In molecular variational quantum eigensolver (VQE) calculations for a fixed electron-number sector, the projected-sector energy alone does not certify that a prepared state is physically valid. We show that a state can have zero projected-sector error while almost all of its probability mass lies outside the target particle-number sector. We therefore evaluate ansatz families using three quantities: projected-sector error, leakage outside the physical sector and parameter count. Our noiseless experiments show that particle-preserving UCC-style families eliminate leakage induced by ansatze, but do not guarantee ground-state accuracy. In the parameter-budget comparison experiments, the one-shot ranking rules select identical generator sequences and yield identical errors. The adaptive hybrid procedure achieves lower mean projected-sector errors at selected budgets. Using established Kraus invariant-subspace criteria, we also express channel-induced leakage through a positive operator and discuss global and local depolarizing noise analytically. This gives a practical diagnostic framework for comparing ansatze beyond energy alone.
In molecular variational quantum eigensolver (VQE) calculations for a fixed electron-number sector, the projected-sector energy alone does not certify that a prepared state is physically valid. We show that a state can have zero projected-sector error while almost all of its probability mass lies outside the target particle-number sector. We therefore evaluate ansatz families using three quantities: projected-sector error, leakage outside the physical sector and parameter count. Our noiseless experiments show that particle-preserving UCC-style families eliminate leakage induced by ansatze, but do not guarantee ground-state accuracy. In the parameter-budget comparison experiments, the one-shot ranking rules select identical generator sequences and yield identical errors. The adaptive hybrid procedure achieves lower mean projected-sector errors at selected budgets. Using established Kraus invariant-subspace criteria, we also express channel-induced leakage through a positive operator and discuss global and local depolarizing noise analytically. This gives a practical diagnostic framework for comparing ansatze beyond energy alone.
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.
This is a case study of the variational quantum eigensolver (VQE) method using numerical simulations to test the influence of noise on the accuracy of the underlying circuit ansatz. We investigate a computational chemistry application of VQE to calculate the electronic ground state and its energy for Sodium Hydride (NaH), a prototypical two-electron problem. Using a one-parameter ansatz derived from unitary coupled cluster (UCC) theory, we simulate the effects of noise on the energy expectation value and variance with respect to the ansatz parameter. These numerical simulations provide insights into the accuracy of the prepared quantum state and the efficiency of the classical optimizer that iteratively refines the ansatz. We conduct a comparative study between analytical results derived for the UCC ansatz in the absence of noise and the noisy numerical simulation results obtained using an isotropic depolarizing noise model for each gate. We also compare the relative increase in noise on logically equivalent UCC ansatz circuits generated by randomized compiling. Notably, we observe that the intrinsic variance in the energy due to the simplicity of the ansatz itself compares with the noise induced by the bare circuit.
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.
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.
In recent years, the variational quantum eigensolver (VQE)[1] has carried the hope of the quantum computing community for achieving quantum utility. It aims to find the ground state and corresponding energy of a molecular hamiltonian by classically optimizing the parameters θj of a variational quantum circuit. In order to guarantee the conservation of qunatities such as particle number or spin, physically inspired ansätze such as the UCCSD ansatz are most promising. ExcitationSolve provides a quantum-aware optimizer for such physically inspired ansätze, making best use of prior knowlege about the operators used in the ansatz.
By design, the variational quantum eigensolver (VQE) strives to recover the lowest-energy eigenvalue of a given Hamiltonian by preparing quantum states guided by the variational principle. In practice, the prepared quantum state is indirectly assessed by the value of the associated energy. Novel adaptive derivative-assembled pseudo-trotter (ADAPT) ansatz approaches and recent formal advances now establish a clear connection between the theory of quantum chemistry and the quantum state ansatz used to solve the electronic structure problem. Here we benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves for a few selected diatomic molecules, namely H2, NaH, and KH. Using numerical simulation, we find both methods provide good estimates of the energy and ground state, but only ADAPT-VQE proves to be robust to particularities in optimization methods. Another relevant finding is that gradient-based optimization is overall more economical and delivers superior performance than analogous simulations carried out with gradient-free optimizers. The results also identify small errors in the prepared state fidelity which show an increasing trend with molecular size.