Abstract Near-term quantum devices offer promising avenues for addressing the electronic structure problem in quantum chemistry, yet their limited qubits and susceptibility to noise constrain algorithmic scalability. Although the variational quantum eigensolver (VQE) has shown potential for small-scale systems, further improvements are necessary to handle large basis sets and large many-electron molecules efficiently. In this work, we introduce RO-VQE, an improved approach derived from the earlier optimized orbital algorithm that employs a randomized procedure for selecting and optimizing orbitals. We evaluate RO-VQE on hydrogen chains systems (H2 and H4)—a well-established benchmark for quantum chemistry methods—using minimal, split-valence, and correlation-consistent basis sets. For these systems, RO-VQE improves ground-state energy estimations compared to conventional VQE methods, matching the accuracy of systematic strategies in these test cases. These proof-of-concept results suggest that randomized active-space selection may offer a practical compromise in NISQ-era quantum computations, offering a flexible alternative to more deterministic methods, particularly for systems constrained by limited quantum resources.
Abstract Near-term quantum devices offer promising avenues for addressing the electronic structure problem in quantum chemistry, yet their limited qubits and susceptibility to noise constrain algorithmic scalability. Although the variational quantum eigensolver (VQE) has shown potential for small-scale systems, further improvements are necessary to handle large basis sets and large many-electron molecules efficiently. In this work, we introduce RO-VQE, an improved approach derived from the earlier optimized orbital algorithm that employs a randomized procedure for selecting and optimizing orbitals. We evaluate RO-VQE on hydrogen chains systems (H2 and H4)—a well-established benchmark for quantum chemistry methods—using minimal, split-valence, and correlation-consistent basis sets. For these systems, RO-VQE improves ground-state energy estimations compared to conventional VQE methods, matching the accuracy of systematic strategies in these test cases. These proof-of-concept results suggest that randomized active-space selection may offer a practical compromise in NISQ-era quantum computations, offering a flexible alternative to more deterministic methods, particularly for systems constrained by limited quantum resources.
The variational quantum eigensolver (VQE) has emerged as one of the leading quantum algorithms for solving electronic structure problems on near-term noisy intermediate-scale quantum devices. However, its practical application to quantum chemistry remains challenging due to the limited coherence time, imperfect quantum gate fidelity, and the large number of measurements required, which together confine current electronic structure simulations to relatively small active spaces. In this work, we present an orbital-optimized VQE framework based on orbital compression, designed to improve the accuracy of electronic structure calculations while maintaining relatively small active spaces. Frozen natural orbitals (FNO) and split virtual orbitals (SVO) are first employed to construct compact active spaces for VQE simulations, leading to the FNO/SVO-VQE approach. Orbital optimization is then incorporated to further recover electron correlation effects, resulting in the FNO/SVO-OO-VQE methods. We apply the proposed method to simulate potential energy surfaces for molecular dissociation and the activation energy of formaldehyde decomposition. Numerical results demonstrate that both FNO-OO-VQE and SVO-OO-VQE improve the variational accuracy while substantially reducing measurement cost.
ABSTRACT The variational quantum eigensolver (VQE) has emerged as one of the leading quantum algorithms for solving electronic structure problems on near‐term noisy intermediate‐scale quantum devices. However, its practical application to quantum chemistry remains challenging due to the limited coherence time, imperfect quantum gate fidelity, and the large number of measurements required, which together confine current electronic structure simulations to relatively small active spaces. In this work, we present a measurement‐reduced orbital‐optimized (OO) VQE framework based on orbital compression, designed to improve the accuracy of electronic structure calculations while maintaining relatively small active spaces. Frozen natural orbitals (FNO) and split virtual orbitals (SVO) are first employed to construct compact active spaces for VQE simulations, leading to the FNO/SVO‐VQE approach. Orbital optimization is then incorporated to further recover electron correlation effects, resulting in the FNO/SVO‐OO‐VQE methods. We apply the proposed method to simulate potential energy surfaces for molecular dissociation and the activation energy of formaldehyde decomposition. Numerical results demonstrate that both FNO‐OO‐VQE and SVO‐OO‐VQE improve the variational accuracy while substantially reducing measurement cost.
Near-term quantum computers will be limited in the number of qubits on which they can process information as well as the depth of the circuits that they can coherently carry out. To date, experimental demonstrations of algorithms such as the Variational Quantum Eigensolver (VQE) have been limited to small molecules using minimal basis sets for this reason. In this work we propose incorporating an orbital optimization scheme into quantum eigensolvers wherein a parametrized partial unitary transformation is applied to the basis functions set in order to reduce the number of qubits required for a given problem. The optimal transformation is found by minimizing the ground state energy with respect to this partial unitary matrix. Through numerical simulations of small molecules up to 16 spin orbitals, we demonstrate that this method has the ability to greatly extend the capabilities of near-term quantum computers with regard to the electronic structure problem. We find that VQE paired with orbital optimization consistently achieves lower ground state energies than traditional VQE when using the same number of qubits and even frequently achieves lower ground state energies than VQE methods using more qubits.
Abstract Variational quantum eigensolver (VQE) has emerged as a promising method for investigating ground state properties in quantum chemistry, materials science, and condensed matter physics. However, the conventional VQE method generally lacks systematic improvement and convergence guarantees, particularly when dealing with strongly correlated systems. In light of these challenges, we present a novel framework called orbital expansion VQE (OE-VQE) to address these limitations. The key idea is to devise an efficient convergence path by utilizing shallower quantum circuits, starting from a highly compact active space and gradually expanding it until convergence to the ground state is achieved. To validate the effectiveness of the OE-VQE framework, we conducted benchmark simulations on several small yet representative molecules, including the H 6 chain, H 10 ring and N 2 . The simulation results demonstrate that our proposed convergence paths significantly enhance the performance of conventional VQE. Overall, our work sheds valuable insight into the simulation of molecules based on shallow quantum circuits, offering a promising avenue for advancing the efficiency and accuracy of VQE approaches in tackling complex molecular 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.
The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for noisy intermediate-scale quantum (NISQ) hardware to estimate eigenvalues of many-body Hamiltonians. Unlike fully quantum approaches such as quantum phase estimation (QPE), VQE trades deep coherent circuits for repeated state preparation, measurement, and classical optimization, making it more compatible with limited qubit counts and finite coherence times. Recent developments have focused on reducing quantum resource requirements while retaining chemically meaningful wavefunction structure. In this paper, we examine recent progress in VQE methods for molecular electronic structure with an emphasis on three themes: (i) strategies for circuit and ansatz complexity reduction, including adaptive and selectively screened approaches, (ii) chemically motivated workflows that combine VQE with orbital optimization, fragmentation, and localized active-space ideas to better address strong correlation, and (iii) extensions of VQE to excited-state calculations. Throughout, we emphasize the tradeoffs among parameter count, gate depth, symmetry preservation, measurement overhead, and classical preprocessing, and discuss where these approaches may become most useful for chemically challenging active spaces. We also highlight benchmarking considerations for assessing both accuracy and resource requirements, and conclude with a perspective on regimes in which VQE may offer the greatest long-term value, particularly multireference active spaces and low-lying excited-state manifolds.