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:1801.05417

Quantum Walk Inspired Neural Networks for Graph-Structured Data

Stefan Dernbach, Arman Mohseni-Kabir, Siddharth Pal, Don Towsley, Miles Gepner

Published Jan 16, 2018• 2 citations
arXivHTMLPDF

Abstract

In recent years, new neural network architectures designed to operate on graph-structured data have pushed the state-of-the-art in the field. A large set of these architectures utilize a form of classical random walks to diffuse information. We propose quantum walk neural networks (QWNN), a novel graph neural network architecture based on quantum random walks, the quantum parallel to classical random walks. A QWNN learns a quantum walk on a graph to construct a diffusion operator which can then be applied to graph-structured data. We demonstrate the use of QWNNs on a variety of prediction tasks on graphs involving temperature, biological, and molecular datasets.

DOI
10.48550/arxiv.1801.05417

Related papers

Quantum walk neural networks with feature dependent coins

Stefan Dernbach, Arman Mohseni-Kabir, Siddharth Pal +2 more

Abstract Recent neural networks designed to operate on graph-structured data have proven effective in many domains. These graph neural networks often diffuse information using the spatial structure of the graph. We propose a quantum walk neural network that learns a diffusion operation that is not only dependent on the geometry of the graph but also on the features of the nodes and the learning task. A quantum walk neural network is based on learning the coin operators that determine the behavior of quantum random walks, the quantum parallel to classical random walks. We demonstrate the effectiveness of our method on multiple classification and regression tasks at both node and graph levels.

Applied Network Science•Sep 23, 2019•24 citations

Bosonic Random Walk Networks for Graph Learning

Shiv Shankar Shankar, Don Towsley

The development of Graph Neural Networks (GNNs) has led to great progress in machine learning on graph-structured data. These networks operate via diffusing information across the graph nodes while capturing the structure of the graph. Recently there has also seen tremendous progress in quantum computing techniques. In this work, we explore applications of multi-particle quantum walks on diffusing information across graphs. Our model is based on learning the operators that govern the dynamics of quantum random walkers on graphs. We demonstrate the effectiveness of our method on classification and regression tasks.

arXiv:2101.00082•Dec 31, 2020•1 citation

Enable Quantum Graph Neural Networks on a Single Qubit With Quantum Walk

Yijie Zhu, Richard Jiang, Qiang Ni +1 more

Quantum computing holds significant potential for advancing machine learning, particularly in handling complex graph-structured data. This paper introduces Single-Qubit Quantum Graph Neural Networks (sQGNNs), a novel model that integrates quantum networks with quantum walk operations to improve generalization in graph learning tasks. By leveraging quantum walks, we demonstrated sQGNNs capture complex relational patterns and enhance network expressiveness beyond classical methods. Our results proved that quantum encoding efficiently represents high-dimensional graph data, preserving dependencies and optimizing memory use. Across benchmark datasets, sQGNNs demonstrate superior generalization and robustness against overfitting, achieving higher accuracy with reduced computational cost. Our results underscore sQGNNs’ promise for scalable, quantum-enhanced graph learning, establishing a foundation for future quantum-assisted machine learning applications.

IEEE Transactions on Artificial Intelligence•Jul 28, 2025•4 citations

Quantum Walk-Based Optimization of Neural Network Architectures

Jincheng Zhang

This paper investigates the application of quantum walks to the optimization of neural network architectures, a problem traditionally addressed through computationally intensive classical methods. The core idea is to leverage the inherent parallelism and probabilistic nature of quantum walks to efficiently explore the vast architecture space of neural networks. We propose a framework where a quantum walk is performed on a graph representing candidate neural network architectures. The walk's evolution is governed by a Hamiltonian operator designed to encourage the selection of architectures with desirable performance characteristics, as measured by a predefined objective function. Through theoretical analysis and conceptual design, we demonstrate the potential for quantum walks to achieve significant speedups compared to traditional NAS algorithms, potentially realizing exponential improvements in the search process. The exploration of this approach opens new avenues for designing high-performing neural networks with reduced computational costs.

•Sep 2, 2026•0 citations

Quantum Graph Neural Networks on a Single Qubit

Yijie Zhu, Richard Jiang

In the NISQ era, implementing practical quantum ma002 chine learning faces challenges due to limited resources. A recent advancement involves a novel single-qubit methodology, allowing for the execution of numerous operations on a single qubit. However, its applicability to complex neural network architectures remains uncertain. This study focuses on graph data, known for its intricate structure and inherent challenges for machine learning. Utilizing the quantum walk, we introduce a graph embedding approach to reduce network parameters, resulting in the design of a novel architecture called the single-qubit Quantum Graph Neural Network (sQGNN). Experimental assessments, including simulations, demonstrate the adaptability of sQGNNs to graphs of varying dimensions and compositions. The resource-efficient nature of sQGNNs is showcased through practical executions on quantum computers, using only one qubit. This capability highlights the efficient utilization of limited qubit resources, paving the way for expansive quantum graph neural networks on resource-constrained Variational Quantum Circuits (VQCs). This breakthrough opens up new possibilities for practical applications within the current NISQ regime.

•Dec 14, 2022•0 citations

Quantum-Inspired Neural Networks with Adaptive Graph Structures

Jincheng Zhang

This paper introduces a novel approach to neural network design, termed Quantum-Inspired Neural Networks (QINNs) with Adaptive Graph Structures. The core idea is to leverage the fundamental principles of quantum mechanics – specifically superposition and entanglement – to create a network architecture that exhibits enhanced information processing capabilities. Traditional neural networks often struggle with complex, non-linear relationships and can suffer from vanishing gradients during training. QINNs address these limitations by employing dynamically evolving graph structures that mimic the interconnectedness and efficient information transfer observed in quantum systems. The network architecture is designed to represent data through a superposition of states, allowing for the exploration of multiple solution paths simultaneously. Furthermore, adaptive graph structures, inspired by entanglement, facilitate the correlation of information between nodes, significantly improving the network's ability to capture intricate patterns. This approach represents a significant departure from simply using quantum concepts as an inspirational element; it's a fundamental integration of quantum principles into the neural network design, leading to potentially superior performance in tasks demanding high computational efficiency and pattern recognition accuracy. The paper outlines the theoretical framework, the proposed architecture, and discusses the potential benefits and future research directions.

•Sep 3, 2026•0 citations
In recent years, new neural network architectures designed to operate on graph-structured data have pushed the state-of-the-art in the field. A large set of these architectures utilize a form of classical random walks to diffuse information. We propose quantum walk neural networks (QWNN), a novel graph neural network architecture based on quantum random walks, the quantum parallel to classical random walks. A QWNN learns a quantum walk on a graph to construct a diffusion operator which can then be applied to graph-structured data. We demonstrate the use of QWNNs on a variety of prediction tasks on graphs involving temperature, biological, and molecular datasets.
Abstract Recent neural networks designed to operate on graph-structured data have proven effective in many domains. These graph neural networks often diffuse information using the spatial structure of the graph. We propose a quantum walk neural network that learns a diffusion operation that is not only dependent on the geometry of the graph but also on the features of the nodes and the learning task. A quantum walk neural network is based on learning the coin operators that determine the behavior of quantum random walks, the quantum parallel to classical random walks. We demonstrate the effectiveness of our method on multiple classification and regression tasks at both node and graph levels.
The development of Graph Neural Networks (GNNs) has led to great progress in machine learning on graph-structured data. These networks operate via diffusing information across the graph nodes while capturing the structure of the graph. Recently there has also seen tremendous progress in quantum computing techniques. In this work, we explore applications of multi-particle quantum walks on diffusing information across graphs. Our model is based on learning the operators that govern the dynamics of quantum random walkers on graphs. We demonstrate the effectiveness of our method on classification and regression tasks.
Quantum computing holds significant potential for advancing machine learning, particularly in handling complex graph-structured data. This paper introduces Single-Qubit Quantum Graph Neural Networks (sQGNNs), a novel model that integrates quantum networks with quantum walk operations to improve generalization in graph learning tasks. By leveraging quantum walks, we demonstrated sQGNNs capture complex relational patterns and enhance network expressiveness beyond classical methods. Our results proved that quantum encoding efficiently represents high-dimensional graph data, preserving dependencies and optimizing memory use. Across benchmark datasets, sQGNNs demonstrate superior generalization and robustness against overfitting, achieving higher accuracy with reduced computational cost. Our results underscore sQGNNs’ promise for scalable, quantum-enhanced graph learning, establishing a foundation for future quantum-assisted machine learning applications.
This paper investigates the application of quantum walks to the optimization of neural network architectures, a problem traditionally addressed through computationally intensive classical methods. The core idea is to leverage the inherent parallelism and probabilistic nature of quantum walks to efficiently explore the vast architecture space of neural networks. We propose a framework where a quantum walk is performed on a graph representing candidate neural network architectures. The walk's evolution is governed by a Hamiltonian operator designed to encourage the selection of architectures with desirable performance characteristics, as measured by a predefined objective function. Through theoretical analysis and conceptual design, we demonstrate the potential for quantum walks to achieve significant speedups compared to traditional NAS algorithms, potentially realizing exponential improvements in the search process. The exploration of this approach opens new avenues for designing high-performing neural networks with reduced computational costs.
In the NISQ era, implementing practical quantum ma002 chine learning faces challenges due to limited resources. A recent advancement involves a novel single-qubit methodology, allowing for the execution of numerous operations on a single qubit. However, its applicability to complex neural network architectures remains uncertain. This study focuses on graph data, known for its intricate structure and inherent challenges for machine learning. Utilizing the quantum walk, we introduce a graph embedding approach to reduce network parameters, resulting in the design of a novel architecture called the single-qubit Quantum Graph Neural Network (sQGNN). Experimental assessments, including simulations, demonstrate the adaptability of sQGNNs to graphs of varying dimensions and compositions. The resource-efficient nature of sQGNNs is showcased through practical executions on quantum computers, using only one qubit. This capability highlights the efficient utilization of limited qubit resources, paving the way for expansive quantum graph neural networks on resource-constrained Variational Quantum Circuits (VQCs). This breakthrough opens up new possibilities for practical applications within the current NISQ regime.
This paper introduces a novel approach to neural network design, termed Quantum-Inspired Neural Networks (QINNs) with Adaptive Graph Structures. The core idea is to leverage the fundamental principles of quantum mechanics – specifically superposition and entanglement – to create a network architecture that exhibits enhanced information processing capabilities. Traditional neural networks often struggle with complex, non-linear relationships and can suffer from vanishing gradients during training. QINNs address these limitations by employing dynamically evolving graph structures that mimic the interconnectedness and efficient information transfer observed in quantum systems. The network architecture is designed to represent data through a superposition of states, allowing for the exploration of multiple solution paths simultaneously. Furthermore, adaptive graph structures, inspired by entanglement, facilitate the correlation of information between nodes, significantly improving the network's ability to capture intricate patterns. This approach represents a significant departure from simply using quantum concepts as an inspirational element; it's a fundamental integration of quantum principles into the neural network design, leading to potentially superior performance in tasks demanding high computational efficiency and pattern recognition accuracy. The paper outlines the theoretical framework, the proposed architecture, and discusses the potential benefits and future research directions.