Predicting Complex Materials Energetics with a Scalable Compact Nine-Qubit Quantum Machine-Learning Model

Accurate machine-learning (ML) prediction of material energies typically relies on large models with thousands to hundreds of thousands of parameters and scales poorly with the system size. Here, we present a compact hybrid classical-quantum ML framework that predicts the energies of complex materials using fewer than ten qubits, regardless of system size. By compressing local atomic descriptors into a fixed-size feature spectrum, we enable amplitude encoding of chemically diverse systems into shallow quantum circuits. We implement quantum convolutional neural networks (QCNNs) and quantum deep neural networks (QDNNs) with fewer than <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mn>100</a:mn> </a:math> trainable parameters and achieve prediction errors below 0.05 eV/atom on chemically complex alloys ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>Co</c:mi> </c:math> <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi/> <e:mn>25</e:mn> </e:msub> </e:math> <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>Ni</g:mi> </g:math> <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msub> <i:mi/> <i:mn>25</i:mn> </i:msub> </i:math> ( <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mi>Hf</k:mi> </k:math> <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>Ti</m:mi> </m:math> <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mi>Zr</o:mi> </o:math> ) <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:msub> <q:mi/> <q:mn>50</q:mn> </q:msub> </q:math> ) and lithium-intercalated metal-organic frameworks. Our results demonstrate the feasibility of scalable quantum assisted materials modeling and introduce a resource-efficient route toward quantum machine learning for atomistic simulations.