This data supports "Large-scale quantum machine learning" by Tobias Haug, Chris N. Self, M. S. Kim (arxiv:2108.01039) https://arxiv.org/abs/2108.01039

Related code can be found in the GitHub repository: (https://github.com/chris-n-self/large-scale-qml). The 'studies' folder here can be dropped inside the code repository in order to run the analysis scripts.

Both 'processed' and 'unprocessed' data is provided. Unprocessed data is the qiskit measurement results for each case study, executed on the IBM Quantum device ibmq_guadalupe and ibmq_toronto. Processed is the Gram matrix evaluated from the measurements and the data vectors needed to fit support vector machine classifiers.

Data for "Towards provably efficient quantum algorithms for large-scale machine-learning models". Error.txt includes the error proxy estimated due to Carleman linearization. The estimates are obtained using Hessian eigenvalues. Hessians.zip contains hessian eigenvalue grids and densities. Most files are for the 7 M parameter mode, and resnet_422-4-* are for the 103 M parameter model. Accuracy.txt contains the sparse training model accuracy on classifying the test set with CIFAR-100, as well as the loss values. Hessian_vrification.ipynb contains the code to generate the supplementary verification of Hessian eigenvalues on the error properties of Carleman linearization plots. The initial conditions are random.

Quantum Machine Learning Market Outlook

According to our latest research, the global quantum machine learning market size reached USD 235 million in 2024, reflecting a robust momentum in the convergence of quantum computing and artificial intelligence technologies. The market is projected to expand at a CAGR of 38.7% from 2025 to 2033, culminating in a forecasted market size of USD 3.24 billion by 2033. The primary growth factor driving this remarkable trajectory is the increasing demand for enhanced computational capabilities to solve complex problems across industries, leveraging the unmatched processing power of quantum systems integrated with machine learning algorithms.

The accelerating adoption of quantum machine learning solutions is fueled by the need for advanced analytics and predictive modeling, particularly in sectors such as healthcare, finance, and pharmaceuticals. Organizations are increasingly recognizing the limitations of classical computing in handling large-scale, high-dimensional datasets, which quantum machine learning can address efficiently. The integration of quantum computing with machine learning algorithms enables the rapid processing and analysis of massive data volumes, facilitating breakthroughs in drug discovery, fraud detection, and optimization problems. This paradigm shift is further supported by significant investments from both public and private sectors, aiming to harness the transformative potential of quantum technologies.

Another critical growth driver for the quantum machine learning market is the surge in collaborative research initiatives and strategic partnerships among technology vendors, research institutions, and end-user industries. Leading quantum computing companies are actively collaborating with academic and industrial partners to accelerate the development and commercialization of quantum machine learning applications. These collaborations are instrumental in bridging the gap between theoretical advancements and real-world implementations, fostering innovation, and expanding the addressable market. Furthermore, government funding and policy support for quantum research and development are catalyzing the ecosystem, encouraging startups and established enterprises alike to invest in quantum machine learning capabilities.

The expanding scope of quantum machine learning across diverse applications is also propelling market growth. In addition to its established use cases in drug discovery and fraud detection, quantum machine learning is making significant inroads into cybersecurity, image and speech recognition, and optimization tasks within supply chain and logistics. The versatility of quantum machine learning algorithms in addressing multifaceted challenges across verticals is attracting a broad spectrum of end-users, from BFSI and healthcare to automotive, aerospace and defense, and energy and utilities. As more industries explore quantum-enabled solutions to gain a competitive edge, the market is poised for sustained expansion over the forecast period.

Regionally, North America continues to dominate the quantum machine learning market, underpinned by a robust quantum technology ecosystem, substantial R&D investments, and the presence of leading market players. However, Asia Pacific is rapidly emerging as a high-growth region, driven by increasing government initiatives, rising adoption of advanced technologies, and a burgeoning startup landscape. Europe also demonstrates significant potential, supported by collaborative research programs and a strong focus on technological innovation. As regional ecosystems mature and regulatory frameworks evolve, the global quantum machine learning market is expected to witness widespread adoption and diversification.

Component Analysis

The quantum machine learning market by component is segmented into hardware, software, and services, each playing a pivotal role in the market’s evolution. The hardware segment comprises quantum processors, quantum annealers, and supporting infrastructure, forming the backbone of quantum machine learning systems. As quantum hardware technology advances, particularly with the development of more stable and scalable qubits, the performance and reliability of quantum machine learning solutions are expected to improve significantly. Leading hardware vendors are investing heavily in research to overcome challenges related to error rates, decoherence, and qubit connectivity, which are essential for the practical deployment of quantum machine learning

Quantum Machine Learning Market Outlook

According to our latest research, the quantum machine learning market size reached USD 325 million in 2024, reflecting robust interest from both technology innovators and enterprise adopters. The market is projected to expand at a striking CAGR of 35.2% from 2025 to 2033, culminating in a forecasted value of USD 4.76 billion by 2033. This tremendous growth is primarily fueled by the convergence of quantum computing capabilities with advanced machine learning algorithms, enabling solutions that address previously unsolvable computational problems across industries.

One of the primary growth drivers for the quantum machine learning market is the exponential increase in data complexity and volume. Traditional machine learning algorithms are often constrained by computational power, especially when processing high-dimensional data sets or solving optimization problems. Quantum machine learning leverages quantum bits (qubits) and quantum parallelism to process and analyze massive, complex datasets at unprecedented speeds. This capability is particularly attractive for sectors such as healthcare, finance, and logistics, where rapid, accurate insights can translate into significant operational and competitive advantages. The evolution of quantum hardware and the development of hybrid quantum-classical algorithms further accelerate the adoption of quantum machine learning solutions.

Another crucial factor propelling market expansion is the strategic investments and collaborations between technology giants, research institutions, and governments. Key players like IBM, Google, and Microsoft are investing heavily in quantum computing research, while startups are innovating specialized quantum machine learning frameworks. Governments across North America, Europe, and Asia Pacific are also funding quantum research initiatives, recognizing the potential of quantum technologies to revolutionize national security, healthcare, and economic competitiveness. These collaborative efforts are not only advancing the technology but also fostering a robust ecosystem that includes software development, hardware innovation, and specialized services tailored to quantum machine learning.

The growing demand for enhanced cybersecurity and fraud detection is also boosting the quantum machine learning market. As cyber threats become more sophisticated, organizations require advanced solutions capable of detecting anomalies and predicting attacks in real time. Quantum machine learning algorithms, with their ability to process complex patterns and large-scale data, offer a significant leap over classical methods in identifying and mitigating security risks. This is particularly relevant for the BFSI and government sectors, where data integrity and security are paramount. The integration of quantum machine learning into cybersecurity frameworks is expected to become a standard practice as the technology matures.

From a regional perspective, North America dominates the quantum machine learning market, driven by a concentration of leading technology companies, academic institutions, and robust government support. Europe follows closely, benefiting from coordinated research initiatives and a strong industrial base, while Asia Pacific is rapidly emerging as a key growth region due to increasing investments in quantum technologies by countries such as China, Japan, and South Korea. The global landscape is characterized by intense competition, rapid technological advancements, and a race to achieve quantum advantage, with each region contributing unique strengths to the overall market trajectory.

Component Analysis

The quantum machine learning market is segmented by component into software, hardware, and services, each playing a pivotal role in the ecosystem’s development. The software segment is currently the largest contributor, accounting for more than 45% of the market share in 2024. This dominance is attributed to the growing need for quantum algorithms, dev

With the development of science and technology, large-scale optimization tasks have become integral to cutting-edge engineering. The challenges of solving these problems arises from ever-growing system sizes, intricate physical space, and the computational cost required to accurately model and optimize target objectives. Taking the design of advanced functional materials as an example, the high-dimensional parameter space and high-fidelity physical simulations can demand immense computational resources for searching and iterations. Although emerging machine learning techniques have been combined with conventional experimental and simulation approaches to explore the design space and identify high-performance solutions, these methods are still limited to a small part of the design space around those materials have been well investigated.

Over the past several decades, continuous development of both hardware and algorithms have addressed some of the challenges. High-performance computing (HPC) architectures and heterogeneous systems have greatly expanded the capacity to perform large-scale calculations and optimizations; On the other hand, the emergence of machine learning frameworks and algorithms have dramatically facilitated the development of advanced models and enable the integration of AI-driven techniques into traditional experiments and simulations more seamlessly. In recent years, quantum computing (QC) has received widespread attention due to its powerful performance on solving global optima and is regarded as a promising solution to large-scale and non-linear optimization problems in the future, and in the meantime, the quantum computing principles also expand the capacity of classical algorithms on exploring high-dimensional combinatorial spaces. In this dissertation, we will show the power of the integration of machine learning algorithms, quantum algorithms and HPC architectures on tackling the challenges of solving large-scale optimization problems.

In the first part of this dissertation, we introduced an optimization algorithm based on a Quantum-inspired Genetic Algorithm (QGA) to design planar multilayer (PML) for transparent radiative cooler (TRC) applications. Results of numerical experiments showed that our QGA-facilitated optimization algorithm can converge to comparable solutions as quantum annealing (QA) and the QGA overperformed on classical genetic algorithm (CGA) on both convergence speed and global search capacity. Our work shows that quantum heuristic algorithms will become powerful tools for addressing the challenges traditional optimization algorithm faced when solving large-scale optimization problems with complex search space.

In the second part of the dissertation, we proposed a quantum annealing-assisted lattice optimization (QALO) algorithm for high-entropy alloy (HEA) systems. The algorithm is developed based on the active learning framework that integrates the field-aware factorization machine (FFM), quantum annealing (QA) and machine learning potential (MLP). When applying to optimize the bulk grain configuration of the NbMoTaW alloy system, our algorithm can quickly obtain low-energy microstructures and the results successfully reproduce the Nb segregation and W enrichment in the bulk phase driven by thermodynamic driving force, which usually be observed in the experiments and MC/MD simulations. This work highlights the potential of quantum computing in exploring the large design space for HEA systems.

In the third part of the dissertation, we employed the Distributed Quantum Approximate Optimization Algorithm (DQAOA) to address large-scale combinatorial optimization problems that exceed the limits of conventional computational resources. This was achieved through a divide-and-conquer strategy, in which the original problem is decomposed into smaller sub-tasks that are solved in parallel on a high-performance computing (HPC) system. To further enhance convergence efficiency, we introduced an Impact Factor Directed (IFD) decomposition method. By calculating impact factors and leveraging a targeted traversal strategy, IFD captures local structural features of the problem, making it effective for both dense and sparse instances. Finally, we explored the integration of DQAOA with the Quantum Framework (QFw) on the Frontier HPC system, demonstrating the potential for efficient management of large-scale circuit execution workloads across CPUs and GPUs.

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Quantum Computing For AI Market Size 2025-2029

The quantum computing for AI market size is forecast to increase by USD 614.6 million at a CAGR of 35.2% between 2024 and 2029.

The market is experiencing significant momentum, driven by continuous and rapid advancements in quantum hardware technology. This technological evolution is enabling the development of increasingly powerful quantum computers, which hold the potential to revolutionize Artificial Intelligence applications by solving complex problems much faster than classical computers. Another key trend in the market is the rise of integrated hybrid quantum-classical systems. These systems combine the strengths of both quantum and classical computing, allowing for the efficient processing of large data sets and the execution of complex algorithms.
Moreover, achieving fault tolerance in quantum systems remains a major challenge, requiring advanced error correction techniques to ensure the reliability and stability of quantum computations. Companies seeking to capitalize on the opportunities presented by the market must address these challenges effectively, investing in research and development to overcome hardware noise and develop robust fault tolerance strategies. Quantum data compression reduces storage requirements, and quantum deep learning enhances neural networks. However, the market faces challenges as well. One significant obstacle is pervasive hardware noise, which can lead to errors and inaccuracies in quantum computations.

What will be the Size of the Quantum Computing For AI Market during the forecast period?

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Quantum finance models are being developed to optimize financial portfolios, while quantum feature extraction enhances AI algorithms' performance. Quantum cryptography applications secure data transmission, and quantum risk management mitigates risks with higher precision. In the realm of natural language processing, quantum natural language models improve language understanding. Quantum circuit optimization streamlines AI workflows, and post-quantum cryptography ensures data security in a quantum world. Quantum reinforcement learning expedites the training of AI agents, and quantum algorithm complexity offers new insights into AI optimization.

Quantum search algorithms discover patterns in vast datasets, and quantum inspired algorithms mimic quantum phenomena for AI solutions. Quantum computing, a revolutionary technology, is transforming the Artificial Intelligence (AI) market dynamics with its potential to solve complex problems that classical computers cannot. Quantum AI applications span various industries, including materials science, computer vision, drug discovery, computational chemistry, and more. Quantum error correction ensures data reliability, and quantum generative models create realistic data. Quantum hardware acceleration boosts AI performance, and quantum recommendation systems personalize user experiences. Quantum software libraries facilitate quantum AI adoption, and quantum hardware advances fuel innovation.

How is this Quantum Computing For AI Industry segmented?

The quantum computing for AI industry research report provides comprehensive data (region-wise segment analysis), with forecasts and estimates in 'USD million' for the period 2025-2029, as well as historical data from 2019-2023 for the following segments.

Technology

  Superconducting qubits
  Trapped ions
  Photonic systems
  Spin qubits


Deployment

  On-premises
  Cloud-based


End-user

  Healthcare and life sciences
  BFSI
  Automotive and aerospace
  Defense and security
  Energy


Geography

  North America

    US
    Canada
    Mexico


  Europe

    France
    Germany
    UK


  APAC

    China
    India
    Japan
    South Korea


  Rest of World (ROW)

By Technology Insights

The Superconducting qubits segment is estimated to witness significant growth during the forecast period. Quantum computing for Artificial Intelligence (AI) is a rapidly advancing field, driven by technological innovations such as quantum supremacy claims, quantum tomography, and quantum circuit design. Error correction codes and quantum cloud computing enable larger-scale quantum computations, while hybrid quantum-classical approaches combine the strengths of both quantum and classical computing. Quantum entanglement, a unique phenomenon in quantum mechanics, is harnessed for quantum machine learning and quantum information theory. Quantum optimization and resource estimation are essential for solving complex problems in various industries. Topological quantum computing and gate-based quantum computing offer distinct approaches to building quantum computers.

The market is experiencing significant growth

Cloud Based Quantum Computing Market Outlook

The global cloud-based quantum computing market size was estimated at USD 2.3 billion in 2023, with a projected growth to USD 15.7 billion by 2032, reflecting a robust CAGR of 23.8% over the forecast period. This extraordinary growth is driven by the increasing need for advanced computational power, necessitated by the complex problem-solving capabilities required in various industries such as healthcare, finance, and manufacturing.

One of the primary growth factors for the cloud-based quantum computing market is the rapid advancement in quantum computing technology itself. Traditional computing is approaching the limits of Moore's law, making quantum computing an attractive alternative. Quantum computers process information in fundamentally new ways, leveraging quantum bits or qubits, which can perform multiple calculations simultaneously. This capability is particularly valuable for solving intricate optimization problems, conducting large-scale simulations, and enhancing machine learning algorithms.

Furthermore, the integration of quantum computing with cloud platforms allows organizations to access these powerful computational resources without the need to invest in expensive quantum hardware. This democratization of quantum computing, enabled by cloud technology, lowers the entry barriers for small and medium enterprises (SMEs) and accelerates innovation across various sectors. The shift towards a subscription-based model also helps organizations manage their operational costs more effectively, contributing to the market's growth.

Technological advancements and increasing research activities in quantum computing are also significant contributors to market expansion. Governments and private organizations worldwide are investing heavily in quantum research and development, with several initiatives aimed at establishing quantum computing infrastructure and expertise. Strategic collaborations and partnerships between tech giants and research institutions further propel the market, enhancing the development and deployment of cloud-based quantum solutions.

Regionally, North America holds the largest share of the cloud-based quantum computing market, driven by substantial investments in quantum R&D and the presence of leading technology companies. However, the Asia-Pacific region is anticipated to witness the highest growth rate, spurred by increasing government initiatives in countries like China and Japan, aimed at establishing a strong quantum computing infrastructure. Europe also plays a significant role, with the European Union funding multiple quantum research projects as part of its Horizon Europe program.

Component Analysis

The cloud-based quantum computing market is segmented into hardware, software, and services. Each of these components plays a crucial role in the deployment and functioning of quantum computing solutions. The hardware segment includes quantum processors, quantum memory, and other physical components essential for quantum computation. This segment is anticipated to experience significant growth due to continuous advancements in quantum chip technology and the development of more stable and scalable quantum processors.

Software forms another critical component of the quantum computing ecosystem. This segment encompasses quantum algorithms, programming languages, and development platforms that facilitate the creation and execution of quantum applications. As quantum hardware evolves, so does the need for sophisticated software capable of leveraging the unique capabilities of quantum computers. The software segment is expected to grow substantially, driven by the increasing demand for quantum algorithms in various applications such as cryptography, optimization, and machine learning.

Services within the quantum computing market include consulting, training, and maintenance services, which are vital for organizations to effectively implement and utilize quantum solutions. Many companies lack the in-house expertise required to develop and deploy quantum applications. Therefore, the services segment is expected to grow rapidly as enterprises seek external expertise to navigate the complexities of quantum computing. This segment also includes quantum computing as a service (QCaaS) offerings, which allow organizations to access quantum computing resources on a pay-per-use basis.

Collectively, these components form an integrated ecosystem that drives the functionality and adoption of cloud-based quantum comp

Clustering algorithms are at the basis of several technological applications, and are fueling the development of rapidly evolving fields such as machine learning. In the recent past, however, it has become apparent that they face challenges stemming from datasets that span more spatial dimensions. In fact, the best-performing clustering algorithms scale linearly in the number of points, but quadratically with respect to the local density of points. In this work, we introduce qCLUE, a quantum clustering algorithm that scales linearly in both the number of points and their density. qCLUE is inspired by CLUE, an algorithm developed to address the challenging time and memory budgets of Event Reconstruction (ER) in future High-Energy Physics experiments. As such, qCLUE marries decades of development with the quadratic speedup provided by quantum computers. We numerically test qCLUE in several scenarios, demonstrating its effectiveness and proving it to be a promising route to handle complex data analysis tasks – especially in high-dimensional datasets with high densities of points.

Density functional theory (DFT) has been a cornerstone in computational science, providing powerful insights into structure–property relationships for molecules and materials through first-principles quantum-mechanical (QM) calculations. However, the advent of atomistic machine learning (ML) is reshaping the landscape by enabling large-scale dynamics simulations and high-throughput screening at DFT-equivalent accuracy with drastically reduced computational cost. Yet, the development of general-purpose atomistic ML models as surrogates for QM calculations faces several challenges, particularly in terms of model capacity, data efficiency, and transferability across chemically diverse systems. This work introduces a novel extension of the polarizable atom interaction neural network (namely, XPaiNN) to address these challenges. Two distinct training strategies have been employed, one direct-learning and the other Δ-ML on top of a semiempirical QM method. These methodologies have been implemented within the same framework, allowing for a detailed comparison of their results. The XPaiNN models, in particular the one using Δ-ML, not only demonstrate competitive performance on standard benchmarks, but also demonstrate the effectiveness against other ML models and QM methods on comprehensive downstream tasks, including noncovalent interactions, reaction energetics, barrier heights, geometry optimization and reaction thermodynamics, etc. This work represents a significant step forward in the pursuit of accurate and efficient atomistic ML models of general-purpose, capable of handling complex chemical systems with transferable accuracy.

Quantum computing is becoming a hot topic and is considered one of the most promising new computing paradigms, especially with its enormous potential in fields such as machine learning, finance, cryptography, and chemistry. However, current quantum computing is still in a very immature state, with significant challenges at every level from software to hardware. This dissertation explores how to help build scalable and robust quantum computing systems from the perspective of software and hardware co-design. Specifically, the dissertation is divided into two main directions: 1) Paradigm shift from gate-level to pulse-level and cross-layer co-design; and 2) Establishing a deeper level of classical-quantum cooperation. In the first direction, this dissertation discussed certain sophisticated quantum operations that may derive substantial benefits from circumventing the conventional decomposition into basic gates at the circuit level. Instead, these operations can be more effectively implemented directly at the physical layer. The advent of applications such as quantum simulations and quantum machine learning indicate that the classic "gate-to-circuit-to-program" paradigm may no longer serve as the most efficient or intuitive approach for quantum design. Exploring designs at the pulse level, as opposed to the gate level, could offer significant advantages. Utilizing quantum pulses over quantum gates has the potential to provide enhanced flexibility, superior fidelity, and greater scalability, along with the capacity for real-time adjustments. In the second direction, a key focus is how to deeply promote the integration of classical machine learning or optimization algorithms with quantum algorithms. Given the current scarcity and high cost of quantum computing resources, it's challenging to conduct large-scale experiments. Therefore, we discuss two hybrid classical-quantum computing frameworks to solve this challenge: one involves sacrificing some classical computing resources to preheat quantum algorithms, and the other divide problems into parts solved by classical computers and parts solved by quantum computers.

Quantum-Enabled Pattern Recognition Market Outlook

According to our latest research, the global quantum-enabled pattern recognition market size reached USD 1.41 billion in 2024, reflecting robust adoption across multiple industries. The market is poised for significant expansion, projected to attain USD 13.8 billion by 2033, growing at a remarkable CAGR of 28.5% during the forecast period from 2025 to 2033. This exceptional growth is primarily attributed to the rapid advancements in quantum computing technologies, which are fundamentally transforming the landscape of artificial intelligence and pattern recognition by delivering unprecedented computational power and efficiency.

The growth trajectory of the quantum-enabled pattern recognition market is shaped by several key factors. Firstly, the exponential increase in data generation across sectors such as healthcare, finance, and telecommunications is fueling the demand for advanced pattern recognition capabilities. Traditional computing methods are often inadequate for processing and analyzing such vast and complex datasets in real-time. Quantum-enabled solutions, leveraging the principles of quantum mechanics, offer a paradigm shift by enabling faster and more accurate identification of patterns, correlations, and anomalies within massive datasets. This capability is particularly valuable in applications like fraud detection, medical diagnostics, and image recognition, where speed and precision are critical. As organizations increasingly seek to gain actionable insights from their data, the adoption of quantum-enabled pattern recognition is expected to surge.

Another significant driver is the ongoing collaboration between technology providers, research institutions, and industry stakeholders to accelerate the development and commercialization of quantum computing hardware and software. Major investments are being channeled into building scalable quantum systems and developing user-friendly quantum machine learning frameworks. These efforts are lowering the entry barriers for enterprises to integrate quantum-enabled pattern recognition into their operations. Additionally, the growing awareness of the transformative potential of quantum technologies is prompting governments worldwide to launch strategic initiatives and funding programs to foster innovation. Such supportive ecosystems are not only accelerating technological advancements but also facilitating early adoption across diverse verticals, further propelling market growth.

The expanding application landscape is also playing a pivotal role in the market’s growth. Quantum-enabled pattern recognition is finding new use cases across industries, from enhancing cybersecurity protocols in the BFSI sector to revolutionizing drug discovery and personalized medicine in healthcare. In the automotive industry, these technologies are being leveraged to improve autonomous driving systems by enabling real-time analysis of sensor data. The retail sector is utilizing quantum-powered pattern recognition for customer behavior analysis and inventory optimization. This broadening of applications is driving demand for tailored solutions, spurring innovation among technology vendors, and creating lucrative opportunities for market expansion.

From a regional perspective, North America currently leads the quantum-enabled pattern recognition market, owing to its advanced technological infrastructure, strong presence of leading quantum computing firms, and robust investment in research and development. Europe follows closely, supported by significant government initiatives and a thriving academic research ecosystem. The Asia Pacific region is emerging as a high-growth market, driven by rapid digital transformation, increasing investments in quantum technologies, and the presence of large-scale manufacturing and IT hubs. Meanwhile, Latin America and the Middle East & Africa are gradually catching up, with growing interest from both public and private sectors. Each region presents unique opportunities and challenges, shaping the global market’s competitive dynamics and growth trajectory.

Road network selection is a pivotal yet challenging task in cartographic generalization. As neural network technology continues to advance, intelligent methods for road network selection have emerged as a key research area. However, the expanding scale of road networks has led to concerns regarding model training efficiency and resource consumption. Quantum neural networks, leveraging their unique properties of superposition and entanglement, present remarkable advantages for handling large-scale, complex, and nonlinear data. In this paper, we propose a novel framework for road network selection based on quantum neural networks. We design a comprehensive feature set that takes into account various factors, including terrain, settlements, and surrounding density. Our study delves into the impact of feature encoding methods and circuit structures on the performance of quantum neural networks in road selection. We also evaluate the proposed model's performance across different scales, regions, and data volumes. The results demonstrate the feasibility and effectiveness of our approach when compared to existing classical neural network models, offering a promising solution for large-scale road network selection.

Quantum Neural Network Software Market Outlook

According to our latest research, the Quantum Neural Network Software market size reached USD 412 million globally in 2024, reflecting the rapid adoption of quantum technologies across diverse industries. With a robust CAGR of 32.4% projected for the period 2025 to 2033, the market is anticipated to surge to approximately USD 4,650 million by 2033. This remarkable growth is being driven by accelerated advancements in quantum computing infrastructure and an increasing demand for high-performance machine learning solutions that can solve complex problems beyond the capabilities of classical neural networks.

The principal growth factor propelling the Quantum Neural Network Software market is the exponential increase in computational power made possible by quantum computing. Quantum neural network software leverages quantum bits (qubits) to perform parallel computations, enabling organizations to solve optimization, pattern recognition, and simulation challenges at unprecedented speeds. The convergence of artificial intelligence and quantum computing is unlocking new frontiers in data analysis, drug discovery, financial modeling, and supply chain optimization. As businesses across sectors seek to harness these capabilities, investment in quantum neural network software platforms and tools is rising sharply, further accelerating market expansion.

Another significant driver is the growing integration of quantum neural network software in mission-critical applications across BFSI, healthcare, automotive, and manufacturing industries. For instance, in healthcare, quantum neural networks are being utilized to accelerate genomic sequencing, optimize treatment plans, and predict disease outbreaks with greater accuracy. In the BFSI sector, these technologies are transforming risk assessment, fraud detection, and portfolio optimization. The automotive industry is leveraging quantum neural network software for autonomous vehicle navigation and real-time sensor data processing. The widespread applicability of these solutions is creating a robust demand pipeline and encouraging continuous innovation among software vendors and service providers.

Furthermore, the increasing availability of cloud-based quantum computing platforms is democratizing access to quantum neural network software for enterprises of all sizes. Major cloud service providers are partnering with quantum hardware developers to offer scalable, pay-as-you-go quantum computing resources. This shift is reducing barriers to entry for small and medium enterprises (SMEs), enabling them to experiment with quantum neural networks without the need for significant upfront investments in specialized hardware. As a result, the market is witnessing a surge in pilot projects and proof-of-concept deployments, which are expected to transition into full-scale implementations over the forecast period.

From a regional perspective, North America continues to dominate the Quantum Neural Network Software market in 2024, accounting for more than 38% of global revenue, driven by strong investments in quantum research, a vibrant startup ecosystem, and robust government support. Europe follows closely, benefiting from collaborative research initiatives and a growing talent pool in quantum computing. The Asia Pacific region is emerging as a high-growth market, with countries like China and Japan making significant strides in quantum technology development. As global competition intensifies, strategic partnerships and cross-border collaborations are expected to play a pivotal role in shaping the market landscape.

Component Analysis

The Component segment of the Quantum Neural Network Software market is broadly categorized into software platforms, services, and tools. Software platforms form the backbone of this segment, providing the essential frameworks and libraries required to design, train, and deploy quantum neural networks. These platforms are increasingly being developed with user-friendly interfaces and integration capabilities, enabling organizations to seamlessly incorporate quantum neural network functionalities into their existing workflows. The rapid evolution of quantum programming languages and development kits is further fueling the adoption of software platforms, as enterprises seek to leverage the latest advancements in quantum algorithms and machine learning models.

Services constitute a vital c

Quantum-Enhanced Speech Synthesis Market Outlook

According to our latest research, the global Quantum-Enhanced Speech Synthesis market size reached USD 1.38 billion in 2024, reflecting a robust trajectory fueled by significant technological advancements and growing enterprise adoption. The market is expanding at a compelling CAGR of 32.8% and is forecasted to reach USD 15.34 billion by 2033. This remarkable growth is primarily attributed to the integration of quantum computing capabilities with advanced speech synthesis algorithms, which is revolutionizing the quality, speed, and contextual accuracy of generated speech across numerous industries.

A key driver for the Quantum-Enhanced Speech Synthesis market is the exponential improvement in computational power enabled by quantum technologies. Traditional speech synthesis models, while effective, are often limited by classical hardware constraints, particularly when processing large-scale, complex linguistic datasets or generating highly naturalistic speech patterns. Quantum computing, with its ability to process vast amounts of data simultaneously and tackle complex optimization problems, is transforming the landscape of speech synthesis. This has led to the development of quantum machine learning and quantum natural language processing models that deliver superior contextual understanding, faster response times, and more human-like speech outputs, making them highly attractive for next-generation virtual assistants, customer service bots, and accessibility tools.

Another significant growth factor is the rising demand for personalized and accessible digital experiences. As digital interactions become increasingly voice-driven, sectors such as healthcare, education, and customer service are seeking advanced speech synthesis solutions to improve user engagement, accessibility, and inclusivity. Quantum-enhanced speech synthesis is uniquely positioned to address these needs by enabling high-precision, real-time voice generation that can adapt to individual user preferences, accents, and languages. This has accelerated adoption among enterprises aiming to differentiate their offerings and comply with global accessibility standards, further propelling market expansion.

The surge in investments from both public and private sectors into quantum computing research and its application in artificial intelligence is also catalyzing market growth. Governments and major technology companies are allocating substantial resources to develop scalable quantum hardware and software platforms, with a particular focus on AI-driven applications such as speech synthesis. These investments are fostering innovation, reducing costs, and facilitating the commercialization of quantum-enhanced speech solutions. As a result, the ecosystem is witnessing a proliferation of startups and established vendors collaborating to push the boundaries of what is possible in speech technology.

Regionally, North America currently leads the Quantum-Enhanced Speech Synthesis market, driven by a strong innovation ecosystem, significant R&D investments, and early adoption across industries such as healthcare, BFSI, and media & entertainment. Europe and Asia Pacific are also witnessing rapid growth, fueled by increasing digital transformation initiatives and government-backed quantum technology programs. Meanwhile, emerging markets in Latin America and the Middle East & Africa are gradually recognizing the potential of quantum-enhanced speech synthesis, particularly for improving accessibility and customer engagement in multilingual and diverse populations.

Technology Analysis

The Quantum-Enhanced Speech Synthesis market is segmented by technology into Quantum Machine Learning, Quantum Natural Language Processing, Quantum Acoustic Modeling, and Others. Quantum Machine Learning (QML) is at the forefront, leveraging quantum algorithms to train and deploy speech models that significantly outperform classical counterparts in terms of speed and accuracy. QML enables the processing of massive speech datasets, allowing for the extraction of nuanced linguistic patterns and the generation of more natural-sounding speech. This technology is particularly valuable for applications requiring real-time response and high contextual awareness, such as interactive voice assistants and automated customer service platforms.

Quantum Natural Language Processing (QNLP)

Quantum-Enhanced Image Reconstruction Market Outlook

As per our latest research, the Quantum-Enhanced Image Reconstruction market size reached USD 1.32 billion in 2024, driven by surging advancements in quantum computing and imaging technologies. The market is expected to grow at a robust CAGR of 31.8% from 2025 to 2033, resulting in a forecasted market size of USD 15.8 billion by 2033. The primary growth factor fueling this expansion is the increasing adoption of quantum-enhanced solutions across critical sectors such as healthcare, aerospace, and industrial inspection, where superior image resolution and processing speed are paramount for operational success and innovation.

A significant driver for the Quantum-Enhanced Image Reconstruction market is the rapid evolution of quantum algorithms and quantum machine learning, which are revolutionizing how image data is processed and interpreted. Quantum algorithms enable the handling of vast and complex datasets at unprecedented speeds, making it possible to reconstruct high-fidelity images from limited or noisy data sources. This is particularly valuable in fields like medical imaging, where early and accurate diagnosis can be life-saving, and in remote sensing, where large-scale environmental monitoring is required. The integration of quantum computing with traditional imaging modalities accelerates image reconstruction processes, reduces noise, and enhances image clarity, thus offering a transformative upgrade over conventional techniques.

Another key growth factor is the expanding application base of quantum-enhanced imaging systems. As industries become more data-driven, the demand for high-resolution, real-time imaging has surged. Quantum sensors and quantum imaging systems are increasingly being deployed in industrial inspection and security & surveillance to detect minute defects or threats that would otherwise go unnoticed using classical imaging solutions. The aerospace and defense sectors, in particular, are investing heavily in quantum technologies to improve reconnaissance, surveillance, and target identification capabilities. Furthermore, the push for automation and precision in manufacturing is driving the adoption of quantum-enhanced inspection systems, which help ensure product quality and operational safety.

The regional outlook for the Quantum-Enhanced Image Reconstruction market indicates that North America currently leads in terms of adoption and innovation, supported by significant investments in quantum research and development by both public and private sectors. Europe follows closely, with robust funding for quantum technology initiatives and a strong presence of leading research institutes. The Asia Pacific region is emerging as a high-growth market, propelled by increasing government initiatives, expanding healthcare infrastructure, and a growing focus on industrial modernization. Latin America and the Middle East & Africa are also showing rising interest, particularly in security, remote sensing, and medical imaging, as these regions seek to leverage quantum technologies for economic and social advancement.

Technology Analysis

The technology segment of the Quantum-Enhanced Image Reconstruction market is marked by rapid innovation and diversification, with quantum algorithms, quantum sensors, quantum machine learning, and quantum imaging systems at the forefront. Quantum algorithms are enabling the processing of high-dimensional image data at speeds and accuracies unattainable by classical methods. These algorithms utilize quantum parallelism and entanglement to solve complex inverse problems in image reconstruction, allowing for the extraction of detailed information from incomplete or noisy datasets. This capability is particularly vital in medical imaging and astronomy, where data quality and completeness are often compromised by physical and environmental limitations.

Quantum sensors represent another transformative technology within this market. Leveraging quantum phenomena such as superposition and entanglement, these sens

CHIPS-FF (Computational High-Performance Infrastructure for Predictive Simulation-based Force Fields) is a universal, open-source benchmarking platform for machine learning force fields (MLFFs). This platform provides robust evaluation beyond conventional metrics such as energy, focusing on complex properties including elastic constants, phonon spectra, defect formation energies, surface energies, and interfacial and amorphous phase properties. Utilizing 16 graph-based MLFF models including ALIGNN-FF, CHGNet, MatGL, MACE, SevenNet, ORB and OMat24, the CHIPS-FF workflow integrates the Atomic Simulation Environment (ASE) with JARVIS-Tools to facilitate automated high-throughput simulations. Our framework is tested on a set of 104 materials, including metals, semiconductors and insulators representative of those used in semiconductor components, with each MLFF evaluated for convergence, accuracy, and computational cost. Additionally, we evaluate the force-prediction accuracy of these models for close to 2 million atomic structures. By offering a streamlined, flexible benchmarking infrastructure, CHIPS-FF aims to guide the development and deployment of MLFFs for real-world semiconductor applications, bridging the gap between quantum mechanical simulations and large-scale device modeling.Enter description here...

According to Cognitive Market Research, the global Quantum Key Distribution market size will be USD 524.8 million in 2025. It will expand at a compound annual growth rate (CAGR) of 33.10% from 2025 to 2033.

North America held the major market share for more than 37% of the global revenue with a market size of USD 194.18 million in 2025 and will grow at a compound annual growth rate (CAGR) of 31.6% from 2025 to 2033.
Europe accounted for a market share of over 29% of the global revenue with a market size of USD 85.46 million.
APAC held a market share of around 24% of the global revenue with a market size of USD 125.95 million in 2025 and will grow at a compound annual growth rate (CAGR) of 36.3% from 2025 to 2033.
South America has a market share of more than 4% of the global revenue with a market size of USD 19.94 million in 2025 and will grow at a compound annual growth rate (CAGR) of 33.5% from 2025 to 2033.
Middle East had a market share of around 4% of the global revenue and was estimated at a market size of USD 20.99 million in 2025 and will grow at a compound annual growth rate (CAGR) of 33.7% from 2025 to 2033.
Africa had a market share of around 2.20% of the global revenue and was estimated at a market size of USD 11.55 million in 2025 and will grow at a compound annual growth rate (CAGR) of 32.7% from 2025 to 2033.
Service Component is the fastest growing segment of the Quantum Key Distribution industry

Market Dynamics of Quantum Key Distribution Market

Key Drivers for Quantum Key Distribution Market

Rising Cybersecurity Threats & Data Breaches to Boost Market Growth

With the increasing frequency and sophistication of cyberattacks, traditional encryption methods are becoming vulnerable to hacking, phishing, and brute-force attacks. Financial institutions, governments, healthcare providers, and defense agencies handle vast amounts of sensitive data, making them prime targets for breaches. Quantum Key Distribution (QKD) ensures unbreakable encryption by leveraging quantum mechanics, preventing eavesdroppers from intercepting communication without detection. As cyber threats evolve, organizations are prioritizing quantum-safe encryption to safeguard critical infrastructure, trade secrets, and national security. Regulatory bodies are also encouraging stronger cybersecurity frameworks, further accelerating the adoption of QKD solutions worldwide. For instance, In May 2023, Agnostiq launched Covalent Cloud, the retail version of Covalent, an open-source project. Covalent Cloud is a highly abstracted, managed, and on-demand platform that provides high-performance computing and quantum computing resources for optimization, machine learning, simulation, and quantum computing.

https://www.hpcwire.com/off-the-wire/agnostiq-releases-covalent-cloud-to-unify-access-to-quantum-and-hpc-resources/

Growing Adoption of Quantum Computing To Boost Market Growth

Quantum computing is advancing rapidly, with tech giants like IBM, Google, and China’s Baidu making significant breakthroughs. Unlike classical computers, quantum computers can break widely used encryption algorithms (RSA, ECC, AES) in seconds, creating a major cybersecurity threat. This has led to a global push for quantum-resistant cryptographic solutions, with QKD emerging as a frontrunner for secure communication networks. Governments and enterprises are investing in QKD to future-proof data security, ensuring protection against potential quantum attacks. The increasing commercialization of quantum computing services is making the transition to quantum-safe encryption solutions a necessity rather than an option.

Restraint Factor for the Quantum Key Distribution Market

High Implementation Costs & Infrastructure Challenges Will Limit Market Growth

QKD technology requires specialized hardware, including single-photon sources, quantum repeaters, and secure key management systems, making deployment expensive and complex. Additionally, QKD over fiber-optic networks is limited to about 100-200 km, requiring costly quantum repeaters or satellite-based solutions for long-distance communication. Many enterprises, especially small and medium-sized businesses (SMEs), find the high costs a barrier to adoption. Integrating QKD with existing telecom infrastructure and IT networks also poses technical challenges, requiring extensive modifications and regulatory approvals. These factors slow down large-scale ado...

In recent years, promising deep learning based interatomic potential energy surface (PES) models have been proposed that can potentially allow us to perform molecular dynamics simulations for large scale systems with quantum accuracy. However, making these models truly reliable and practically useful is still a very non-trivial task. A key component in this task is the generation of datasets used in model training. In this paper, we introduce the Deep Potential GENerator (DP-GEN), an open-source software platform that implements the recently proposed ”on-the-fly” learning procedure (Zhang et al. 2019) and is capable of generating uniformly accurate deep learning based PES models in a way that minimizes human intervention and the computational cost for data generation and model training. DP-GEN automatically and iteratively performs three steps: exploration, labeling, and training. It supports various popular packages for these three steps: LAMMPS for exploration, Quantum Espresso, VASP, CP2K, etc. for labeling, and DeePMD-kit for training. It also allows automatic job submission and result collection on different types of machines, such as high performance clusters and cloud machines, and is adaptive to different job management tools, including Slurm, PBS, and LSF. As a concrete example, we illustrate the details of the process for generating a general-purpose PES model for Cu using DP-GEN.

Quantum-AI Synthetic Data Generator Market Outlook

According to our latest research, the global Quantum-AI Synthetic Data Generator market size reached USD 1.98 billion in 2024, reflecting robust momentum driven by the convergence of quantum computing and artificial intelligence technologies in data generation. The market is experiencing a significant compound annual growth rate (CAGR) of 32.1% from 2025 to 2033. At this pace, the market is forecasted to reach USD 24.8 billion by 2033. This remarkable growth is propelled by the escalating demand for high-quality synthetic data across industries to enhance AI model training, ensure data privacy, and overcome data scarcity challenges.

One of the primary growth drivers for the Quantum-AI Synthetic Data Generator market is the increasing reliance on advanced machine learning and deep learning models that require vast amounts of diverse, high-fidelity data. Traditional data sources often fall short in volume, variety, and compliance with privacy regulations. Quantum-AI synthetic data generators address these challenges by producing realistic, representative datasets that mimic real-world scenarios without exposing sensitive information. This capability is particularly crucial in regulated sectors such as healthcare and finance, where data privacy and security are paramount. As organizations seek to accelerate AI adoption while minimizing ethical and legal risks, the demand for sophisticated synthetic data solutions continues to rise.

Another significant factor fueling market expansion is the rapid evolution of quantum computing and its integration with AI algorithms. Quantum computing’s superior processing power enables the generation of complex, large-scale datasets at unprecedented speeds and accuracy. This synergy allows enterprises to simulate intricate data patterns and rare events that would be difficult or impossible to capture through conventional means. Additionally, the proliferation of AI-driven applications in sectors like autonomous vehicles, predictive maintenance, and personalized medicine is amplifying the need for synthetic data generators that can support advanced analytics and model validation. The ongoing advancements in quantum hardware, coupled with the growing ecosystem of AI tools, are expected to further catalyze innovation and adoption in this market.

Moreover, the shift toward digital transformation and the growing adoption of cloud-based solutions are reshaping the landscape of the Quantum-AI Synthetic Data Generator market. Enterprises of all sizes are embracing synthetic data generation to streamline data workflows, reduce operational costs, and accelerate time-to-market for AI-powered products and services. Cloud deployment models offer scalability, flexibility, and seamless integration with existing data infrastructure, making synthetic data generation accessible even to resource-constrained organizations. As digital ecosystems evolve and data-driven decision-making becomes a competitive imperative, the strategic importance of synthetic data generation is set to intensify, fostering sustained market growth through 2033.

From a regional perspective, North America currently leads the market, driven by early technology adoption, substantial investments in quantum and AI research, and a vibrant ecosystem of startups and established technology firms. Europe follows closely, benefiting from strong regulatory frameworks and robust funding for AI innovation. The Asia Pacific region is witnessing the fastest growth, fueled by expanding digital economies, government initiatives supporting AI and quantum technology, and increasing awareness of synthetic data’s strategic value. As global enterprises seek to harness the power of quantum-AI synthetic data generators to gain a competitive edge, regional dynamics will continue to shape market trajectories and opportunities.

Component Analysis

The Component segment of the Quantum-AI Synthetic Data Generator

Supplementary files for article Quantum-corrected thickness-dependent thermal conductivity in amorphous silicon redicted by machine learning molecular dynamics simulations

Amorphous silicon (a-Si) is an important thermal-management material and also serves as an ideal playground for studying heat transport in strongly disordered materials. Theoretical prediction of the thermal conductivity of a-Si in a wide range of temperatures and sample sizes is still a challenge. Herein we present a systematic investigation of the thermal transport properties of a-Si by employing large-scale molecular dynamics (MD) simulations with an accurate and efficient machine learned neuroevolution potential (NEP) trained against abundant reference data calculated at the quantum-mechanical density-functional-theory level. The high efficiency of NEP allows us to study the effects of finite size and quenching rate in the formation of a-Si in great detail. We find that a simulation cell up to 64000 atoms (a cubic cell with a linear size of 11 nm) and a quenching rate down to 1011 K s−1 are required for almost convergent thermal conductivity. Structural properties, including short- and medium-range order as characterized by the pair-correlation function, angular-distribution function, coordination number, ring statistics, and structure factor are studied to demonstrate the accuracy of NEP and to further evaluate the role of quenching rate. Using both the heterogeneous and homogeneous nonequilibrium MD methods and the related spectral decomposition techniques, we calculate the temperature- and thickness-dependent thermal conductivity values of a-Si and show that they agree well with available experimental results from 10 K to room temperature. Our results also highlight the importance of quantum effects in the calculated thermal conductivity and support the quantum-correction method based on the spectral thermal conductivity.