Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2407.14281 · IEEE International Conference on Quantum Computing and Engineering (QCE)

QuOp: A Quantum Operator Representation for Nodes

Andrew Vlasic, Salvador Aguiñaga

Published Aug 30, 2025• 0 citations
arXivHTMLPDF

Abstract

We derive an intuitive and novel method to represent nodes in a graph with special unitary operators, or quantum operators, which does not require parameter training and is competitive with classical methods on scoring similarity between nodes. This method opens up future possibilities to apply quantum algorithms for NLP or other applications that need to detect anomalies within a network structure. Specifically, this technique leverages the advantage of quantum computation, representing nodes in higher dimensional Hilbert spaces. To create the representations, the local topology around each node with a predetermined number of hops is calculated and the respective adjacency matrix is used to derive the Hamiltonian. As a consequence of this simplicity, the set of adjacency matrices of size$2^{n} \times 2^{n}$generates a sub-vector space of the Lie algebra of the special unitary operators,$\mathfrak{s u}\left(2^{n}\right)$. This sub-vector space in turn generates a subgroup of the Lie group of special unitary operators,$\text{SU}\left(2^{n}\right)$. Applications of our quantum embedding method, in comparison with the classical algorithms GloVe (a natural language processing embedding method) and FastRP (a general graph embedding method), display superior performance in measuring similarity between nodes in graph structures.

DOI
10.1109/qce65121.2025.00046

Related papers

Quantum Graph Embeddings for Complex Data Analysis

Jincheng Zhang

Quantum Graph Embeddings represent a novel approach to data analysis, leveraging the power of quantum algorithms to create and manipulate graph structures. This paper introduces a method for generating quantum graphs with enhanced representation capabilities, specifically designed for complex data analysis. We explore the potential of quantum algorithms to efficiently explore graph structure, identify key nodes and connections, and ultimately uncover hidden patterns and relationships within datasets. The core mechanism focuses on creating a scalable and adaptable framework for data representation, addressing limitations inherent in traditional graph embedding techniques. This work proposes a method that is inherently scalable, potentially offering significant advantages in the analysis of intricate and high-dimensional datasets.

•Sep 4, 2026•0 citations

Word and Text Similarity Using Classical Word Embeddings in Quantum NLP Systems

Damir Ćavar, Koushik Reddy Parukola

Word embeddings and vector representations for linguistic units are important in Natural Language Processing (NLP) and AI systems. Engineering of such models involves significant effort, large amounts of data, and costly computations. Many models and systems have been released to the general public, enabling significant research and development in the classical NLP domain. We demonstrate how word and text embeddings as n-dimensional dense vectors of n real numbers in classical computers can be mapped to highly compressed quantum states or quantum embedding using log(n) qubits. In similarity experiments performed on classical and quantum computers, we show no significant information loss that would affect vector distance scores representing words’ semantic similarity. The results show that existing NLP embedding models in classical computing environments can be used in quantum computing. We discuss the issues and limitations of this approach in the context of current quantum computing environments.

IEEE International Conference on Acoustics, Speech, and Signal Processing Workshops (ICASSPW)•Apr 6, 2025•3 citations

Scoring Anomalous Vertices Through Quantum Walks

Andrew Vlasic, Anh T. Pham

Abstract With the constant flow of data from vast sources over the past decades, a plethora of advanced analytical techniques have been developed to extract relevant information from different data types ranging from labeled data, quasi‐labeled data, and data with no labels known a priori. For data with at best quasi‐labels, graphs are a natural representation and have important applications in many industries and scientific disciplines. Specifically, for unlabeled data, anomaly detection on graphs is a method to determine which data points do not posses the latent characteristics that are present in most other data. There have been a variety of classical methods to compute an anomalous score for the individual vertices of a respective graph, such as checking the local topology of a node, random walks, and complex neural networks. Leveraging the structure of the graph, the first quantum algorithm is proposed to calculate the anomaly score of each node by continuously traversing the graph with a uniform starting position for all nodes. The proposed algorithm incorporates well‐known characteristics of quantum walks, and, taking into consideration the noisy intermediate‐scale quantum (NISQ) era and subsequent intermediate‐scale quantum (ISQ) era, an adjustment to the algorithm is provided to mitigate the increasing depth of the circuit. This algorithm is rigorously shown to converge to the expected probability with respect to the initial condition.

arXiv:2311.09855•Annalen der Physik•Feb 16, 2025•4 citations

VQNE: Variational Quantum Network Embedding with Application to Network Alignment

Xinyu Ye, Ge Yan, Junchi Yan

Learning of network embedding with vector-based node representation has attracted wide attention over the decade. It differs from the general setting of graph node embedding whereby the node attributes are also considered and yet may incur privacy issues. In this paper, we depart from the classic CPU/GPU architecture to consider the well-established network alignment problem based on network embedding, and develop a quantum machine learning approach with a low qubit cost for its near-future applicability on Noisy Intermediate-Scale Quantum (NISQ) devices. Specifically, our model adopts the discrete-time quantum walk (QW) and conducts the QW on the tailored merged network to extract structure information from the two aligning networks without the need for quantum state preparation which otherwise requires high quantum gate cost. Then the quantum states from QW are fed to a quantum embedding ansatz (i.e., parameterized circuit) to learn the latent representation of each node. The key part of our approach is to connect these two quantum modules to achieve a pure quantum paradigm without involving classical modules. To our best knowledge, there has not been any classic-quantum hybrid approach to network embedding, let alone a pure quantum paradigm being free from the bottleneck of communication between classic devices and quantum devices, which is still an open problem. Experimental results on two real-world datasets show the effectiveness of our quantum embedding approach in comparison with classical embedding approaches. Our model is readily and efficiently implemented in Python with a full-amplitude simulation of the QW and the quantum circuit. Therefore, our model can be readily deployed on an existing NISQ device with all the circuits provided, and only 13 qubits are needed in the experiments, which is rarely attained in existing quantum graph learning works.

ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD)•Aug 4, 2023•9 citations

Quantum-Inspired Graph Clustering using Amplitude Estimation

Jincheng Zhang

Graph clustering, the process of grouping nodes in a graph based on their relationships, is a cornerstone of numerous data analysis applications, including social network analysis, bioinformatics, and anomaly detection. Traditional graph clustering algorithms often struggle with scalability and computational complexity, particularly when dealing with large graphs. This paper proposes a novel approach to graph clustering that leverages quantum-inspired amplitude estimation techniques. By mimicking the probabilistic nature of quantum algorithms, we approximate the probability distribution of node assignments within clusters, significantly accelerating the clustering process. Our method utilizes a modified version of the Lloyd-Max algorithm, incorporating amplitude estimation to reduce the number of iterations required to converge to a stable clustering solution. We demonstrate, through theoretical analysis and algorithmic design, that this approach can achieve comparable or superior clustering performance compared to conventional methods, while exhibiting a markedly reduced computational footprint. The core contribution lies in adapting amplitude estimation principles – originally developed for quantum computing – to a classical graph clustering context, offering a potentially transformative solution for tackling computationally intensive graph clustering problems. The efficiency gains are particularly pronounced in scenarios with high-dimensional node feature spaces.

•Sep 5, 2026•0 citations

Hamiltonian Simulation and Linear Combination of Unitary Decomposition of Structured Matrices

Robin Ollive, Stéphane Louise

To process a problem with a Quantum Processing Unit (QPU), it must be transformed into a sequence of quantum operators, or gates. These operators are either packed into a query (i.e. quantum algorithm primitive) that encodes the problem, or used to construct the cost function for Variationnal Quantum Algorithm (VQA). Typical queries are the problem Hamiltonian Simulation (HS) and the problem Block-Encoding (BEing). To construct the circuits associated with the quantum description, the problem must be mapped as a Linear Combination of Hamiltonian (LCH) or a Linear Combination of nitaries (LCU) matrices. All the summed Hamiltonian matrices or unitary matrices must have a known decomposition in basic gates. The complexity of this query should be incorporated into the quantum algorithm's query complexity, thereby limiting the processing possibilities of QPU for many problems. In this work, we propose Hamiltonian matrices used to map the problem of interest, and that behave like a single qubit when expressed in the appropriate basis. It leads to a framework, the Special Tripotent Hamiltonian (STH) Framework, able to implement most of the typical problems considered for quantum computing. These methods address many problems implemented on QPUs, ranging from second-quantization chemistry operators to graphs associated with Partial Differential Equations (PDE), sparse matrices, and higher-order optimization problems. This work underlines interesting properties associated with the STH basic gate decomposition. These include the ability to switch between LCH and LCU, map non-Hermitian problems, and construct the quantum circuit queries required for quantum computing. We also provide a list of STH that are used for the matrix decomposition of many structured matrices. These structured matrices are associated with graph adjacency matrices that can be combined to implement structured matrices.

quant-pharXiv:2603.17816•Mar 19, 2026•0 citations
We derive an intuitive and novel method to represent nodes in a graph with special unitary operators, or quantum operators, which does not require parameter training and is competitive with classical methods on scoring similarity between nodes. This method opens up future possibilities to apply quantum algorithms for NLP or other applications that need to detect anomalies within a network structure. Specifically, this technique leverages the advantage of quantum computation, representing nodes in higher dimensional Hilbert spaces. To create the representations, the local topology around each node with a predetermined number of hops is calculated and the respective adjacency matrix is used to derive the Hamiltonian. As a consequence of this simplicity, the set of adjacency matrices of size2n×2n2^{n} \times 2^{n}2n×2ngenerates a sub-vector space of the Lie algebra of the special unitary operators,su(2n)\mathfrak{s u}\left(2^{n}\right)su(2n). This sub-vector space in turn generates a subgroup of the Lie group of special unitary operators,SU(2n)\text{SU}\left(2^{n}\right)SU(2n). Applications of our quantum embedding method, in comparison with the classical algorithms GloVe (a natural language processing embedding method) and FastRP (a general graph embedding method), display superior performance in measuring similarity between nodes in graph structures.
Quantum Graph Embeddings represent a novel approach to data analysis, leveraging the power of quantum algorithms to create and manipulate graph structures. This paper introduces a method for generating quantum graphs with enhanced representation capabilities, specifically designed for complex data analysis. We explore the potential of quantum algorithms to efficiently explore graph structure, identify key nodes and connections, and ultimately uncover hidden patterns and relationships within datasets. The core mechanism focuses on creating a scalable and adaptable framework for data representation, addressing limitations inherent in traditional graph embedding techniques. This work proposes a method that is inherently scalable, potentially offering significant advantages in the analysis of intricate and high-dimensional datasets.
Word embeddings and vector representations for linguistic units are important in Natural Language Processing (NLP) and AI systems. Engineering of such models involves significant effort, large amounts of data, and costly computations. Many models and systems have been released to the general public, enabling significant research and development in the classical NLP domain. We demonstrate how word and text embeddings as n-dimensional dense vectors of n real numbers in classical computers can be mapped to highly compressed quantum states or quantum embedding using log(n) qubits. In similarity experiments performed on classical and quantum computers, we show no significant information loss that would affect vector distance scores representing words’ semantic similarity. The results show that existing NLP embedding models in classical computing environments can be used in quantum computing. We discuss the issues and limitations of this approach in the context of current quantum computing environments.
Abstract With the constant flow of data from vast sources over the past decades, a plethora of advanced analytical techniques have been developed to extract relevant information from different data types ranging from labeled data, quasi‐labeled data, and data with no labels known a priori. For data with at best quasi‐labels, graphs are a natural representation and have important applications in many industries and scientific disciplines. Specifically, for unlabeled data, anomaly detection on graphs is a method to determine which data points do not posses the latent characteristics that are present in most other data. There have been a variety of classical methods to compute an anomalous score for the individual vertices of a respective graph, such as checking the local topology of a node, random walks, and complex neural networks. Leveraging the structure of the graph, the first quantum algorithm is proposed to calculate the anomaly score of each node by continuously traversing the graph with a uniform starting position for all nodes. The proposed algorithm incorporates well‐known characteristics of quantum walks, and, taking into consideration the noisy intermediate‐scale quantum (NISQ) era and subsequent intermediate‐scale quantum (ISQ) era, an adjustment to the algorithm is provided to mitigate the increasing depth of the circuit. This algorithm is rigorously shown to converge to the expected probability with respect to the initial condition.
Learning of network embedding with vector-based node representation has attracted wide attention over the decade. It differs from the general setting of graph node embedding whereby the node attributes are also considered and yet may incur privacy issues. In this paper, we depart from the classic CPU/GPU architecture to consider the well-established network alignment problem based on network embedding, and develop a quantum machine learning approach with a low qubit cost for its near-future applicability on Noisy Intermediate-Scale Quantum (NISQ) devices. Specifically, our model adopts the discrete-time quantum walk (QW) and conducts the QW on the tailored merged network to extract structure information from the two aligning networks without the need for quantum state preparation which otherwise requires high quantum gate cost. Then the quantum states from QW are fed to a quantum embedding ansatz (i.e., parameterized circuit) to learn the latent representation of each node. The key part of our approach is to connect these two quantum modules to achieve a pure quantum paradigm without involving classical modules. To our best knowledge, there has not been any classic-quantum hybrid approach to network embedding, let alone a pure quantum paradigm being free from the bottleneck of communication between classic devices and quantum devices, which is still an open problem. Experimental results on two real-world datasets show the effectiveness of our quantum embedding approach in comparison with classical embedding approaches. Our model is readily and efficiently implemented in Python with a full-amplitude simulation of the QW and the quantum circuit. Therefore, our model can be readily deployed on an existing NISQ device with all the circuits provided, and only 13 qubits are needed in the experiments, which is rarely attained in existing quantum graph learning works.
Graph clustering, the process of grouping nodes in a graph based on their relationships, is a cornerstone of numerous data analysis applications, including social network analysis, bioinformatics, and anomaly detection. Traditional graph clustering algorithms often struggle with scalability and computational complexity, particularly when dealing with large graphs. This paper proposes a novel approach to graph clustering that leverages quantum-inspired amplitude estimation techniques. By mimicking the probabilistic nature of quantum algorithms, we approximate the probability distribution of node assignments within clusters, significantly accelerating the clustering process. Our method utilizes a modified version of the Lloyd-Max algorithm, incorporating amplitude estimation to reduce the number of iterations required to converge to a stable clustering solution. We demonstrate, through theoretical analysis and algorithmic design, that this approach can achieve comparable or superior clustering performance compared to conventional methods, while exhibiting a markedly reduced computational footprint. The core contribution lies in adapting amplitude estimation principles – originally developed for quantum computing – to a classical graph clustering context, offering a potentially transformative solution for tackling computationally intensive graph clustering problems. The efficiency gains are particularly pronounced in scenarios with high-dimensional node feature spaces.
To process a problem with a Quantum Processing Unit (QPU), it must be transformed into a sequence of quantum operators, or gates. These operators are either packed into a query (i.e. quantum algorithm primitive) that encodes the problem, or used to construct the cost function for Variationnal Quantum Algorithm (VQA). Typical queries are the problem Hamiltonian Simulation (HS) and the problem Block-Encoding (BEing). To construct the circuits associated with the quantum description, the problem must be mapped as a Linear Combination of Hamiltonian (LCH) or a Linear Combination of nitaries (LCU) matrices. All the summed Hamiltonian matrices or unitary matrices must have a known decomposition in basic gates. The complexity of this query should be incorporated into the quantum algorithm's query complexity, thereby limiting the processing possibilities of QPU for many problems. In this work, we propose Hamiltonian matrices used to map the problem of interest, and that behave like a single qubit when expressed in the appropriate basis. It leads to a framework, the Special Tripotent Hamiltonian (STH) Framework, able to implement most of the typical problems considered for quantum computing. These methods address many problems implemented on QPUs, ranging from second-quantization chemistry operators to graphs associated with Partial Differential Equations (PDE), sparse matrices, and higher-order optimization problems. This work underlines interesting properties associated with the STH basic gate decomposition. These include the ability to switch between LCH and LCU, map non-Hermitian problems, and construct the quantum circuit queries required for quantum computing. We also provide a list of STH that are used for the matrix decomposition of many structured matrices. These structured matrices are associated with graph adjacency matrices that can be combined to implement structured matrices.