In the field of quantum chemistry, the variational quantum eigensolver (VQE) has emerged as a highly promising approach to determine molecular energies and properties within the noisy intermediate-scale quantum (NISQ) era. The central challenges of this approach lie in the design of an expressive ansatz capable of representing the exact ground state wavefunction while concurrently being efficient to avoid numerical instabilities during the classical optimization. Owing to the constraints of current quantum hardware, the ansatz must remain sufficiently compact while retaining the flexibility to capture essential correlation effects. To address these challenges, we propose a systematic dynamic ansatz construction strategy in which the dominant operator blocks are initially identified through commutativity screening, combined with an energy sorting criteria. Subsequently, the ansatz is progressively expanded in a stepwise manner via iterative operator block reordering. To minimize the overhead, the higher order correlation terms are incorporated via reduced lower-body tensor factorization in each operator block, while the adaptive construction strategy ensures that the optimization is guided along the optimal trajectory to mitigate potential numerical instabilities due to the presence of local traps. Benchmark applications to various molecular systems demonstrate that this strategy of progressive operator-block addition achieves accurate energetics with significantly fewer parameters while efficiently bypassing local traps. Moreover, in strongly correlated regions, such as bond dissociation, the method successfully reproduces the ground state, where other contemporary approaches often fail.
In the field of quantum chemistry, the variational quantum eigensolver (VQE) has emerged as a highly promising approach to determine molecular energies and properties within the noisy intermediate-scale quantum (NISQ) era. The central challenges of this approach lie in the design of an expressive ansatz capable of representing the exact ground state wavefunction while concurrently being efficient to avoid numerical instabilities during the classical optimization. Owing to the constraints of current quantum hardware, the ansatz must remain sufficiently compact while retaining the flexibility to capture essential correlation effects. To address these challenges, we propose a systematic dynamic ansatz construction strategy in which the dominant operator blocks are initially identified through commutativity screening, combined with an energy sorting criteria. Subsequently, the ansatz is progressively expanded in a stepwise manner via iterative operator block reordering. To minimize the overhead, the higher order correlation terms are incorporated via reduced lower-body tensor factorization in each operator block, while the adaptive construction strategy ensures that the optimization is guided along the optimal trajectory to mitigate potential numerical instabilities due to the presence of local traps. Benchmark applications to various molecular systems demonstrate that this strategy of progressive operator-block addition achieves accurate energetics with significantly fewer parameters while efficiently bypassing local traps. Moreover, in strongly correlated regions, such as bond dissociation, the method successfully reproduces the ground state, where other contemporary approaches often fail.
In the field of quantum chemistry, the variational quantum eigensolver (VQE) has emerged as a highly promising approach to determine molecular energies and properties within the noisy intermediate-scale quantum (NISQ) era. The central challenges of this approach lie in the design of an expressive Ansatz capable of representing the exact ground state wavefunction while concurrently being efficient to avoid numerical instabilities during the classical optimization. Owing to the constraints of current quantum hardware, the Ansatz must remain sufficiently compact while retaining the flexibility to capture essential correlation effects. To address these challenges, we propose a systematic dynamic Ansatz construction strategy in which the dominant operator blocks are initially identified through commutativity screening, combined with an energy sorting criterion. Subsequently, the Ansatz is progressively expanded in a stepwise manner via iterative operator block reordering. To minimize the overhead, the higher order correlation terms are incorporated via reduced lower-body tensor factorization in each operator block, while the adaptive construction strategy ensures that the optimization is guided along the optimal trajectory to mitigate potential numerical instabilities due to the presence of local traps. Benchmark applications to various molecular systems demonstrate that this strategy of progressive operator-block addition achieves accurate energetics with significantly fewer parameters while efficiently bypassing local traps. Moreover, in strongly correlated regions, such as bond dissociation, the method successfully reproduces the ground state, where other contemporary approaches often fail.
Determining the exponentially scaled ground state wavefunction and the associated molecular properties remains one of the central challenges in quantum chemistry. Hybrid quantum-classical algorithms implemented on quantum computers offer a promising route toward addressing this problem. However, despite several successful demonstrations on small molecular systems, accurate simulations of large and chemically realistic molecules remain difficult due to the limited capability of noisy intermediate scale quantum (NISQ) hardware. To bypass the limitations of NISQ devices, while simultaneously retaining the accuracy of the ground state energy estimations, we propose a dynamic ansatz construction strategy based on operator commutativity and energy driven screening within density matrix embedding theory (DMET) framework. The partitioning of the full system allows us to dynamically construct the ansatz over individual embedded subsystems, allowing each embedding problem be solved individually to a desired accuracy. The embedding Hamiltonian is updated in a self-consistent manner with dynamically formulated wavefunction, and their coupled optimization leads to accurate and efficient description of the overall system. To assess the performance of this approach, we apply it to several molecular systems and chemical processes with up to 144 qubits. These simulations require at most 20 qubits at a time and demonstrate improved accuracy and significantly reduced quantum gate requirements compared with conventional ansatze. We further investigate the impact of various fragmentation strategies and demonstrate the adaptability of our approach at each step of the DMET self-consistency cycle that leads to significantly improved accuracy for strongly correlated system.
Determining the exponentially scaled ground state wavefunction and the associated molecular properties remains one of the central challenges in quantum chemistry. Hybrid quantum-classical algorithms implemented on quantum computers offer a promising route toward addressing this problem. However, despite several successful demonstrations on small molecular systems, accurate simulations of large and chemically realistic molecules remain difficult due to the limited capability of noisy intermediate-scale quantum (NISQ) hardware. To bypass the limitations of NISQ devices, while simultaneously retaining the accuracy of the ground state energy estimations, we propose a dynamic ansatz construction strategy based on operator commutativity and energy driven screening within the density matrix embedding theory (DMET) framework. The partitioning of the full system allows us to dynamically construct the ansatz over individual embedded subsystems, allowing each embedding problem to be solved individually to a desired accuracy. The embedding Hamiltonian is updated in a self-consistent manner with the dynamically formulated wavefunction, and their coupled optimization leads to an accurate and efficient description of the overall system. To assess the performance of this approach, we apply it to several molecular systems, including C10 (100 qubits), conformers of l-glucose (144 qubits), and the reactant, intermediate, and product structures of the methyl vinyl ketone and cyclopentadiene Diels-Alder reaction (124 qubits). These simulations require at most 20 qubits at a time and demonstrate improved accuracy and significantly reduced quantum gate requirements compared with conventional ansatze. We further investigate the impact of various fragmentation strategies and demonstrate the adaptability of our approach at each step of the DMET self-consistency cycle that leads to significantly improved accuracy for strongly correlated systems. These results highlight the emerging feasibility of addressing large-scale chemical problems of industrial relevance on near-term quantum devices.
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.
Recent advancements in quantum information and quantum technology have stimulated a good deal of interest in the development of quantum algorithms toward the determination of the energetics and properties of many-fermionic systems. While the variational quantum eigensolver is the most optimal algorithm in the noisy intermediate scale quantum era, it is imperative to develop compact Ansätze with low-depth quantum circuits that are physically realizable in quantum devices. Within the unitary coupled cluster framework, we develop a disentangled Ansatz construction protocol that can dynamically tailor an optimal Ansatz using the one- and two-body cluster operators and a selection of rank-two scatterers. The construction of the Ansatz may potentially be performed in parallel over multiple quantum processors through energy sorting and operator commutativity prescreening. With a significant reduction in the circuit depth toward the simulation of molecular strong correlation, our dynamic Ansatz construction protocol is shown to be highly accurate and resilient to the noisy circumstances of the near-term quantum hardware.
Designing compact ansätze in Variational Quantum Eigensolver (VQE) is crucial for solving energetic problems of practical molecules on near-term quantum devices. However, existing Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT) ansätze face two challenges: improper operator selection and accumulation of degraded operators. In this paper, we propose the Hamiltonian-Aware (HA) ADAPT-VQE algorithm to address these issues. First, we establish a novel excitation operator selection criterion. It breaks the local constraint of existing criteria by incorporating Hamiltonian information, prioritizes physically meaningful excitation operators, and incurs no extra classical or quantum computational overhead. Furthermore, we develop a problem-adaptive method for discriminating and pruning redundant excitation operators stemming from improper selection and inevitable degradation. This method balances redundant operator pruning and convergence guarantee, and is applicable to ansätze with arbitrary scales. Systematic numerical experiments on typical strongly correlated molecular systems demonstrate that our HA-ADAPT-VQE avoids energy plateaus and outperforms baseline algorithms in terms of energy error, ansatz size, and measurement cost. This work offers an efficient, robust ansatz construction paradigm, facilitating the development and practical deployment of large-scale VQE in quantum chemistry.