Solving for molecular excited states remains one of the key challenges of modern quantum chemistry. Traditional methods are constrained by existing computational capabilities, limiting the complexity of the molecules that can be studied or the accuracy of the results that can be obtained. Several quantum computing methods have been suggested to address this limitation. However, these typically have hardware requirements which may not be achieved in the near term. We propose a variational quantum machine learning based method to determine molecular excited states aiming at being as resilient as possible to the defects of early Noisy Intermediate Scale Quantum (NISQ) computers and demonstrate an implementation for H2 on IBMQ. Our method uses a combination of two parametrized quantum circuits, working in tandem, combined with a Variational Quantum Eigensolver (VQE) to iteratively find the eigenstates of a molecular Hamiltonian.
Solving for molecular excited states remains one of the key challenges of modern quantum chemistry. Traditional methods are constrained by existing computational capabilities, limiting the complexity of the molecules that can be studied or the accuracy of the results that can be obtained. Several quantum computing methods have been suggested to address this limitation. However, these typically have hardware requirements which may not be achieved in the near term. We propose a variational quantum machine learning based method to determine molecular excited states aiming at being as resilient as possible to the defects of early Noisy Intermediate Scale Quantum (NISQ) computers and demonstrate an implementation for H2 on IBMQ. Our method uses a combination of two parametrized quantum circuits, working in tandem, combined with a Variational Quantum Eigensolver (VQE) to iteratively find the eigenstates of a molecular Hamiltonian.
Solving for molecular excited states remains one of the key challenges of modern quantum chemistry. Traditional methods are constrained by existing computational capabilities, limiting the complexity of the molecules that can be studied or the accuracy of the results that can be obtained. Several quantum computing methods have been suggested to address this limitation. However, these typically have hardware requirements which may not be achieved in the near term. We propose a variational quantum machine learning based method to determine molecular excited states aiming at being as resilient as possible to the defects of early noisy intermediate scale quantum computers and demonstrate an implementation for H2 on IBM Quantum Computers. Our method uses a combination of two parametrized quantum circuits, working in tandem, combined with a variational quantum eigensolver to iteratively find the eigenstates of a molecular Hamiltonian.
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 ansatze that can accurately approximate the molecular states and that can be implemented by shallow quantum circuits. In this paper, we introduce the ``excited iterative qubit-excitation-based variational quantum eigensolver'' (e-IQEB-VQE) protocol to calculate molecular excited state energies. The e-IQEB-VQE constructs efficient problem-tailored ansatze by iteratively appending evolutions of qubit excitation operators. The e-IQEB-VQE is an adaptation of the IQEB-VQE protocol, designed to be less dependent on the choice of an initial reference state. We perform classical numerical simulations for LiH and BeH2 to benchmark the performance of the IQEB-VQE. We demonstrate that the e-IQEB-VQE can construct highly accurate ansatze that require at least an order of magnitude fewer CNOTs than standard fixed UCC ansatze, such as the UCCSD and the GUCCSD.
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.
High Resolution Image Download MS PowerPoint Slide The recent developments of quantum computing present novel potential pathways for quantum chemistry as the scaling of the computational power of quantum computers could be harnessed to naturally encode and solve electronic structure problems. Theoretically exact quantum algorithms for chemistry have been proposed (e.g., quantum phase estimation), but the limited capabilities of current noisy intermediate-scale quantum devices motivated the development of less demanding hybrid algorithms. In this context, the variational quantum eigensolver (VQE) algorithm was successfully introduced as an effective method to compute the ground-state energies of small molecules. This study investigates the folded spectrum (FS) method as an extension of the VQE algorithm for the computation of molecular excited states. It provides the possibility of directly computing excited states around a selected target energy using the same or quantum circuit as for the ground-state calculation. Inspired by the variance-based methods from the quantum Monte Carlo literature, the FS method minimizes the energy variance, thus, in principle, requiring a computationally expensive squared Hamiltonian to be applied. We alleviate this potentially poor scaling by employing a Pauli grouping procedure to identify sets of commuting Pauli strings that can be evaluated simultaneously. This allows for a significant reduction in the computational cost. We applied the FS-VQE method to small molecules (H 2, LiH), obtaining all electronic excited states with chemical accuracy on ideal quantum simulators. Furthermore, we explore the application of quantum error mitigation techniques, demonstrating improved energy accuracy on noisy simulators compared with simulations without mitigation.
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.
Determining the spectral structure of molecular Hamiltonians is one of the most important and challenging research fields in quantum chemistry. In the near future, such a problem may be solvable by means of quantum simulation. However, constrained by a handful of qubits and noisy quantum gates available in the near-term quantum devices, hybrid quantum-classical algorithms based on variational methods such as variational quantum eigensolver have become a preferable choice. Here we propose an interesting variational quantum algorithm for obtaining the excited states of many-body Hamiltonians. To obtain the kth excited states, the previous variational quantum deflation algorithm requires the use of k different variational circuits, which is now reduced to only two circuits with our algorithm. The feasibility of the algorithm was numerically tested on the hydrogen molecule with and without random noise, where the chemical accuracy is reached for both cases. This algorithm is expected to significantly reduce the resource requirements of quantum simulation.