Exploiting the Variational Quantum Eigensolver for Determining Ground State Energy of Protocatechuic Acid
Gleydson Fernandes de Jesus, Erico S. Teixeira, Lucas Queiroz Galvão, Maria Heloísa Fraga da Silva, Mauro Q. Nooblath Neto, Fernandez, Bruno Oziel, Clebson Cruz
The Variational Quantum Eigensolver (VQE) is a promising hybrid algorithm, utilizing both quantum and classical computers to obtain the ground state energy of molecules. In this context, this study applies VQE to investigate the ground state of protocatechuic acid, analyzing its performance with various Ansätze and active spaces. Subsequently, all VQE results were compared to those obtained with the Hartree-Fock (HF) method. The results demonstrate that Ansätze, like unitary coupled-cluster singles and doubles (UCCSD) and variations of Hardware-Efficient, generally achieve accuracy close to that of HF. Furthermore, the increase in active space has led to the models becoming more difficult to converge to values with a greater distance from the correct energy. In summary, the findings of this study reinforce the use of VQE as a powerful tool for analyzing molecular ground state energies. Finally, the results underscore the critical importance of Ansatz selection and active space size in VQE performance, providing valuable insights into its potential and limitations.
The Variational Quantum Eigensolver (VQE) is a promising hybrid algorithm, utilizing both quantum and classical computers to obtain the ground state energy of molecules. In this context, this study applies VQE to investigate the ground state of protocatechuic acid, analyzing its performance with various Ansätze and active spaces. Subsequently, all VQE results were compared to those obtained with the Hartree-Fock (HF) method. The results demonstrate that Ansätze, like unitary coupled-cluster singles and doubles (UCCSD) and variations of Hardware-Efficient, generally achieve accuracy close to that of HF. Furthermore, the increase in active space has led to the models becoming more difficult to converge to values with a greater distance from the correct energy. In summary, the findings of this study reinforce the use of VQE as a powerful tool for analyzing molecular ground state energies. Finally, the results underscore the critical importance of Ansatz selection and active space size in VQE performance, providing valuable insights into its potential and limitations.
The Variational Quantum Eigensolver (VQE) is a hybrid algorithm that combines quantum and classical computing to determine the ground-state energy of molecular systems. In this context, this study applies VQE to investigate the ground state of protocatechuic acid, analyzing its performance with various Ansatzes and active spaces. Subsequently, all VQE results were compared to those obtained with the CISD and FCI methods. The results demonstrate that Ansatzes, like Unitary Coupled Cluster Singles and Doubles (UCCSD) and variations of Hardware-Efficient Ansatzes, generally achieve accuracy close to that of FCI. In conclusion, this study highlights the effectiveness of VQE as a robust method for investigating molecular ground-state energies. Additionally, the findings emphasize the pivotal role of Ansatz design and active space selection in optimizing VQE performance, offering meaningful insights into its capabilities and constraints.
Abstract Quantum computing is a technology that utilizes the principles of quantum mechanics to perform complex computational processes. In this work, we use Qiskit Module from IBM to do quantum computational calculation using Variational Quantum Eigensolver (VQE) algorithm. VQE is a hybrid quantum-classical method that combines a quantum computer to measure energies and a classical computer to process the measurement results and update the parameters of the quantum computer. The purpose of VQE is to find the ground state energy of a chemical system. In the previous study, many of the VQE calculations have been done on simple molecules. So, in this study, we would like to use Hydrazine molecule as our object of VQE calculation. Furthermore, these results will be compared with the results from the classical calculation (MP2, CCSD(T), QCISD(T), and CASSCF) methods for testing the effectiveness of VQE using Unitary Coupled-Cluster Single and Double excitations (UCCSD) Ansatz. The quantum algorithm based on the UCCSD Ansatz led to a simplification of the algorithm by reducing the circuit depth. Then, the possibility to use active space approximation, can be used to reduce the quantum gates while trying to keep a good level of accuracy. In this study, we chose (2,2) and (4,4) active spaces. Based on the results, as we increase the size of the active space during the evaluation of the single-point energy, the estimated ground states obtained from the VQE algorithm yield nearly identical values. Conversely, in CASSCF calculations, expanding the active space introduces more energy corrections, thus making it more sensitive. Additionally, when examining potential energy surfaces, VQE demonstrates results that gradually align with CCSD(T) and QCISD(T) methods.
Classical simulation of molecular electronic structure is often limited by the rapid increase in computational cost associated with describing electron correlation. The Variational Quantum Eigensolver (VQE) is one hybrid quantum-classical approach ideally adapted to the Noisy Intermediate-Scale Quantum (NISQ) regime. This work applies the VQE algorithm to compute ground state energies of a set of molecules:H2,H3+,LiH,HF,OH−,H2O,BH3,CH4, andNH3. The approach utilizes the Unitary Coupled Cluster for Single and Double excitations (UCCSD) ansatz along with the Bravyi-Kitaev transformation for fermionic-to-qubit encoding. Quantum simulation outputs are systematically benchmarked against Full Configuration Interaction (FCI), a numerically exact traditional approach, and Unrestricted Hartree-Fock (UHF). The results establish a robust consistency of the VQE-obtained molecular ground state energies against standard FCI and UHF benchmarks. This research provides a critical benchmark, confirming that VQE has the capability for high-precision molecular simulations and playing the role of a pivotal stepping stone toward revolutionizing applications in drug discovery and materials science.
While numerical simulations are presented in most papers introducing new methods to enhance the VQE performance, comprehensive, comparative, and applied studies remain relatively rare. We present a comprehensive, yet concise guide for the implementation of the VQE for molecular problems on NISQ devices, specifically applied to estimate the ground state energy of the BeH2 molecule using hardware-efficient and chemically informed ansätze. This work clarifies several under-documented aspects in the literature, such as the construction of the electronic Hamiltonian, the transformation of fermionic operators into qubit operators via second quantization, and the mathematical framework's details for the unitary coupled cluster single and double (UCCSD) ansatz. Our methodology, implemented using Qiskit 1.2, the latest release as of the date of this writing, is demonstrated on a noiseless simulator and further tested with noisy quantum circuits. The resilience of the VQE to quantum noise remains an open question. This study compares the computational accuracy of ground state energy estimations for molecules using the VQE across three different current quantum hardware noise models. Furthermore, our experiment on IBM's 156-qubit actual quantum computer revealed valuable insights on the real performance of the VQE on current quantum hardware.
Assessment of the variational quantum eigensolver (VQE) for bond dissociation of H2, H3+, and CH5+
Abstract Context The variational quantum eigensolver (VQE) is a quantum-classical algorithm for estimating molecular ground-state energies. However, the accuracy depends on the choice of ansatz , active space, and initial variational parameters. Hence, it is relevant to perform assessments of VQE. The dissociation profiles of H 2 2 , H 3+ 3 + , and CH 5+ 5 + were chosen for these assessments. For H 2 2 and H 3+ 3 + , the UCCSD, GateFabric, and k -UpCCGSD ansätze reproduced the dissociation profiles with high accuracy. For CH 5+ 5 + , GateFabric and k -UpCCGSD provided the best compromise between accuracy and scalability. Hardware-efficient ansätze (HEA), particularly HEA-A and HEA-B, produced significant deviations from the reference energies. The results also demonstrate that larger numbers of parameters or logic gates do not necessarily improve VQE performance. Furthermore, some ansätze , especially GRSD and EHA, showed sensitivity to the initialization of the parameters. Methods Reference geometries and energies were obtained at the CISD/STO-3 G level using Gaussian 09. VQE simulations were performed with the PennyLane library employing the Jordan-Wigner mapping. The ansätze evaluated were UCCSD, k -UpCCGSD, GateFabric, GRSD, HEA-A, HEA-B, HEA-C, and Entanglement-variational Hardware-efficient Ansatz (EHA). Dissociation profiles were generated by varying interatomic distances and angular coordinates for H 2 2 and H 3+ 3 + , as well as the C-H 2 2 dissociation coordinate for CH 5+ 5 + . Active-space ranging from 2/2 to 8/8 electrons/orbitals was employed for CH 5+ 5 + . Variational parameters were optimized using stochastic gradient descent with a convergence threshold of 1×10−6 1 × 10
High Resolution Image Download MS PowerPoint Slide Quantum computers have the potential to efficiently solve the electronic structure problem but are currently limited by noise and shallow circuits. We present an enhanced Variational Quantum Eigensolver (VQE) ansatz based on the Qubit Coupled Cluster (QCC) approach that requires optimization of only n parameters, where n is the number of Pauli string generators, rather than the typical n + 2 m parameters, where m is the number of qubits. We evaluate the ground state energies and molecular dissociation curves of strongly correlated molecules, namely O 3 and Li 4, using active spaces of varying sizes in conjunction with our enhanced QCC ansatz, Unitary Coupled Cluster Single–Double (UCCSD) ansatz, and the classical Coupled Cluster Singles and Doubles (CCSD) method. Compared to UCCSD, our approach significantly reduces the number of parameters while maintaining high accuracy. Numerical simulations demonstrate the effectiveness of our approach, and experiments on superconducting and trapped-ion quantum computers showcase its practicality on real hardware. By eliminating the need for symmetry-restoring gates and reducing the number of parameters, our enhanced QCC ansatz enables accurate quantum chemistry calculations on near-term quantum devices for strongly correlated systems.