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Chemistry Letters

Concurrent processing of VQE-UCCSD calculations with the FMO scheme

Hideo Doi, Kenji Sugisaki, Tatsuya Nakano, Takahiro Katagiri, Yuji Mochizuki

Published Jul 22, 2025• 1 citation
Publisher

Abstract

Abstract The fragmentation-based method has attracted interest as a way to reduce the computational cost of quantum chemical computations. Using the variational quantum eigensolver (VQE) of unitary coupled cluster singles and doubles (UCCSD), concurrent processing was used alongside the fragment molecular orbital scheme for the Li(I)–(H₂)n (n = 4 and 6) clusters on a supercomputer with a graphical processing unit (GPU)-accelerated quantum simulator. Energy and timing data of VQE-UCCSD are presented to highlight issues in practical applications.

DOI
10.1093/chemle/upaf145

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Abstract The fragmentation-based method has attracted interest as a way to reduce the computational cost of quantum chemical computations. Using the variational quantum eigensolver (VQE) of unitary coupled cluster singles and doubles (UCCSD), concurrent processing was used alongside the fragment molecular orbital scheme for the Li(I)–(H₂)n (n = 4 and 6) clusters on a supercomputer with a graphical processing unit (GPU)-accelerated quantum simulator. Energy and timing data of VQE-UCCSD are presented to highlight issues in practical applications.
Abstract The fragment molecular orbital (FMO) scheme is one of the popular fragmentation‐based methods and has the potential advantage of making the circuit shallow for quantum chemical calculations on quantum computers. In this study, we used a GPU‐accelerated quantum simulator (cuQuantum) to perform the electron correlation part of the FMO calculation as unitary coupled‐cluster singles and doubles (UCCSD) with the variational quantum eigensolver (VQE) for hydrogen‐bonded (FH) and (FH)‐HO systems with the STO‐3G basis set. VQE‐UCCSD calculations were performed using both canonical and localized MO sets, and the results were examined from the point of view of size‐consistency and orbital‐invariance affected by the Trotter error. It was found that the use of localized MO leads to better results, especially for (FH)‐HO. The GPU acceleration was substantial for the simulations with larger numbers of qubits, and was about a factor of 6.7–7.7 for 18 qubit systems.
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 [Formula: see text] system using the STO-3G basis set, and an error of 1.376 mHa with 16 qubits in a [Formula: see text] 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.
In this study, the variational quantum eigensolver (VQE) on a quantum simulator is used in calculating ground state electronic structure properties of the LiHn, n = 1–3, complexes including their singly charged ions. Results calculated using classical electronic structure algorithms are also included. We investigate the use of the unitary coupled cluster with singles and doubles (UCCSD) Ansatz using VQE within Qiskit and compare results to full configuration interaction (FCI) calculations. Computed ground state energies, electron affinities, ionization potentials, and dipole moments are considered. We report the first-of-its-kind simulated quantum computing results of selected LiHn species and use the parity orbital to qubit mapping scheme. We find that VQE/UCCSD results are comparable to classical coupled clusters with singles and doubles for all considered systems with respect to FCI. A VQE calculation cost evaluation is included in which we evaluate performance using both Jordan–Wigner and parity orbital to qubit mapping schemes. We also discuss some of the current limitations of utilizing VQE for the study of chemical systems.
The Variational Quantum Eigensolver (VQE) is a quantum algorithm for estimating ground-state energies, with promising applications in material science, drug discovery, and battery research. A key challenge is the limited number of qubits available on current quantum devices, which restricts the size of molecular systems that can be studied. To address this limitation, we apply the Fragment Molecular Orbital (FMO) method in combination with VQE, referred to as FMO-VQE. This approach divides a system into smaller fragments, making the quantum calculations more tractable. While earlier studies demonstrated this method only for hydrogen clusters, we extend the application to lithium cobalt oxide, a widely used cathode material in lithium-ion batteries. Using FMO-VQE, we estimate the ground-state energy of this complex system while reducing the number of required qubits from 24 to 14, without significant loss of accuracy compared to classical methods. This reduction highlights the potential of FMO-VQE to overcome hardware limitations and make quantum simulations of larger molecules feasible. The results suggest a practical path for applying near-term quantum computers to real-world challenges, opening opportunities for advancements in the battery industry and drug design.
Abstract Variational quantum eigensolver (VQE) for electronic structure calculations is believed to be one major potential application of near term quantum computing. Among all proposed VQE algorithms, the unitary coupled cluster singles and doubles excitations (UCCSD) VQE ansatz has achieved high accuracy and received a lot of research interest. However, the UCCSD VQE based on fermionic excitations needs extra terms for the parity when using Jordan–Wigner transformation. Here we introduce a new VQE ansatz based on the particle preserving exchange gate to achieve qubit excitations. The proposed VQE ansatz has gate complexity up-bounded to O ( n 4 ) for all-to-all connectivity where n is the number of qubits of the Hamiltonian. Numerical results of simple molecular systems such as BeH 2 , H 2 O, N 2 , H 4 and H 6 using the proposed VQE ansatz gives very accurate results within errors about 10 −3 Hartree.