH Zurich) · 2025

Graph neural networks (GNNs) are effective for processing graph-structured data but face challenges with large graphs due to high memory requirements and inefficient sparse matrix operations on GPUs. Quantum computing offers a promising avenue to address these issues and inspires new algorithmic approaches. In particular, quantum GNNs (QGNNs) have been explored in recent literature. However, current quantum hardware limits the dimension of the data that can be effectively encoded. Existing approaches either simplify datasets manually or use artificial graph datasets. This work introduces the guided graph compression (GGC) framework, which uses a graph autoencoder to reduce both the number of nodes and the dimensionality of node features. The compression is guided to enhance the performance of a downstream classification task, which can be applied either with a quantum or a classical classifier. The framework is evaluated on the Jet Tagging task, a classification problem of fundamental importance in high energy physics that involves distinguishing particle jets initiated by quarks from those by gluons. We compare GGC to a model that uses the autoencoder as a preprocessing step and to a baseline classical GNN classifier. Our numerical results demonstrate that GGC outperforms both alternatives, while also facilitating the testing of novel QGNN ansatzes on realistic datasets.

Cited by 0Open access

Distributing Arbitrary Quantum Graph States by Graph Transformation

Tingxiang Ji, Jianqing Liu, Zheshen Zhang · arXiv (Cornell University) · 2024

Quantum graph state is a special class of nonlocal state among multiple quantum particles, underpinning several nonclassical and promising applications such as quantum computing and quantum secret sharing. Recently, establishing quantum graph states among physically distant nodes has gained increasing popularity owing to its potential in expanding current quantum applications in scale. Existing research on this topic relies on a two-step approach: first distributing low-dimension elementary entanglement to target nodes, and then fusing them into a high-dimension quantum graph state. However, most existing studies focus solely on minimizing costs (e.g., the number of elementary entanglements consumed) to entangle target nodes, while neglecting the structure of the final quantum graph state. This can easily result in weak system entanglement, jeopardizing the graph state under partial measurement or noises. In this paper, we aim to establish any arbitrary quantum graph states of strong entanglement structures at a much lower cost than the state of the art. The method is to search for and establish an alternative state to the target state that is of lowest cost in creation. Subsequently, we transform such an alternative state back to the target state via compressed single-qubit Clifford operations. To verify the performance of our developed algorithm, we conduct comprehensive simulations based on an open dataset containing all graph state structures up to 8 qubits. The results demonstrate fast algorithm convergence, an increased success probability in distributing any graph states, and $53.57\%$ saving in ERP cost compared with the state-of-the-art baseline.

Cited by 0Open access