Medical MNIST

downloaded from: http://quantum-machine.org/datasets/

Abstract

Computational de novo design of new drugs and materials requires rigorous and unbiased exploration of chemical compound space. However, large uncharted territories persist due to its size scaling combinatorially with molecular size. We report computed geometric, energetic, electronic, and thermodynamic properties for 134k stable small organic molecules made up of CHONF. These molecules correspond to the subset of all 133,885 species with up to nine heavy atoms (CONF) out of the GDB-17 chemical universe of 166 billion organic molecules. We report geometries minimal in energy, corresponding harmonic frequencies, dipole moments, polarizabilities, along with energies, enthalpies, and free energies of atomization. All properties were calculated at the B3LYP/6-31G(2df,p) level of quantum chemistry. Furthermore, for the predominant stoichiometry, C7H10O2, there are 6,095 constitutional isomers among the 134k molecules. We report energies, enthalpies, and free energies of atomization at the more accurate G4MP2 level of theory for all of them. As such, this data set provides quantum chemical properties for a relevant, consistent, and comprehensive chemical space of small organic molecules. This database may serve the benchmarking of existing methods, development of new methods, such as hybrid quantum mechanics/machine learning, and systematic identification of structure-property relationships.

Download Available via figshare.

How to cite When using this dataset, please make sure to cite the following two papers:

L. Ruddigkeit, R. van Deursen, L. C. Blum, J.-L. Reymond, Enumeration of 166 billion organic small molecules in the chemical universe database GDB-17, J. Chem. Inf. Model. 52, 2864–2875, 2012.

R. Ramakrishnan, P. O. Dral, M. Rupp, O. A. von Lilienfeld, Quantum chemistry structures and properties of 134 kilo molecules, Scientific Data 1, 140022, 2014. [bibtex]

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

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PREDICTING MOLECULAR PROPERTIES WITH MACHINE LEARNING

Introduction and Objectives

The computational de novo design of new drugs and materials requires a thorough and unbiased exploration of chemical compound space. However, this space remains largely unexplored due to its combinatorial scaling with molecular size. To address this challenge, a dataset of 134,000 stable small organic molecules composed of carbon (C), hydrogen (H), oxygen (O), nitrogen (N), and fluorine (F) has been meticulously computed. These molecules represent a subset of all 133,885 species with up to nine heavy atoms (C, O, N, F) from the GDB-17 chemical universe, which encompasses 166 billion organic molecules.

For each molecule, computed geometric, energetic, electronic, and thermodynamic properties are provided, including:

This dataset offers a relevant, consistent, and comprehensive exploration of chemical space for small organic molecules, providing a valuable resource for benchmarking existing methods, developing new methodologies (such as hybrid quantum mechanics/machine learning approaches), and systematically identifying structure-property relationships [1].

[1] Ramakrishnan, Raghunathan, et al. "Quantum chemistry structures and properties of 134 kilo molecules." Scientific data 1.1 (2014): 1-7.

In this notebook, we aim to leverage this dataset (QM9) to predict the molecular properties of these small organic molecules using the Coulomb matrix representation. Specifically, we will focus on using the eigenvalues of the Coulomb matrix, which serve as a crucial descriptor for capturing the electronic structure of molecules for predicting molecular properties.

By the end of this notebook, you will have:

• Explored the dataset and visualized key molecular properties
• Generated Coulomb matrices for the molecules in the dataset
• Calculate the eigenvalues of the Coulomb matrices and predicting properties using machine learning models
• Evaluated the performance of these models in accurately predicting molecular properties

Let's begin by loading and exploring the dataset.

Enjoy! ⚛

Properties in the QM9 Dataset

Dataset Structure

For each molecule, atomic coordinates and calculated properties are stored in a file named dataset_index.xyz. The XYZ format 1 is a widespread plain text format for encoding Cartesian coordinates of molecules, with no formal specification. It contains a header line specifying the number of atoms n a, a comment line, and n a lines containing element type and atomic coordinates, one atom per line. The comment line is used to store all scalar properties, Mulliken charges are added as a fifth column. Harmonic vibrational frequencies, SMILES and InChI [2] are appended as respective additional lines.

[1] https://open-babel.readthedocs.io/en/latest/FileFormats/XYZ_cartesian_coordinates_format.html

[2] https://iupac.org/who-we-are/divisions/division-details/inchi/

QM9 xyz format

| Line | Content | |------|----------------------------------------------------------...

QM9 provides quantum chemical properties (at DFT level) for a relevant, consistent, and comprehensive chemical space of small organic molecules. This database may serve the benchmarking of existing methods, development of new methods, such as hybrid quantum mechanics/machine learning, and systematic identification of structure-property relationships.

This dataset contains performance metrics for various quantum gates, both with and without noise, based on 1000 runs per condition for each gate. The dataset includes data from quantum circuits that utilize gates such as H, X, Y, Z, S, T, CNOT, Toffoli, Fredkin, SWAP, RX, RY, and RZ. Each row includes the following information: the gate type, run number, number of qubits, depth, circuit size, execution time, error rate, fidelity, energy consumption, quantum volume, depolarization rate, and noise model used. The data is split into two categories: one with noise and one without noise.

Key Features: 1. Quantum gate performance metrics for a variety of gates. 2. Both noisy and noise-free scenarios. 3. Provides insights into error rates, energy consumption, quantum volume, and more.

This dataset is useful for researchers and developers aiming to understand and compare the performance of quantum gates under different noise conditions.

The datasets and final machine learning model files for the manuscript "Machine learning from quantum chemistry to predict experimental solvent effects on reaction rates". Citation should refer directly to the manuscript:

• Chung, Y.; Green, W. H. Machine learning from quantum chemistry to predict experimental solvent effects on reaction rates. ChemRxiv 2023, doi: 10.26434/chemrxiv-2023-f20bg

To use the machine learning models, please refer to the sample files and instructions on https://github.com/yunsiechung/chemprop/tree/RxnSolvKSE_ML.

Detailed information can be found in README.md file.

Details on the files

In the pretraining and finetuning set csv files, each column represents:

1. rxn_smiles: atom-mapped reaction SMILES
2. solvent_smiles: solvent SMILES
3. ddGsolv: solvation free energy of activation of a reaction-solvent pair at 298K in kcal/mol (main prediction target)
4. ddHsolv: solvation enthalpy of activation of a reaction-solvent pair at 298K in kcal/mol (main prediction target)
5. dGsolv_reactant: solvation free energy of reactant(s) at 298K in kcal/mol (additional feature)
6. dGsolv_product: solvation free energy of product(s) at 298K in kcal/mol (additional feature)
7. dHsolv_reactant: solvation enthalpy of reactant(s) at 298K in kcal/mol (additional feature)
8. dHsolv_product: solvation enthalpy of product(s) at 298K in kcal/mol (additional feature)

Data sets under 'RxnSolvKSE_dataset_v1.0.zip'

• pretraining_set: contains the dataset used for pre-training
  • all_data: contains all calculated data
    • pretraining_rxn_solvent_ddGsolv_ddHsolv_with_features_all.csv: contains both main prediction targets and additional feature for reaction-solvent pairs
    • pretraining_solvent_info.csv: list of all solvents
    • pretraining_unique_rxn.csv: list of all reactions, both forward and reverse directions
  • chosen_500k_data: contains the chosen 500k data
    • pretraining_rxn_solvent_ddGsolv_ddHsolv_500k.csv: contains main prediction targets for reaction-solvent pairs
    • pretraining_features_react_prod_dGsolv_dHsolv_500k.csv: contains additional features for reaction-solvent pairs
• finetuning_set: contains the dataset used for fine-tuning
  • all_data: contains all calculated data
    • finetuning_rxn_solvent_ddGsolv_ddHsolv_with_features_all.csv: constains both main prediction targets and additional features for reaction-solvent pairs. The rxn_key column indicates whether the reaction is bimolecular hydrogen abstraction (bihabs), unimolecular hydrogen migration (intrahabs), or radical addition to a multiple bond (raddition). The 'fwd' and 'rev' each indicate forward and reverse reactions.
    • finetuning_solvent_info.csv: list of all solvents
    • finetuning_unique_rxn.csv: list of all reactions, both forward and reverse directions
  • chosen_data: contains chosen data
    • finetuning_rxn_solvent_ddGsolv_ddHsolv_chosen.csv: contains main prediction targets for reaction-solvent pairs
    • finetuning_features_react_prod_dGsolv_dHsolv_chosen.csv: contains additional features for reaction-solvent pairs
• experimental_set/expt_rxn_atom_mapped_smiles.csv: contains the atom-mapped reaction SMILES used for the experimental data.The original experimental data can be found at https://zenodo.org/record/7747557.

Machine learning model files under 'RxnSolvKSE_ML_model_files.zip'

• Contains the Chemprop machine learning model files for predicting ddGsolv and ddHsolv for a reaction-solvent pair. It takes atom-mapped reaction SMILES and solvent SMILES as inputs.
• To use these ML models, please refer to the sample files and instructions on https://github.com/yunsiechung/chemprop/tree/RxnSolvKSE_ML

Snapshot img

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?

Explore in-depth regional segment analysis with market size data - historical 2019-2023 and forecasts 2025-2029 - in the full report.
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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

Here, we introduce QM7-X, a comprehensive dataset of > 40 physicochemical properties for ~4.2 M equilibrium and non-equilibrium structures of small organic molecules with up to seven non-hydrogen (C, N, O, S, Cl) atoms. To span this fundamentally important region of chemical compound space (CCS), QM7-X includes an exhaustive sampling of (meta-)stable equilibrium structures---comprised of constitutional/structural isomers and stereoisomers, e.g., enantiomers and diastereomers (including cis-trans-and conformational isomers)---as well as 100 non-equilibrium structural variations thereof to reach a total of ~4.2 M molecular structures. Computed at the tightly converged quantum-mechanical PBE0+MBD level of theory, QM7-X contains global (molecular) and local (atom-in-a-molecule) properties ranging from ground state quantities (such as atomization energies and dipole moments) to response quantities (such as polarizability tensors and dispersion coefficients). By providing a systematic, extensive, and tightly converged dataset of quantum-mechanically computed physical and chemical properties, we expect that QM7-X will play a critical role in the development of next-generation machine-learning based models for exploring greater swaths of CCS and performing in silico design of molecules with targeted properties.

The dataset is provided in eight HDF5 based files (compressed in .XZ files). One can also find here a README file with technical usage details and examples of how to access the information stored in the dataset (see createDB.py).

*The paper explaining the generation of data stored in QM7-X can be found in Sci Data 8, 43 (2021). DOI: 10.1038/s41597-021-00812-2 . arXiv: https://arxiv.org/abs/2006.15139 .

Quantum Random Access Memory Market Outlook

According to our latest research, the Quantum Random Access Memory (QRAM) market size reached USD 112.5 million in 2024 at the global level. The market is projected to expand at a robust CAGR of 29.8% during the forecast period, reaching an estimated USD 1,040.6 million by 2033. This significant growth trajectory is being driven by the rapid advancements in quantum computing technologies, increasing investments from both public and private sectors, and the critical need for high-speed, high-capacity memory solutions in next-generation computing systems. As per our latest research, the QRAM market is witnessing accelerated adoption across diverse industries due to its unparalleled potential to revolutionize data processing and storage paradigms.

The primary growth factor for the Quantum Random Access Memory market is the surging demand for quantum computing capabilities across various sectors. As organizations strive to solve complex computational problems that are beyond the reach of classical computers, the need for advanced memory architectures such as QRAM becomes paramount. QRAM enables quantum computers to access and manipulate large datasets with unprecedented speed and efficiency, making it a cornerstone technology for quantum algorithms and applications. The integration of QRAM into quantum processors allows for exponential improvements in computational throughput, which is vital for applications ranging from cryptography and optimization to machine learning and materials science. This technological leap is fueling substantial investments in QRAM research and development, further accelerating market expansion.

Another significant driver propelling the QRAM market is the escalating emphasis on cybersecurity and encryption. As quantum computers become more capable, traditional cryptographic methods are increasingly vulnerable to quantum attacks. QRAM plays a pivotal role in the development of quantum-safe encryption protocols, enabling the secure storage and retrieval of quantum information. The financial sector, government agencies, and defense organizations are particularly invested in quantum cryptography, leveraging QRAM to safeguard sensitive data against emerging quantum threats. This growing focus on quantum-secure communication and data protection is expected to drive sustained demand for QRAM solutions, positioning the technology as a critical enabler of next-generation cybersecurity infrastructure.

The expanding adoption of artificial intelligence (AI) and data-centric applications is also contributing to the growth of the Quantum Random Access Memory market. QRAM facilitates the efficient handling of massive datasets required for AI training and inference, particularly within quantum machine learning frameworks. By enabling rapid access to quantum data, QRAM enhances the performance and scalability of AI models, opening new frontiers in predictive analytics, drug discovery, financial modeling, and beyond. The convergence of AI and quantum computing is creating a synergistic effect, amplifying the need for advanced memory solutions and driving innovation across the QRAM ecosystem.

From a regional perspective, North America currently leads the Quantum Random Access Memory market, owing to its strong presence of quantum technology vendors, robust research infrastructure, and substantial government funding. Europe and Asia Pacific are also emerging as significant contributors, with increasing investments in quantum computing initiatives and collaborative research programs. The regional landscape is characterized by strategic partnerships between academic institutions, technology companies, and government agencies, fostering a dynamic environment for QRAM innovation and commercialization. As the global race for quantum supremacy intensifies, regions with proactive policy frameworks and vibrant technology ecosystems are poised to capture a substantial share of the QRAM market.

Technology Analysis

The Quantum Random Access Memo

Supplemental Material: Hierarchical quantum embedding by machine learning for large molecular assemblies

This archive contains all software and data to reproduce the results of

Hierarchical quantum embedding by machine learning for large molecular assemblies, Moritz Bensberg, Marco Eckhoff, Raphael T. Husistein, Matthew S. Teynor, Valentina Sora, William Bro-Jørgensen, F. Emil Thomasen, Anders Krogh, Kresten Lindorff-Larsen, Gemma C. Solomon, Thomas Weymuth, and Markus Reiher, **to be submitted**, 2025.

Note that for reproducing the transfer learning, the base machine learning potential provided in Ref. [1] is required.

Citation
-------------
Please cite this repository and Ref. [2] when reusing the data.

Databases
-----------------
├──model-complex-shrunk-QMQM.tar.xz : The database containing all QM/MM and QM/QM/MM results for the MCL1-19G protein-ligand complex.
| ├──calculations.bson : The calculations collection exported as a bson file. To reimport it into a running mongo database use `mongoimport`. The calculation objects correspond to input and output of individual single point calculations.
| ├──calculations.metadata.json : The metadata of the calculations collection.
| ├──properties.bson : The property collection (i.e., collection of properties such as energies, charges etc.)
| ├──properties.metadata.json
| ├──structures.bson : The structure collection (i.e., collection of all cartesian coordinates and element symbols).
| └──structures.metadata.json
├──model-ligand-solvent-QMQM.tar.xz : The database containing all QM/MM and QM/QM/MM results for the solvated 19G ligand.
| ├──calculations.bson : The calculations collection exported as a bson file. To reimport it into a running mongo database use `mongoimport`. The calculation objects correspond to input and output of individual single point calculations.
| ├──calculations.metadata.json : The metadata of the calculations collection.
| ├──properties.bson : The property collection (i.e., collection of properties such as energies, charges etc.)
| ├──properties.metadata.json
| ├──structures.bson : The structure collection (i.e., collection of all cartesian coordinates and element symbols).
| └──structures.metadata.json

Machine Learning Potentials (MLPs)
-----------------------------------------------------------
├──machine_learning_potentials.tar.gz
| ├──model-complex-shrunk-QMQM.tar.gz : MLP for the solvated MCL1-19G protein-ligand complex.
| └──model-ligand-solvent-QMQM.tar.gz : MLP for the solvated 19G ligand.

Work Distributions
------------------------------
├──work_distributions.tar.gz
| ├──model-complex-shrunk-QMQM.tar.gz : Work values for the MCL1-19G protein-ligand complex.
| | ├──0-5_output_10ps : Work values for each run with index 0-5.
| ├──model-ligand-solvent-QMQM.tar.gz : Work values for the solvated 19G ligand.
| | └──0-5_output_10ps : Work values for each run with index 0-5.

Software
---------------
├──software.tar.gz
| ├──puffin : Code for the "puffin" clients to be run on a HPC cluster.
| ├──swoose : The QM/MM software Swoose.
| ├──serenity_wrapper : The SCINE framework wrapper for the quantum chemistry program Serenity.
| ├──utils-open-source : The scine_utilities version used in this project.
| ├──pipeline : A collection of Python scripts/executables to generate plots, populate the database, and run the active learning.
| ├──NEQ_switching_ani2x : Software to run the NEQ switching simulations.
| ├──EEForce : OpenMM/MLP interface for element embracing machine learning potentials.
| └──SymmetryFunctions : Library to calculate the element embracing symmetry functions for element embracing machine learning potentials.

Transfer-Learning Gradient Study
------------------------------------------------
├──episodic_memory.tar.gz : The data for the study investigating the effect of energy derivatives on the transfer learning.
| ├──input.data_q4bio-model-complex-shrunk_MMMM : Contains all of the MCL1-19G protein-ligand complex structures used in the study, including their MM energies and forces.
| ├──input.data_q4bio-model-complex-shrunk_MMMM_T : Contains all of the MCL1-19G protein-ligand complex structures used in the study, including their QM energies and forces.
| ├──input.data_q4bio-model-ligand_solvent_MMMM : Contains all of the solvated 19G ligand structures used in the study, including their MM energies and forces.
| └──input.data_q4bio-model-ligand_solvent_MMMM_T : Contains all of the solvated 19G ligand structures used in the study, including their QM energies and forces.

References
------------------
[1] Supplementary Material: Machine Learning Enhanced Calculation of Quantum-Classical Binding Free Energies, Moritz Bensberg, Marco Eckhoff, F. Emil Thomasen, William Bro-Jørgensen, Matthew S. Teynor, Valentina Sora, Thomas Weymuth, Raphael T. Husistein, Frederik E. Knudsen, Anders Krogh, Kresten Lindorff-Larsen, Markus Reiher, and Gemma C. Solomon, ERDA, 2025, DOI: **archive under construction**, url: https://sid.erda.dk/cgi-sid/ls.py?share_id=L6JhSY0c1P.

[2] Hierarchical quantum embedding by machine learning for large molecular assemblies, Moritz Bensberg, Marco Eckhoff, Raphael T. Husistein, Matthew S. Teynor, Valentina Sora, William Bro-Jørgensen, F. Emil Thomasen, Anders Krogh, Kresten Lindorff-Larsen, Gemma C. Solomon, Thomas Weymuth, and Markus Reiher, arXiv 2025, DOI: 10.48550/ARXIV.2503.03928.

THE REVISED MD17 dataset:=========================Citation:======== Anders S. Christensen and O. Anatole von Lilienfeld (2020) "On the role of gradients for machine learning of molecular energies and forces" https://arxiv.org/abs/2007.09593The molecules are taken from the original MD17 dataset by Chmiela et al., and 100,000 structures are taken, and the energies and forces are recalculated at the PBE/def2-SVP level of theory using very tight SCF convergence and very dense DFT integration grid. As such, the dataset is practically free from nummerical noise. One warning: As the structures are taken from a molecular dynamics simulation (i.e. time series data), they are not guaranteed to be independent samples. This is easily evident from the autocorrelation function for the original MD17 datasetIn short: DO NOT train a model on more than 1000 samples from this dataset. Data already published with 50K samples on the original MD17 dataset should be considered meaningless due to this fact and due to the noise in the original data.The data:=========The ten molecules are save in Numpy .npz format.The keys correspond to:'nuclear_charges' : The nuclear charges for the molecule'coords' : The coordinates for each conformation (in units of ångstrom)'energies' : The total energy of each conformation (in units of kcal/mol)'forces' : The cartesian forces of each conformation (in units of kcal/mol/ångstrom)'old_indices' : The index of each conformation in the original MD17 dataset'old_energies' : The energy of each conformation taken from the original MD17 dataset (in units of kcal/mol)'old_forces' : The forces of each conformation taken from the original MD17 dataset (in units of kcal/mol/ångstrom)*Note that for Azobenzene, only 99988 samples are available due to 11 failed DFT calculations, and the original dataset only contained 99999 structures.Data splits:============Five training and test splits are saved in CSV format containing the corresponding indices.

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.

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

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

Quantum-AI Fraud Heatmap Market Outlook

According to our latest research, the global Quantum-AI Fraud Heatmap market size reached USD 2.18 billion in 2024, reflecting the growing integration of advanced quantum and artificial intelligence technologies in anti-fraud solutions. The market is expanding at a robust CAGR of 27.5% and is forecasted to reach USD 18.19 billion by 2033. This remarkable growth is primarily driven by escalating cyber threats, the proliferation of digital transactions, and the urgent need for real-time fraud detection across industries.

The primary growth factor for the Quantum-AI Fraud Heatmap market is the exponential rise in sophisticated cyberattacks targeting financial, healthcare, and government sectors. As digital transformation accelerates, businesses are increasingly vulnerable to complex fraud schemes that traditional detection systems struggle to identify. Quantum-AI Fraud Heatmap solutions leverage the combined power of quantum computing and AI-driven analytics, enabling organizations to detect anomalies and fraudulent patterns in real-time with unprecedented accuracy. The surge in online banking, digital payments, and e-commerce transactions further amplifies the demand for advanced fraud detection systems, as enterprises seek to safeguard sensitive customer data and maintain regulatory compliance. The integration of machine learning algorithms with quantum processing capabilities allows these solutions to analyze vast datasets rapidly, delivering actionable insights that are vital for preempting fraud in today’s dynamic threat landscape.

Another significant driver is the increasing regulatory pressure on organizations to implement robust fraud prevention measures. Governments and regulatory bodies worldwide are enacting stringent compliance mandates, such as GDPR, PCI DSS, and CCPA, to protect consumer data and ensure transparency in financial transactions. Quantum-AI Fraud Heatmap platforms are becoming indispensable tools for enterprises striving to meet these regulatory requirements, as they offer real-time monitoring, automated reporting, and advanced risk assessment features. The ability of these solutions to adapt to evolving fraud tactics and provide continuous protection has made them a preferred choice among leading banks, insurance companies, and e-commerce platforms. Additionally, the growing awareness of the financial and reputational risks associated with data breaches is prompting organizations to invest heavily in next-generation fraud detection technologies.

The rapid adoption of cloud computing and the proliferation of Internet of Things (IoT) devices are also fueling the Quantum-AI Fraud Heatmap market’s expansion. Cloud-based deployment models offer scalability, flexibility, and cost-efficiency, making them attractive to organizations of all sizes. The integration of fraud heatmap solutions with IoT networks enables real-time monitoring of transactional data across multiple endpoints, enhancing the ability to detect and mitigate threats instantly. Furthermore, advancements in quantum encryption and AI-powered behavioral analytics are enabling enterprises to stay ahead of cybercriminals by identifying subtle deviations from normal user behavior. This technological synergy is expected to drive continuous innovation in the market, creating new opportunities for solution providers and end-users alike.

Regionally, North America dominates the Quantum-AI Fraud Heatmap market, accounting for the largest revenue share in 2024, followed by Europe and Asia Pacific. The region’s leadership can be attributed to the presence of major technology vendors, high digital adoption rates, and a mature regulatory environment. However, Asia Pacific is anticipated to witness the fastest growth during the forecast period, driven by rapid digitalization, increasing cyber threats, and the rising adoption of advanced fraud detection solutions across emerging economies such as China, India, and Singapore. Latin America, the Middle East, and Africa are also experiencing steady growth, supported by government initiatives to strengthen cybersecurity infrastructure and the expansion of digital financial services.

Parametrization of small organic molecules for classical molecular dynamics simulations is not trivial. The vastness of the chemical space makes approaches using building blocks challenging. The most common approach is therefore an individual parametrization of each compound by deriving partial charges from semiempirical or ab initio calculations and inheriting the bonded and van der Waals (Lennard-Jones) parameters from a (bio)molecular force field. The quality of the partial charges generated in this fashion depends on the level of the quantum-chemical calculation as well as on the extraction procedure used. Here, we present a machine learning (ML) based approach for predicting partial charges extracted from density functional theory (DFT) electron densities. The training set was chosen with the goal to provide a broad coverage of the known chemical space of druglike molecules. In addition to the speed of the approach, the partial charges predicted by ML are not dependent on the three-dimensional conformation in contrast to the ones obtained by fitting to the electrostatic potential (ESP). To assess the quality and compatibility with standard force fields, we performed benchmark calculations for the free energy of hydration and liquid properties such as density and heat of vaporization.

Many challenges persist in developing accurate computational models for predicting solvation free energy (ΔGsol). Despite recent developments in Machine Learning (ML) methodologies that outperformed traditional quantum mechanical models, several issues remain concerning explanatory insights for broad chemical predictions with an acceptable speed–accuracy trade-off. To overcome this, we present a novel supervised ML model to predict the ΔGsol for an array of solvent–solute pairs. Using two different ensemble regressor algorithms, we made fast and accurate property predictions using open-source chemical features, encoding complex electronic, structural, and surface area descriptors for every solvent and solute. By integrating molecular properties and chemical interaction features, we have analyzed individual descriptor importance and optimized our model though explanatory information form feature groups. On aqueous and organic solvent databases, ML models revealed the predictive relevance of solutes with increasing polar surface area and decreasing polarizability, yielding better results than state-of-the-art benchmark Neural Network methods (without complex quantum mechanical or molecular dynamic simulations). Both algorithms successfully outperformed previous ΔGsol predictions methods, with a maximum absolute error of 0.22 ± 0.02 kcal mol–1, further validated in an external benchmark database and with solvent hold-out tests. With these explanatory and statistical insights, they allow a thoughtful application of this method for predicting other thermodynamic properties, stressing the relevance of ML modeling for further complex computational chemistry problems.

HOMO and LUMO orbital energies for 111725 organic molecules calculated at the B3LYP/6-31G*//PM6 or B3LYP/6-31G*//PM7 level of theory.Related publication:* Florbela Pereira, Kaixia Xiao, Diogo A. R. S. Latino, Chengcheng Wu, Qingyou Zhang and Joao Aires-de-Sousa:Machine Learning Methods to Predict Density Functional Theory B3LYP Energies of HOMO and LUMO Orbitals.J. Chem. Inf. Model. (2017)DOI: 10.1021/acs.jcim.6b00340 This data set is publicly available at http://dx.doi.org/10.6084/m9.figshare.3384184.v1 Files-----frontier_orbitals_111725mols_sdf.tar.gz - 111275 molecules in the MDL SDFile formatfrontier_orbitals_111725mols.xlsx - HOMO and LUMO orbital energies for 111275 neutral organic moleculescoordinates_111725mols_xyz.zip - atomic coordinates used for the DFT calculation of the 111275 moleculesPM7_frontier_orbitals.xlsx - HOMO and LUMO energies calculated by the PM7 semi-empirical method.Molecules---------For the database creation, molecular structural motifs were retrieved from organic electronics studies, and collections of dyes, metabolites and electrophiles/nucleophiles [1-5]. The database was populated by retrieval of similar examples from the ZINC database [6], the PubChem database [7] and by computationally combining motifs and lists of substituents with the ChemAxon Reactor software, JChem 15.4.6, 2015, ChemAxon (http://www.chemaxon.com). The structures were standardized with ChemAxon Standardizer (JChem 15.4.6, 2015, ChemAxon, http://www.chemaxon.com) and OpenBabel (Open Babel Package, version 2.3.1 http://openbabel.org) for neutralization and inclusion of all hydrogen atoms. The molecular structures include atomic elements C, H, B, N, O, F, Si, P, S, Cl, Se, and Br.Molecular geometries were relaxed by the PM6 or PM7 methods using the MOPAC software [8] and orbital energies were calculated by the GAMESS program [9] with the B3LYP functional and the 6-31G* basis set. Structures were calculated with the geometry obtained with the PM6 or PM7 semi-empirical method. Format------Each molecule is stored in its own file, ending in ".sdf". These are the starting structures, previous to geometry relaxation with the MOPAC program. The format is the standard MDL SDFile generated with ChemAxon Standardizer and OpenBabel.The atomic coordinates obtained with the PM6 and PM7 methods are stored in files ending in ".xyz", one for each molecule. Each file comprises a header line specifying the number of atoms n, a line with the id of the structure, and n lines containing the element and atomic coordinates, one atom per line.Orbital energies are stored in the frontier_orbitals_111725mols.xlsx file. Two different sheets are used for the main database and a data set used as final test set in the related publication. PM7 values are stored in the PM7_frontier_orbitals.xlsx with the same format. Column Content of .xlsx files------1 Molecule ID (as appears in the corresponding .sdf file name)2 HOMO energy in eV.3 LUMO energy in eV.References----------[1] Po R, Bianchi G, Carbonera C, Pellegrino A: All that glisters is not gold: an analysis of the synthetic complexity of efficient polymer donors for polymer solar cells. Macromolecules 2015, 48:453-461.[2] Hachmann J, Olivares-Amaya R, Atahan-Evrenk S, Amador-Bedolla C, Sanchez-Carrera RS, Gold-Parker A, Vogt L, Brockway AM, Aspuru-Guzik A: The Harvard Clean Energy Project: large-scale computational screening and design of organic photovoltaics on the world community grid. J Phys Chem Lett 2011, 2:2241-2251.[3] O’Boyle NM, Campbell CM, Hutchison GR: Computational design and selection of optimal organic photovoltaic materials. J Phys Chem C 2011, 115:16200-16210.[4] Mayr H, Ofial AR: Kinetics of electrophile-nucleophile combinations: a general approach to polar organic reactivity. Pure Appl Chem 2005, 77:1807-1821.[5] Kanehisa M, Goto S: KEGG: Kyoto Encyclopedia of Genes and Genomes. Nucleic Acids Res 2000, 28:27-30.[6] Irwin JJ, Sterling T, Mysinger MM, Bolstad ES, Coleman RG: ZINC: a free tool to discover chemistry for biology. J Chem Inf Model 2012, 52:1757-1768.[7] Kim S, Thiessen PA, Bolton EE, Chen J, Fu G, Gindulyte A, Han L, He J, He S, Shoemaker BA, Wang J, Yu B, Zhang J, Bryant SH: PubChem Substance and Compound databases. Nucleic Acids Res 2016, 44(D1):D1202-13. [8] MOPAC2009 and MOPAC2012, James J. P. Stewart, Stewart Computational Chemistry, Colorado Springs, CO, USA, http://OpenMOPAC.net (2008-2012).[9] Schmidt MW, Baldridge KK, Boatz JA, Elbert ST, Gordon MS, Jensen JJ, Koseki S, Matsunaga N, Nguyen KA, Su S, Windus TL, Dupuis M, Montgomery JA: General atomic and molecular electronic structure system. J Comput Chem 1993, 14:1347-1363. GAMESS Version 1 May 2013 (R1).