Quantum-inspired Chemical Rule for Discovering Topological Materials

TL;DR

Efficient discovery of topological materials remains challenging due to symmetry-indicator limitations and the cost of first-principles calculations. The authors introduce a quantum-inspired chemical rule $g^Q(M)$ derived from a quantum–classical hybrid neural network (QANN) that adds pairwise inter-element correlations; the rule is validated by an equivalent complex-valued neural network (CVNN) to ensure interpretability. The rule is defined as $g^Q(M)= \sum_E f_E(M)\tau_E + \sum_{E\neq \mathcal{E}} \sqrt{f_E(M) f_{\mathcal{E}}(M)} \tau_{E\mathcal{E}}$, combining elemental topogivities $\tau_E$ with pairwise terms $\tau_{E\mathcal{E}}$, and a decision is made by the sign of $g^Q(M)$. High-throughput screening with DFT validation identifies five previously unreported topological compounds and yields overall accuracy around 84%, demonstrating a scalable, symmetry-agnostic front-end for topological materials discovery.

Abstract

Topological materials exhibit unique electronic structures that underpin both fundamental quantum phenomena and next-generation technologies, yet their discovery remains constrained by the high computational cost of first-principles calculations and the slow, resource-intensive nature of experimental synthesis. Recent machine-learning approaches, such as the heuristic topogivity rule, offer data-driven alternatives by quantifying each element's intrinsic tendency toward topological behavior. Here, we develop a quantum-classical hybrid artificial neural network (QANN) that extends this rule into a quantum-inspired formulation. Within this framework, the QANN maps compositional descriptors to quantum probability amplitudes, naturally introducing pairwise inter-element correlations inaccessible to classical heuristics. The physical validity of these correlations is substantiated by constructing an equivalent complex-valued neural network (CVNN), confirming both the consistency and interpretability of the formulation. Retaining the simplicity of chemical reasoning while embedding quantum-native features, our quantum-inspired rule enables efficient and generalizable topological classification. High-throughput screening combined with first-principles (DFT) validation reveals five previously unreported topological compounds, demonstrating the enhanced predictive power and physical insight afforded by quantum-inspired heuristics.

Figures (4)

• Figure 1: QANN-based diagnosis and discovery of topological materials. (a) Schematic illustration of the quantum-inspired heuristic rule $g^{Q}(M)$ for topological diagnosis. For a given compound (e.g., $AB_{2}$ or $AB_{2}C_{3}$ ), the diagnostic value is obtained in two steps: first, by computing the weighted average of the constituent elements’ topogivities ( $\tau_{A}, \tau_{B}, \tau_{C}$ ) according to their stoichiometric ratios; and second, by evaluating the weighted average of pairwise quantum topogivities ( $\tau_{AB}, \tau_{AC}, \tau_{BC}$ ) between distinct elements, with weights given by the product of their relative abundances. The overall diagnostic value—sum of the two contributions—encodes both the topological classification (sign) and the confidence level (magnitude). (b) High-throughput discovery workflow using quantum-inspired chemical rule. Chemical formulae are first used for topological property prediction, followed by screening of high-confidence candidates. The shortlisted materials are then validated via DFT calculations, leading to the identification of previously unreported topological materials. (c) The general workflow of our QANN model, which integrates data preprocessing, a quantum circuit, and a classical neural network. Further details are given in Section S1 of the Supporting Information (SI).
• Figure 2: Periodic table of topogivities. Color-coding and numerical values represent QANN topogivities $\tau_{\rm E}$. Gray elements indicate those not present in the dataset. The complete model contains 1,485 topogivity values (54 elemental topogivities shown here plus 1,431 cross-correlation terms not included in the periodic table representation).
• Figure 3: Model performance and dataset analysis. (a) Distribution of labeled materials grouped by elemental complexity (binary, ternary, quaternary, etc.). (b) Summary of model performance in 10-fold cross-validation and on the final held-out test set (reported as mean $\pm$ standard deviation (std) across folds). (c) Cross-validation accuracy and balanced accuracy, averaged over 10 folds, resolved by material complexity (element count). (d) Generalization performance on the independent test set: accuracy and balanced accuracy as functions of material elemental count. (e) Test-set accuracy for topologically trivial compounds within negative $g^Q(M)$ bins. (f) Test-set accuracy for topologically nontrivial compounds within positive $g^Q(M)$ bins. In panels (b) and (d)--(f), the red line shows the score obtained on the final test set using the aggregated parameter values employed to compute $g^{Q}(M)$.
• Figure 4: Orbital projected electronic band structures of representative compounds illustrating diverse topological behaviors for (a) Ag$_3$Sb, (b) Ca, (c) Pd$_3$(PbS)$_2$, (d) P$_3$Sc$_7$, (e) As$_2$Ta, and (f) PdS$_4$U$_2$.