Abstract
Multivariate (MTV) porous materials exhibit unique structural complexities based on their diverse spatial arrangements of multiple building block combinations. These materials possess potential synergistic functionalities that exceed the sum of their individual components. However, the exponentially increasing design complexity of these materials poses significant challenges for accurate ground-state configuration prediction and design. To address this, we propose a Hamiltonian model for quantum computing that integrates compositional, structural, and balance constraints directly into the Hamiltonian, enabling efficient optimization of the MTV configurations. The model employs a graph-based representation to encode linker types as qubits. Our framework enables quantum encoding of a vast linker design space, allowing representation of exponentially many configurations with linearly scaling qubit resources, and facilitating efficient search for optimal structures based on predefined design variables. To validate our model, a variational quantum circuit was constructed and executed using the Sampling Variational Quantum Eigensolver (VQE) algorithm in the IBM Qiskit. Simulations on experimentally known MTV porous materials (e.g., Cu-THQ-HHTP, Py-MV-DBA-COF, MUF-7, and SIOC-COF2) successfully reproduced their ground-state configurations, demonstrating the validity of our model. Furthermore, VQE calculations were performed on a real IBM 127-qubit quantum hardware for validation purposes signaling a first step toward a practical quantum algorithm for the rational design of porous materials.