Solving molecular energy levels via the Variational Quantum Eigensolver (VQE) algorithm represents one of the most promising applications for demonstrating practically meaningful quantum advantage in the noisy intermediate-scale quantum (NISQ) era. To strike a balance between ansatz complexity and computational stability in VQE calculations, we propose the HiUCCSD, a novel symmetry-respecting ansatz engineered from the intrinsic information of the Hamiltonian. We theoretically prove the effectiveness of HiUCCSD within the scope of Abelian point groups. Furthermore, we compare the performance of HiUCCSD and the established SymUCCSD via VQE and Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT)-VQE numerical experiments on ten molecules with distinct point groups. The results show that HiUCCSD achieves equivalent performance to SymUCCSD for Abelian point group molecules, while avoiding the potential performance failure of SymUCCSD in the case of non-Abelian point group molecules. Across the studied molecular systems, HiUCCSD cuts the parameter count by 18%-83% for VQE and reduces the excitation operator pool size by 27%-84% for ADAPT-VQE, as compared with the UCCSD ansatz. With enhanced robustness and broader applicability, HiUCCSD offers a new ansatz option for advancing large-scale molecular VQE implementation.
Solving molecular energy levels via the Variational Quantum Eigensolver (VQE) algorithm represents one of the most promising applications for demonstrating practically meaningful quantum advantage in the noisy intermediate-scale quantum (NISQ) era. To strike a balance between ansatz complexity and computational stability in VQE calculations, we propose the HiUCCSD, a novel symmetry-respecting ansatz engineered from the intrinsic information of the Hamiltonian. We theoretically prove the effectiveness of HiUCCSD within the scope of Abelian point groups. Furthermore, we compare the performance of HiUCCSD and the established SymUCCSD via VQE and Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT)-VQE numerical experiments on ten molecules with distinct point groups. The results show that HiUCCSD achieves equivalent performance to SymUCCSD for Abelian point group molecules, while avoiding the potential performance failure of SymUCCSD in the case of non-Abelian point group molecules. Across the studied molecular systems, HiUCCSD cuts the parameter count by 18%-83% for VQE and reduces the excitation operator pool size by 27%-84% for ADAPT-VQE, as compared with the UCCSD ansatz. With enhanced robustness and broader applicability, HiUCCSD offers a new ansatz option for advancing large-scale molecular VQE implementation.
Point group symmetry has been exploited for designing compact ansätze in the Variational Quantum Eigensolver (VQE), thereby facilitating the computation of molecular energy levels on current Noisy Intermediate-Scale Quantum (NISQ) devices. However, the widely used Symmetry-reduced Unitary Coupled Cluster Singles and Doubles (SymUCCSD) is restricted to molecules with Abelian point groups and often yields deficient ansätze for non-Abelian molecular systems. In this paper, we propose Hamiltonian-informed UCCSD (HiUCCSD), a novel shallow ansatz engineered based on the intrinsic information encoded in the molecular Hamiltonian. We theoretically prove the effectiveness of HiUCCSD for molecules belonging to Abelian point groups. Furthermore, numerical results for 10 molecular systems with distinct symmetries demonstrate that HiUCCSD may also be applicable to non-Abelian point group systems. Compared with the standard UCCSD ansatz, HiUCCSD reduces the parameter count and circuit size of VQE by 18-83% and 26-83%, respectively, and shrinks the size of the excitation operator pool for Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT)-VQE by 27-84% across the studied molecules. Given its superior performance and broad applicability, we expect that HiUCCSD will facilitate the realization of large-scale molecular VQE implementations.
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.
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.
Calculations of molecular spectral properties, like photodissociation rates and absorption bands, rely on knowledge of the excited state energies of the molecule of interest. Protocols based on the variational quantum eigensolver (VQE) are promising candidates to calculate such energies on emerging noisy intermediate-scale quantum (NISQ) computers. The successful implementation of these protocols on NISQ computers, relies on ans\"atze that can accurately approximate the molecular states and that can be implemented by shallow quantum circuits. We introduce the excited qubit-excitation-based adaptive (e-QEB-ADAPT)-VQE protocol to calculate molecular-excited-state energies. The e-QEB-ADAPT-VQE constructs efficient problem-tailored ans\"atze by iteratively appending evolutions of qubit excitation operators. The e-QEB-ADAPT-VQE also improves on previous ADAPT-VQE protocol in that it is designed to be independent on the choice of initial reference state. We perform classical numerical simulations for LiH and BeH2 to benchmark the performance of the e-QEB-ADAPT-VQE. We demonstrate that the e-QEB-ADAPT-VQE can construct highly accurate ans\"atze that require at least an order of magnitude fewer cnot gates than standard fixed unitary coupled-cluster ans\"atze, such as the UCCSD and the GUCCSD. We also show that the e-QEB-ADAPT-VQE is more successful in constructing ans\"atze for excited molecular states than other ADAPT-VQE protocols.
The adaptive derivative-assembled pseudo-trotter variational quantum eigensolver (ADAPT-VQE) is a promising hybrid quantum-classical algorithm for molecular ground state energy calculation, yet its practical scalability is hampered by redundant excitation operators and excessive measurement costs. To address these challenges, we propose Param-ADAPT-VQE, a novel improved algorithm that selects excitation operators based on a parameter-based criterion instead of the traditional gradient-based metric. This strategy effectively eludes redundant operators. We further develop a sub-Hamiltonian technique and integrate a hot-start VQE optimization strategy, achieving a significant reduction in measurement costs. Numerical experiments on typical molecular systems demonstrate that Param-ADAPT-VQE outperforms the original ADAPT-VQE in computational accuracy, ansatz size, and measurement costs. Furthermore, our scheme retains the fundamental framework of ADAPT-VQE and is thus fully compatible with its various modified versions, enabling further performance improvements in specific aspects. This work presents an efficient and scalable enhancement to ADAPT-VQE, mitigating the core obstacles that impede its practical implementation in the field of molecular quantum chemistry.
Variational quantum eigensolvers (VQEs) are among the most promising quantum algorithms for solving electronic structure problems in quantum chemistry, particularly during the noisy intermediate-scale quantum (NISQ) era. In this study, we investigate the capabilities and limitations of VQE algorithms implemented on current quantum hardware for determining molecular ground-state energies, focusing on the adaptive derivative-assembled pseudo-Trotter ansatz VQE (ADAPT-VQE). To address the significant computational challenges posed by molecular Hamiltonians, we explore various well known strategies to simplify the Hamiltonian, optimize the ansatz, and improve classical parameter optimization through modifications of the COBYLA optimizer. These enhancements are integrated into a tailored quantum computing implementation designed to minimize the circuit depth and computational cost. Using benzene as a benchmark system, we demonstrate the application of these optimizations on an IBM quantum computer. Despite these improvements, our results highlight the limitations imposed by current quantum hardware, particularly the impact of quantum noise on state preparation and energy measurement. The noise levels in today's devices prevent meaningful evaluations of molecular Hamiltonians with sufficient accuracy to produce reliable quantum chemical insights. Finally, we extrapolate the requirements for future quantum hardware to enable practical and scalable quantum chemistry calculations using VQE algorithms. This work provides an assessment of current quantum algorithms for molecular modeling on real quantum hardware, highlighting the impact of noise and hardware limitations on the achievable accuracy.