This study explores the application of quantum neural networks (QNN) and variational quantum regression (VQR) in seismic inversion, leveraging quantum computing’s advantages in superposition, entanglement, and interference. Implemented using variational quantum circuits (VQC) and tested on the Qiskit simulator, QNN captures complex seismic data relationships, while VQR focuses on regression tasks. Results demonstrate their potential in geophysical applications but highlight challenges in model generalization and scalability. As quantum computing advances beyond the NISQ era, quantum intelligence is expected to provide new insights for efficient seismic inversion.
This study explores the application of quantum neural networks (QNN) and variational quantum regression (VQR) in seismic inversion, leveraging quantum computing’s advantages in superposition, entanglement, and interference. Implemented using variational quantum circuits (VQC) and tested on the Qiskit simulator, QNN captures complex seismic data relationships, while VQR focuses on regression tasks. Results demonstrate their potential in geophysical applications but highlight challenges in model generalization and scalability. As quantum computing advances beyond the NISQ era, quantum intelligence is expected to provide new insights for efficient seismic inversion.
Seismic inversion-including post-stack, pre-stack, and full waveform inversion is compute and memory-intensive. Recently, several approaches, including physics-informed machine learning, have been developed to address some of these limitations. Motivated by the potential of quantum computing, we report on our attempt to map one such classical physics-informed algorithm to a quantum framework. The primary goal is to investigate the technical challenges of this mapping, given that quantum algorithms rely on computing principles fundamentally different from those in classical computing. Quantum computers operate using qubits, which exploit superposition and entanglement, offering the potential to solve classically intractable problems. While current quantum hardware is limited, hybrid quantum-classical algorithms-particularly in quantum machine learning (QML)-demonstrate potential for near-term applications and can be readily simulated. We apply QML to subsurface imaging through the development of a hybrid quantum physics-informed neural network (HQ-PINN) for post-stack and pre-stack seismic inversion. The HQ-PINN architecture adopts an encoder-decoder structure: a hybrid quantum neural network encoder estimates P- and S-impedances from seismic data, while the decoder reconstructs seismic responses using geophysical relationships. Training is guided by minimizing the misfit between the input and reconstructed seismic traces. We systematically assess the impact of quantum layer design, differentiation strategies, and simulator backends on inversion performance. We demonstrate the efficacy of our approach through the inversion of both synthetic and the Sleipner field datasets. The HQ-PINN framework consistently yields accurate results, showcasing quantum computing's promise for geosciences and paving the way for future quantum-enhanced geophysical workflows.
This paper presents the concept of quantum neural networks (QNN), a new framework that combines quantum computing with topological data analysis to process data defined on simplicial complexes. Based on the fundamentals of topological signal processing and variational quantum circuits, QNN aim to use the structure of simplicial complexes to perform efficient calculations and extract higher-order relational patterns from data. The proposed architecture uses quantum layers (QL), which map interactions between simplices into quantum circuits, providing both in-order and inter-order interactions. The paper describes two QL variants: basic and schematic, providing flexibility for applications with varying complexity. In addition, the paper explores the theoretical foundations of simplicial complexes, quantum neural networks, and the interaction between classical and quantum approaches in data encoding, state evolution and optimization. By leveraging quantum algorithms and eliminating current hardware limitations, QNN promise scalability and enhanced performance for applications in optimization, numerical simulation, and complex systems modeling. This research demonstrates the potential of QNN to advance the field of quantum machine learning, paving the way for future developments of quantum algorithms and their practical applications.
Due to the increasing volume and complexity of seismic datasets, seismic processing is confronted with increasing computational demands, which necessitate the implementation of innovative solutions such as quantum computing. This study applies the Quantum Fourier Transform (QFT), implemented via the Qiskit framework, to two geophysical applications: computing instantaneous seismic attributes and performing Multi-Dimensional Convolution (MDC). We present a workflow for preparing seismic data for QFT processing, demonstrating results with accuracy comparable to conventional Fourier Transform (FT)-based methods. Although executed on a quantum simulator, the approach is compatible with quantum hardware, promising significant performance gains through qubit superposition. This work offers a new framework for integrating quantum algorithms into geophysical processing workflows, highlighting their potential to improve efficiency and scalability as quantum technology advances.
Quantum Neural Networks (QNNs) represent a novel computational paradigm that merges the principles of quantum computing with the architecture of artificial neural networks. Through the quantum phenomena of superposition, entanglement, and interference, QNNs enable parallel computation in high-dimensional Hilbert spaces, offering the potential to surpass the representational limits of classical models. This review provides a comprehensive overview of the theoretical foundations and architectures of QNNs, including Quantum Perceptrons, Variational Quantum Circuits (VQCs), Quantum Convolutional Neural Networks (QCNNs), and Quantum Recurrent Neural Networks (QRNNs). Furthermore, it discusses hybrid quantum–classical training mechanisms and key challenges such as barren plateaus, decoherence, and sampling complexity. The review also highlights recent applications of QNNs in medical diagnostics, materials science, and financial forecasting, demonstrating their potential to accelerate computation and improve predictive accuracy. Finally, future research directions are discussed in relation to computational efficiency, model interpretability, and integration with next-generation quantum hardware.
Quantum neural networks (QNNs) represent a cutting-edge approach to machine learning and artificial intelligence, harnessing the principles of quantum mechanics to process and analyze data in fundamentally new ways. Unlike classical neural networks, which operate on classical bits and are limited by the laws of classical physics, QNNs use quantum bits (qubits) and exploit quantum phenomena such as superposition and entanglement to achieve unprecedented computational power and efficiency. This chapter explores the principles and applications of QNNs, including their potential for solving complex optimisation problems, pattern recognition tasks, and quantum simulation tasks. We discuss various QNN architectures, training algorithms, and applications, highlighting their advantages and challenges compared to classical neural networks. Additionally, we explore the potential impact of QNNs on fields such as quantum computing, quantum communication, and quantum sensing, as well as their implications for society and the economy. Overall, this chapter provides insights into the emerging field of quantum neural networks and sets the stage for further research and innovation in this exciting area.
Quantum machine learning (QML) has emerged as a promising interdisciplinary field that integrates principles of quantum computing with machine learning techniques to address complex computational challenges. By leveraging quantum phenomena such as superposition and entanglement, QML aims to enhance learning efficiency, improve model performance, and enable the exploration of high-dimensional feature spaces that are intractable for classical methods. This paper presents a comprehensive review of recent developments in QML, covering fundamental concepts, algorithmic taxonomies, data encoding techniques, implementation challenges, and real-world applications. Key approaches, including quantum support vector machines (QSVM), variational quantum circuits (VQC), and quantum neural networks (QNN), are systematically analyzed. Furthermore, critical challenges, including noisy intermediate-scale quantum (NISQ) limitations, barren plateaus, data encoding bottlenecks, and the lack of demonstrated quantum advantage, are discussed in detail. The review also highlights emerging applications in material informatics, energy systems, healthcare, and optimization problems. Finally, future research directions are outlined, emphasizing the need for advancements in quantum hardware, scalable algorithms, hybrid frameworks, and standardized benchmarking. This work aims to provide a structured perspective on the current state of QML and to identify opportunities in deploy it effectively in solve real-world problems.