Molecular ground-state energies help determine conformer rankings, reaction energetics, and electronic effects in computational drug discovery, but accurate calculations become difficult when strong correlation or large active spaces are important. Variational quantum eigensolvers estimate these energies by optimizing a parameterized quantum state, making ansatz design central to both accuracy and cost. We study a fixed-topology Givens-exchange ansatz that avoids architecture search. The circuit starts from the computational-basis state with the lowest diagonal Hamiltonian expectation and applies local RY rotations with two ordered all-pair Givens exchange blocks. Parameters are optimized using Hamiltonian expectation values, while exact diagonalization is used only after optimization to compute errors and fidelities. Across six fixed seeds, coefficient-verified LiH-6 and H2O-8 Hamiltonians, together with a BeH2-6 public-specification candidate, are chemically accurate in every run. The corresponding six-seed mean errors are 0.000000124 Hartree, equivalent to 0.000124 milli-Hartree; 0.000128558 Hartree, equivalent to 0.128558 milli-Hartree; and 0.000002152 Hartree, equivalent to 0.002152 milli-Hartree, respectively. On LiH-6 and H2O-8, these mean errors are lower than the published point errors of the compared quantum-architecture-search methods, while the ansatz uses a larger pre-compilation macro budget. The method is therefore an accurate, reproducible, and search-free reference template for molecular variational eigensolvers.
Molecular ground-state energies help determine conformer rankings, reaction energetics, and electronic effects in computational drug discovery, but accurate calculations become difficult when strong correlation or large active spaces are important. Variational quantum eigensolvers estimate these energies by optimizing a parameterized quantum state, making ansatz design central to both accuracy and cost. We study a fixed-topology Givens-exchange ansatz that avoids architecture search. The circuit starts from the computational-basis state with the lowest diagonal Hamiltonian expectation and applies local RY rotations with two ordered all-pair Givens exchange blocks. Parameters are optimized using Hamiltonian expectation values, while exact diagonalization is used only after optimization to compute errors and fidelities. Across six fixed seeds, coefficient-verified LiH-6 and H2O-8 Hamiltonians, together with a BeH2-6 public-specification candidate, are chemically accurate in every run. The corresponding six-seed mean errors are 0.000000124 Hartree, equivalent to 0.000124 milli-Hartree; 0.000128558 Hartree, equivalent to 0.128558 milli-Hartree; and 0.000002152 Hartree, equivalent to 0.002152 milli-Hartree, respectively. On LiH-6 and H2O-8, these mean errors are lower than the published point errors of the compared quantum-architecture-search methods, while the ansatz uses a larger pre-compilation macro budget. The method is therefore an accurate, reproducible, and search-free reference template for molecular variational eigensolvers.
In recent years, the Variational Quantum Eigensolver (VQE) has emerged as one of the most popular algorithms for solving the electronic structure problem on near-term quantum computers. The utility of VQE is often hindered by the limitations of current quantum hardware, including, but not limited to, short qubit coherence times and low gate fidelities. These limitations become particularly pronounced when VQE is used along with deep quantum circuits, such as those required by the ”Unitary Coupled Cluster Singles and Doubles” (UCCSD) ansatz, often resulting in significant errors. To address these issues, we propose a low-depth ansatz based on parallelized Givens rotations, which can recover substantial correlation energy while drastically reducing circuit depth and two-qubit gate counts for an arbitrary active space (AS). Also, considering the current hardware architectures with low qubit counts, we introduce a systematic way to select molecular orbitals to define active spaces (ASs) that retain significant electron correlation. We validate our approach by computing bond dissociation profiles of water and strongly correlated systems, such as molecular nitrogen and oxygen, across various ASs. Noiseless simulations using the new ansatz yield ground-state energies comparable to those from the UCCSD ansatz while reducing circuit depth by 50–70%. Moreover, in noisy simulations, our approach achieves energy error rates an order of magnitude lower than that of UCCSD. Considering the efficiency and practical usage of our ansatz, we hope that it becomes a potential choice for performing quantum chemistry calculations on near-term quantum devices.
Variational quantum eigensolver ansätze hold considerable promise for ground-state energy calculations on near-term quantum hardware, yet most promising ansatz designs currently strongly depend on how well the molecular orbital basis captures the electronic correlation of the system. Computing optimized orbital coefficients via classical routines is computationally expensive and must be performed independently for each molecular geometry -- a bottleneck that limits scalability across chemical space. We present a graph neural network framework that predicts optimized orbital coefficients directly from molecular geometry and pair-wise bonding structure. Trained on hydrogenic systems of modest size (H4 and H6) across tens of thousands of geometries, our model transfers to larger, unseen systems (H8, H10 and H12) without retraining -- demonstrating strong out-of-distribution generalization with respect to system size. When evaluating on structured and random configurations, and comparing against energies obtained with full classical optimization, our model reaches mean absolute energy errors O(102) and O(10) milli-Hartrees, respectively. Beyond energy estimation, the predicted orbitals serve as high-quality warm-start initializations that substantially reduce optimizer iterations to ground-state energy convergence. These results establish graph neural networks as an effective and scalable strategy for accelerating orbital optimization in hybrid quantum-classical workflows, directly reducing the classical pre-processing overhead that currently limits the practical deployment of variational quantum eigensolver on near-term quantum hardware.
Ground state preparation is a central application of quantum algorithms for electronic structure. We introduce the classical reservoir approach, a low cost variational ansatz tailored to near-term hardware, requiring only nearest-neighbor interactions on a machine with square-lattice connectivity. Unlike traditional methods built from the classically efficient Hartree Fock theory, our ansatz operates in localized molecular orbitals to study previously unexplored regions of the variational parameter space. Numerical benchmarks demonstrate chemical accuracy across diverse systems and bond lengths; notably, significantly reduced circuit depths are attainable when relaxed error thresholds (e.g., tens of E_h) are permissible. We benchmark the method on hydrogen chains, N_2, O_2, CO, BeH_2, and H_2O, the latter corresponding to an effective 24 qubit calculation.
Abstract We present a comprehensive quantum chemical study of nine molecules H₂, HeH⁺, LiH, BeH₂, H₂O, NH₃, CH₄, CO₂, and N₂ using the Variational Quantum Eigensolver (VQE) algorithm implemented in Qiskit 2.4.1. Molecular Hamiltonians are constructed in the STO-3G minimal basis set, transformed to qubit operators via the Jordan-Wigner mapping, and optimized using the n-local hardware-efficient ansatz with the SLSQP optimizer. Ground state energies are benchmarked against Full Configuration Interaction (FCI)/STO-3G reference values from authoritative literature sources. VQE achieves accuracies from 96.46% (HeH⁺) to 99.99% (H₂), average 98.68%. Potential energy surfaces are generated for all nine molecules and compared with high level ab initio literature PES references including the Kolos-Wolniewicz H₂ curve, the Polyansky water surface, and the Bytautas-Ruedenberg N₂ FCI surface. Equilibrium bond lengths agree with experiment to within 0.000–0.006 Å. Quantum ansatz circuits are analyzed in detail for all molecules. These results confirm the viability of near-term VQE algorithms for molecular quantum chemistry across diverse bond types and geometries.
Accurate prediction of binding energies between drug candidates and target molecules is essential in computational drug discovery, as stronger (more negative) binding energies suggest higher efficacy. This energy corresponds to the ground state of the molecular system and can be computed using methods such as Full Configuration Interaction (FCI), Hartree-Fock (HF), Variational Quantum Eigensolver (VQE), and Quantum Phase Estimation (QPE). While FCI offers benchmark accuracy, its computational cost renders it impractical for larger systems. HF scales efficiently but at the expense of precision. QPE, though theoretically robust, is currently constrained by hardware limitations. VQE emerges as a practical alternative for Noisy Intermediate-Scale Quantum (NISQ) devices, balancing accuracy and feasibility. Nevertheless, quantum noise significantly affects VQE performance. To address this, we incorporate Zero Noise Extrapolation (ZNE) to mitigate errors and improve energy estimates. This study compares these approaches and demonstrates the efficacy of the VQEZNE framework in generating reliable binding energy calculations for drug design applications.
Abstract The variational quantum Eigensolver (VQE) provides a scalable route to molecular ground-state energies on near-term quantum hardware, but its accuracy degrades rapidly as system size grows because hardware-efficient ansätze cannot span the full correlation subspace. We introduce a physics-informed ridge regression correction that is trained on the difference between VQE and Hartree–Fock (HF) energies and applied as a postprocessing step requiring no additional quantum resources. The feature set─the VQE–HF energy gap ΔE, its square ΔE2, the active-space qubit count, the number of active electrons, and two cross-term interactions─captures the dominant drivers of ansatz error in a low-dimensional, interpretable form. The model is benchmarked on H2, H2O, NH3, CH4, C2H6, and CH3OH using the STO-3G basis set and a state vector VQE simulator using a two-layer Ry-CNOT hardware-efficient ansatz. To assess cross-molecule generalizability, the corrected framework is further tested on CO2, N2, and HCN under both untrained and trained conditions. Absolute energy errors fall from a range of 0.02–0.79 Ha (raw VQE) to 0.0007–0.094 Ha after correction, corresponding to improvement factors of 3× to 640× relative to CASCI reference values. Zero-shot generalization tests yield factors of 9–58×, and including molecules in training improves results by a further order of magnitude in several cases. The three extended molecules exhibit improvement factors of 4–6× in untrained settings and 5–6× after training, providing preliminary evidence of transferability across chemically distinct systems. These findings suggest that the VQE–HF energy gap encodes physically transferable information about correlation-energy saturation, and that even the smallest training set can produce practically useful corrections for near-term quantum chemistry.