Data-Driven Quantum Materials Informatics

• Data-driven quantum materials informatics is a paradigm that fuses curated datasets, physically informed descriptors, and ML models to predict and discover quantum materials.
• It leverages high-dimensional embeddings, graph-based encodings, and ensemble algorithms to overcome computational bottlenecks in exploring complex chemical spaces.
• The approach enables accelerated screening, robust uncertainty quantification, and interpretable feature attribution for next-generation quantum materials design.

Data-driven quantum materials informatics is a research paradigm that leverages large-scale electronic-structure databases, physically meaningful descriptors, and advanced ML models to accelerate the prediction and discovery of materials with quantum-relevant properties such as coherence, topology, strong correlation, and defect engineering potential. By systematically combining curated datasets with interpretable or high-capacity ML architectures, this approach overcomes both the vastness and complexity of chemical space and the computational bottlenecks of high-level quantum simulations, providing scalable, generalizable, and often physically interpretable workflows for next-generation quantum materials design, characterization, and control.

1. Curation and Feature Engineering of Quantum Materials Datasets

Curated quantum materials databases serve as the foundation for data-driven informatics. Robust dataset construction involves merging experimental and theoretical repositories (e.g., Materials Project, ICSD, OQMD), applying strict physical and chemical filters (thermodynamic stability, electronic band gap, spin multiplicity, polarity), and comprehensive featurization using domain-specific tools such as Matminer. The resulting training sets capture a broad spectrum of properties—composition, space group, band gap, coordination geometry, and advanced DFT-informed descriptors (e.g., static dielectric constant $\varepsilon_s$, defect formation energies $\Delta E_f$) essential for downstream modeling (Mahshook et al., 4 Jun 2025).

Recent efforts emphasize the importance of domain-informed and multi-scale descriptors: band-structure curvature, bond-orientational order (Steinhardt $Q_\ell$), statistical RDF moments, partial charge distributions, and explicit spin and symmetry features. The OpenQDC repository, for example, aggregates nearly 400 million geometries from 37 quantum-mechanical datasets, unifying more than 250 methods and standardizing energy and force data, thereby facilitating MLIP development and benchmarking (Gabellini et al., 2024). Additionally, platforms such as JARVIS incorporate calibrated high-level methods (DFT, QMC, GW, DMFT), graph neural network embeddings, and experimental reference datasets to enable reproducible, multi-modal materials informatics (Wines et al., 2023).

Preprocessing pipelines rigorously address unit conversion, extensivity-preserving energy referencing (e.g., subtraction of isolated-atom energies), one-hot or amplitude encodings for atom and symmetry types, and the elimination of duplicate or physically implausible entries. This systematic curation enables ML tasks ranging from regression (band gap, formation energy, $T_c$) to classification (topological class, quantum-compatibility, magnetic ordering) (Nop et al., 2024, Hebnes et al., 2022).

2. Descriptor Design and Physically Informed Embeddings

Effective quantum materials informatics hinges on descriptors that encode the key physical drivers of quantum phenomena. Two major classes dominate:

• Physically Interpretable Descriptors: Band gap $\Delta E_g$, atomic/isotopic composition (spin-zero nuclei), structure symmetry, site-resolved valence occupancy, dielectric constants, and formation energies. For quantum-defect host prediction, features such as high $\varepsilon_s$, wide $\Delta E_g$, simple stoichiometry, closed-shell configurations, and low nuclear-spin noise are critical (Mahshook et al., 4 Jun 2025). For topological classification, amplitude encoding of composition vectors enables the emergence of quantum-inspired pairwise correlators (capturing inter-element interference effects) that are inaccessible to classical linear models (Xu et al., 15 Dec 2025).
• High-dimensional and ML-derived Embeddings: Graph-based encodings (e.g., CGNN, ALIGNN), message-passing over atomic/bond graphs, set transformers, and 3D voxelized convolutional representations (CCNN) support prediction of arbitrary quantum material properties (Nop et al., 2024). Faithful, injective cell embeddings ensure one-to-one mapping between the primitive cell and its descriptor, facilitating compositional and structural generalization.

Hybrid approaches increasingly integrate both paradigms, combining interpretable features for screening and physically agnostic ML descriptors for capturing higher-order, non-additive effects and cross-material transferability (Xu et al., 15 Dec 2025, Graña et al., 12 Mar 2025).

3. Machine Learning Models and Ensemble Algorithms

Structure-agnostic heterogeneous ensembles (containing logistic regression, SVM, random forests, gradient boosting, $k$NN, naive Bayes, and others) are standard for robust classification and regression (Mahshook et al., 4 Jun 2025, Hebnes et al., 2022). Feature selection and interpretability are achieved through permutation feature importance (PFI), accumulated local effects (ALE), partial-dependence plots, and SHAP sample-wise explanations. Advanced workflows define near-optimal “Rashomon” sets to prune the ensemble and eliminate conflicting decision boundaries.

For strongly correlated and many-body materials, machine learning “error-correction” surrogates replace computationally intensive quantum impurity solvers in DMFT, enabling $10^2$–$10^3\times$ acceleration while retaining high fidelity (Sheridan et al., 2021). Hybrid classical–quantum models, such as quantum neural networks (QNNs), quantum kernel support-vector regressors (QSVR), and factorization-machines combined with quantum approximate optimization (FM+QAOA), extend coverage to exponentially large chemical encodings and exploit quantum-native correlations (Graña et al., 12 Mar 2025, Gujarati et al., 2020, Hirai, 2023).

Diffusion-model-based generative frameworks, incorporating quantum-mechanical descriptors (DOS, ELF, linear response) and multi-fidelity ML potentials (PBE, SCAN, HSE06, CCSD(T)), de-bias exploration and validation in regions where DFT is unreliable, achieving significant gains in strongly correlated subspaces (Roy et al., 13 Dec 2025).

4. Discovery, Screening, and Active Learning Workflows

Data-driven informatics enables screening and discovery over vast chemical and structural spaces not tractable via brute-force DFT:

• Quantum Defect Host Discovery: Using an ensemble model trained on a curated semiconductors dataset, materials are ranked by a constrained voting mechanism, delivering a test MCC of $0.985$ and test $F_1 \approx 0.996$. Known hosts (diamond, SiC) and new candidates (WS$_2$, MgO, CaS, TiO$_2$) are recovered at high confidence. DFT validation confirms the existence of deep, isolated defect levels and dielectric screening commensurate with extended $T_2$ coherence (Mahshook et al., 4 Jun 2025).
• Topological Materials Classification: Quantum-inspired rules derived from QANN capture essential pairwise amplitude correlations, enabling scalable screening and DFT validation of previously unreported topological phases such as Ca$_3$PbO (Z$_2$ TI), SrAgTe$_2$ (Dirac), Ba$_2$SnS$_3$ (Weyl), LaBi (TCI), and YPd$_2$Sb (nodal-line), with overall test-set accuracy $>94\%$ (Xu et al., 15 Dec 2025).
• Disordered Systems and Quantum Clustering: Quantum circuit-based algorithms enable encoding and prediction over exponentially large configuration spaces (substitutionally disordered alloys, LixCoO$_2$, or molecular graphs), incorporating anomaly detection and data correction loops that yield RMSE/MAE <0.03 eV/cation, matching full cluster-expansion performance (Gujarati et al., 2020). Quantum-enhanced extremal learning protocols demonstrate that the fraction of search space required for successful extrapolation to optimal compounds decreases as the encoded space grows (Graña et al., 12 Mar 2025).
• High-Throughput Hybrid 2D Materials: Active learning and CatBoost ensembles identify the 50 most stable post-intercalation bilayer/organic hybrids from a design space of $\sim 10^5$ candidates, validated by DFT and mechanical Born criteria. Properties such as strong vdW stabilization, bandgap tunability, and enhanced mechanical stiffness emerge as robust trends (Kastuar et al., 2024).
• Automated Robust Multi-fidelity Discovery: Quantum-aware generative AI with active learning across PBE, SCAN, HSE06, and CCSD(T) levels massively increases the rate of stable (e.g., correlated oxide) discovery in high-divergence regimes—achieving a 3–5$\times$ improvement over DFT-only generative baselines (Roy et al., 13 Dec 2025).

5. Interpretability, Uncertainty, and Physical Rules

A central goal of quantum materials informatics is to recover interpretable, physically grounded rules for material selection and optimization. Mechanisms include:

• Feature Attribution: ALE and SHAP elucidate which materials features (bandgap, stoichiometry norms, dielectric constants, symmetry, site environment) most promote (or inhibit) target quantum properties (Mahshook et al., 4 Jun 2025, Hebnes et al., 2022).
• Chemical Rules: Quantum-inspired models directly yield closed-form scoring functions (e.g., topogivity $g^Q$) with decipherable self- and pairwise amplitudes (e.g., $$\sum_E \tau_E f_E + \sum_{E<\mathcal{E}} \tau_{E\mathcal{E}} \sqrt{f_E f_{\mathcal{E}}}$$), shedding light on favorable elemental and compositional motifs for nontrivial topology (Xu et al., 15 Dec 2025).
• Confidence and Calibration: Ensemble probability thresholds and Matthews correlation coefficients (MCC >0.95) guide high-reliability selection of candidates for computationally expensive follow-up. Deep ensembles, bootstrap error estimates, and divergence-based acquisition criteria (e.g., $D=|E_{\rm PBE}-E_{\rm MF}|$) drive robust active learning in multi-fidelity settings, achieving well-calibrated sampling and bias reduction (Roy et al., 13 Dec 2025).
• Uncertainty Quantification: Bayesian ML, bootstrapped ensembles, and hybrid quantum–classical kernels support outlier detection, flag regions of poor generalization, and enable dynamic adaptation of follow-up calculations (Gabellini et al., 2024, Gujarati et al., 2020).

6. Practical Implementations and Infrastructure

The field is underpinned by robust software ecosystems, workflow engines, and standardized best practices:

• Data Commons and API Access: OpenQDC and MPDD provide standardized, memory-mapped storage of QM calculations, ensuring unit consistency, extensivity correction, and easy batch access for direct ML model consumption (Gabellini et al., 2024, Krajewski, 2024).
• Benchmarking and Leaderboards: Public leaderboards (OpenQDC, JARVIS-Leaderboard) track canonical ML models (SchNet, TorchMD-Net, DimeNet) on a growing set of open tasks, illuminating open modeling challenges, especially for large, charged, or transition-metal-rich systems (Gabellini et al., 2024, Wines et al., 2023).
• Integration with First-principles and Experimental Data: Coupled DFT/ML/CALPHAD pipelines, quantum-computing model export (e.g., VQE and VQD on Wannier TB Hamiltonians), and experimental validation (SQUID, XRD, magnetometry) enable full-cycle informatics-to-laboratory transfer (Wines et al., 2023, Krajewski, 2024).
• Adoption of Quantum Datapaths: Quantum circuits, QNNs, and quantum-kernel models are implemented on both classical simulators and near-term hardware; active learning, kernel selection, and noise/memory constraints are areas of continuing development (Graña et al., 12 Mar 2025, Hirai, 2023, Lourenço et al., 2024).

7. Perspectives and Future Directions

The field is progressing toward:

• Universal, physically interpretable ML models that scale over the entire chemical and structural complexity of crystalline, amorphous, and interfacial quantum materials. Amplitude-encoded and equivariant models are expected to become critical for symmetry-centric properties (topology, magnetism, superconductivity) (Nop et al., 2024, Xu et al., 15 Dec 2025).
• Adaptive, closed-loop materials discovery and autonomous experimentation realized via active learning, real-time uncertainty quantification, and seamless feedback between computation, ML, and high-throughput synthesis.
• Expansion beyond standard DFT regimes with increased deployment of multi-fidelity and quantum-aware generative frameworks, facilitating the exploration and discovery of materials in strongly correlated or DFT-failure domains (Roy et al., 13 Dec 2025).
• End-to-end pipelines integrating modern data curation, descriptor engineering, machine learning, generative modeling, physics-based simulation, and experimental validation, as exemplified by the next-generation JARVIS, OpenQDC, and emerging quantum–classical hybrid architectures.

Data-driven quantum materials informatics thus constitutes a foundational paradigm for accelerating the discovery, characterization, and rational design of materials with quantum functionality, systematically bridging the gap between electronic-structure theory, machine intelligence, and experimental realization (Mahshook et al., 4 Jun 2025, Gabellini et al., 2024, Xu et al., 15 Dec 2025, Wines et al., 2023).