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

Hsu-Kai Cheng1,2, Po-Yu Yang2, Jyh-Pin Chou1, and Chun-Wei Pao2,3,4,*

  • *Contact author: cwpao@gate.sinica.edu.tw
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PRX Energy 5, 013004 – Published 22 January, 2026

DOI: https://doi.org/10.1103/j1lk-1cvs

Abstract

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 100 trainable parameters and achieve prediction errors below 0.05 eV/atom on chemically complex alloys (Co25Ni25(HfTiZr)50) 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.

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Machine learning accelerates the discovery of advanced energy materials, yet accurate models typically require thousands of parameters and vast training datasets. Furthermore, emerging quantum machine learning approaches often scale poorly, generally requiring hardware resources that grow with the material's size–often one qubit per atom–which exceeds current capabilities for practical systems. To overcome these limitations, the authors developed a compact hybrid framework that predicts the energy of complex materials using fewer than ten qubits, regardless of the system's size. By compressing local atomic environments into a fixed-size feature spectrum, the authors successfully modeled chemically complex high-entropy intermetallic alloys and lithium-ion battery materials with high accuracy using quantum circuits containing fewer than 100 parameters. This approach demonstrates a scalable, resource-efficient pathway for leveraging near-term quantum computers to design next-generation materials for sustainable energy applications.

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PRX Energy 5, 013004– Published 22 January, 2026
  • Received 9 June 2025
  • Revised 6 November 2025
  • Accepted 22 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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