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 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.
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.
The accurate treatment of electron correlation in extended molecular systems remains computationally challenging using classical electronic structure methods. Hybrid quantum-classical algorithms offer a potential route to overcome these limitations; however, their practical deployment on existing quantum computers requires strategies that both reduce problem size and mitigate hardware noise. In this work, we investigate ground-state energy calculations of ligand-like molecules using Sample-based Quantum Diagonalization (SQD) within the Density Matrix Embedding Theory (DMET) framework, focusing on low-symmetry systems with diverse bonding motifs that exhibit subsystem-dependent variations in fragment-environment entanglement. These entanglement-based variations directly influence bath orbital construction, impurity sizes, and the structure of the embedded Hamiltonians, posing nontrivial challenges for both embedding and quantum sampling. By combining DMET fragmentation with SQD-based construction of reduced configuration spaces through quantum sampling and iterative configuration recovery, we perform quantum simulations on IBM's Eagle R3 (IBM Sherbrooke) and IBM's Heron R3 (IBM Boston) superconducting quantum hardware thereby, showing that the entanglement structure across embedding subsystems plays a central role in determining the efficiency and accuracy of the simulations. Despite these complexities, we show that the DMET-SQD framework yields ground-state energies in strong agreement with DMET-FCI benchmarks, achieving chemical accuracy (1 kcal/mol) across all systems studied. These results demonstrate that SQD-based quantum simulations can be robustly extended to low-symmetry, chemically realistic, industry relevant molecules, and highlight the importance of entanglement-aware embedding strategies for scalable quantum electronic structure calculations.
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.
Scientific simulations demand methods combining scalability with predictive accuracy. Density Functional Theory (DFT) on High-Performance Computing (HPC) enables large-scale electronic-structure simulations but is limited by approximations affecting strongly correlated systems and band-gap predictions. Quantum computing offers a pathway to address this, though current Noisy Intermediate-Scale Quantum (NISQ) hardware remains constrained by qubit resources, noise, and execution cost.
This work presents a hybrid DFT-Quantum Embedding (QDFT) framework integrating classical HPC-based DFT with a quantum electronic-structure solver. Large systems are partitioned to isolate a chemically relevant active space, treated via the Variational Quantum Eigensolver (VQE), while the remaining degrees of freedom are described by DFT. The framework incorporates active-space selection, embedded Hamiltonian construction, symmetry preservation, operator mapping, self-consistent density updating, and modular classical-quantum coupling.
We focus on noiseless quantum simulation to systematically evaluate accuracy, convergence, active-space dependence, computational cost, and HPC scalability without hardware noise. Detailed profiling identifies computational bottlenecks and highlights limitations of CPU-based quantum simulation. A QPU runtime-estimation methodology is additionally developed to assess execution requirements on actual quantum hardware.
Results demonstrate quantum embedding's potential to improve selected electronic-structure properties while retaining classical HPC's scalability. Noisy quantum simulation and QPU execution remain key future directions, providing a pathway toward practical, scalable HPC-quantum hybrid simulations as hardware matures.
Variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for noisy intermediate-scale quantum (NISQ) computers. It is promising for quantum chemical calculations (QCC) because it can calculate the ground-state energy of a target molecule. Although VQE has a potential to achieve a higher accuracy than classical approximation methods in QCC, it is challenging to achieve it on current NISQ computers due to the significant impact of noises. Density matrix embedding theory (DMET) is a well-known technique to divide a molecule into multiple fragments, which is available to mitigate the noise impact on VQE. However, our preliminary evaluation shows that the naive combination of DMET and VQE does not outperform a gold standard classical method. In this work, we present three approaches to mitigate the noise impact for the DMET+VQE combination. (1) The size of quantum circuits used by VQE is decreased by reducing the number of bath orbitals which represent interactions between multiple fragments in DMET. (2) Reduced density matrices (RDMs), which are used to calculate a molecular energy in DMET, are calculated accurately based on expectation values obtained by executing quantum circuits using a noise-less quantum computer simulator. (3) The parameters of a quantum circuit optimized by VQE are refined with mathematical post-processing. The evaluation using a noisy quantum computer simulator shows that our approaches significantly improve the accuracy of the DMET+VQE combination. Moreover, we demonstrate that on a real NISQ device, the DMET+VQE combination applying our three approaches achieves a higher accuracy than the gold standard classical method.