Fragment molecular orbital-based variational quantum eigensolver for quantum chemistry in the age of quantum computing

Quantum computers offer significant potential for complex system analysis, yet their application in large systems is hindered by limitations such as qubit availability and quantum hardware noise. While the variational quantum eigensolver (VQE) was proposed to address these issues, its scalability remains limited. Many efforts, including new ansätze and Hamiltonian modifications, have been made to overcome these challenges. In this work, we introduced the novel Fragment Molecular Orbital/Variational Quantum Eigensolver (FMO/VQE) algorithm. This method combines the fragment molecular orbital (FMO) approach with VQE and efficiently utilizes qubits for quantum chemistry simulations. Employing the UCCSD ansatz, the FMO/VQE achieved an absolute error of just 0.053 mHa with 8 qubits in a \({{\text{H}}}_{24}\) ${\text{H}}_{24}$ system using the STO-3G basis set, and an error of 1.376 mHa with 16 qubits in a \({{\text{H}}}_{20}\) ${\text{H}}_{20}$ system with the 6-31G basis set. These results indicated a significant advancement in scalability over conventional VQE, maintaining accuracy with fewer qubits. Therefore, our FMO/VQE method exemplifies how integrating fragment-based quantum chemistry with quantum algorithms can enhance scalability, facilitating more complex molecular simulations and aligning with quantum computing advancements.