The accurate prediction and understanding of molecular energy and chemical reactivity are fundamental pursuits in the field of molecular quantum chemistry. With the limitations of the current noisy intermediate scale quantum computer (NISQ) era, the Variational Quantum Eigensolver (VQE) algorithm offers a promising approach to efficiently estimate the stable energy state of a given molecule. This study is focused on predicting the ground state and single electron detachment energy of the hydride ion because of its high electron electron correlation and numerous applications in astrophysics and quantum chemistry. The hydride ion is the first three body quantum problem for which the ground state energy has been calculated theoretically using the Chandrasekhar Wavefunction, which takes high electron-electron correlation into account. For the calculation of hydride ion, we used the VQE algorithm with two types of quantum computational ansatz, (i) chemistry inspired ansatz based on unitary CC (UCC) and (ii) hardware efficient based ansatz (HEA). To check the versatility of the algorithm, we analyzed two proton transfer reactions involving the hydride ion and finds the energy to be exothermic with a much improved result compared to previous studies. Overall, the VQE algorithm with a quantum computational approach is found to be reliable in calculating stable state energy, single electron detachment energy, and reaction energy for proton transfer reactions involving a highly correlated molecule with a low relative percentage error.
The accurate prediction and understanding of molecular energy and chemical reactivity are fundamental pursuits in the field of molecular quantum chemistry. With the limitations of the current noisy intermediate scale quantum computer (NISQ) era, the Variational Quantum Eigensolver (VQE) algorithm offers a promising approach to efficiently estimate the stable energy state of a given molecule. This study is focused on predicting the ground state and single electron detachment energy of the hydride ion because of its high electron electron correlation and numerous applications in astrophysics and quantum chemistry. The hydride ion is the first three body quantum problem for which the ground state energy has been calculated theoretically using the Chandrasekhar Wavefunction, which takes high electron-electron correlation into account. For the calculation of hydride ion, we used the VQE algorithm with two types of quantum computational ansatz, (i) chemistry inspired ansatz based on unitary CC (UCC) and (ii) hardware efficient based ansatz (HEA). To check the versatility of the algorithm, we analyzed two proton transfer reactions involving the hydride ion and finds the energy to be exothermic with a much improved result compared to previous studies. Overall, the VQE algorithm with a quantum computational approach is found to be reliable in calculating stable state energy, single electron detachment energy, and reaction energy for proton transfer reactions involving a highly correlated molecule with a low relative percentage error.
Abstract Because of remarkable reactivity and strong electron‐electron correlation effects, the precise prediction of ground state energy and chemical reactivity of hydride ion is an essential objective in quantum chemistry. Leveraging variational quantum algorithms offers a promising avenue for studying molecular properties using current noisy intermediate‐scale quantum devices. This work utilises the variational approach to anticipate the ground state, reactivity, and single‐electron detachment energy of the three‐body hydride ion. We investigated both Hardware‐Efficient Ansatz (HEA) and Chemistry‐inspired ansatz based on a Unitary Coupled Cluster (UCC) on both noiseless and noisy IBM simulators. Modern error‐mitigating techniques, such as Zero‐Noise Extrapolation (ZNE) with unitary folding and measurement error mitigation, have been implemented to significantly reduce errors in noisy environments. This study contributes to our understanding of the quantum computational nuances of the hydride ion and addresses the question of whether quantum computers can retain the correlation energies for these correlated ions.
Abstract Materials simulations involving strongly correlated electrons pose fundamental challenges to state‐of‐the‐art electronic structure methods but are hypothesized to be the ideal use case for quantum computing algorithms. To date, no quantum computer has simulated a molecule of a size and complexity relevant to real‐world applications, despite the fact that the variational quantum eigensolver (VQE) algorithm can predict chemically accurate total energies. Nevertheless, because of the many applications of moderately sized, strongly correlated systems, such as molecular catalysts, the successful use of the VQE stands as an important waypoint in the advancement toward useful chemical modeling on near‐term quantum processors. In this paper, we take a significant step in this direction. We lay out the steps, write, and run parallel code for an (emulated) quantum computer to compute the bond dissociation curves of the TiH, LiH, NaH, and KH diatomic hydride molecules using the VQE. TiH was chosen as a relatively simple chemical system that incorporates d orbitals and strong electron correlation. Because current VQE implementations on existing quantum hardware are limited by qubit error rates, the number of qubits available, and the allowable gate depth, recent studies using it have focused on chemical systems involving s and p block elements. Through VQE + UCCSD calculations of TiH, we evaluate the near‐term feasibility of modeling a molecule with d‐orbitals on real quantum hardware. We demonstrate that the inclusion of d‐orbitals and the use of the UCCSD ansatz, which are both necessary to capture the correct TiH physics, dramatically increase the cost of this problem. We estimate the approximate error rates necessary to model TiH on current quantum computing hardware using VQE + UCCSD and show them to likely be prohibitive until significant improvements in hardware and error correction algorithms are available.
This software supports the paper, "Exploring the scaling limitations of the variational quantum eigensolver with the bond dissociation of hydride diatomic molecules," published in the International Journal of Quantum Chemistry, whose abstract is as follows: Materials simulations involving strongly correlated electrons pose fundamental challenges to state-of-the-art electronic structure methods but are hypothesized to be the ideal use case for quantum computing. To date, no quantum computer has simulated a molecule of a size and complexity relevant to real-world applications, despite the fact that the variational quantum eigensolver (VQE) algorithm can predict chemically accurate total energies. Nevertheless, because of the many applications of moderately-sized, strongly correlated systems, such as molecular catalysts, the successful use of the VQE stands as an important waypoint in the advancement toward useful chemical modeling on near-term quantum processors. In this paper, we take a significant step in this direction. We lay out the steps, write, and run parallel code for an (emulated) quantum computer to compute the bond dissociation curves of the TiH, LiH, NaH, and KH diatomic hydride molecules using VQE. TiH was chosen as a relatively simple chemical system that incorporates d orbitals and strong electron correlation. Because current VQE implementations on existing quantum hardware are limited by qubit error rates, the number of qubits available, and the allowable gate depth, recent studies have focused on chemical systems involving s and p block elements. Through VQE + UCCSD calculations of TiH, we evaluate the near-term feasibility of modeling a molecule with d-orbitals on real quantum hardware. We demonstrate that the inclusion of d-orbitals and the use of the UCCSD ansatz, which are both necessary to capture the correct TiH physics, dramatically increase the cost of this problem. We estimate the approximate error rates necessary to model TiH on current quantum computing hardware using VQE+UCCSD and show them to likely be prohibitive until significant improvements in hardware and error correction algorithms are available.
Abstract Quantum computing leverages the quantum resources of superposition and entanglement to efficiently solve computational problems considered intractable for classical computers. Examples include calculating molecular and nuclear structure, simulating strongly interacting electron systems, and modeling aspects of material function. While substantial theoretical advances have been made in mapping these problems to quantum algorithms, there remains a large gap between the resource requirements for solving such problems and the capabilities of currently available quantum hardware. Bridging this gap will require a co-design approach, where the expression of algorithms is developed in conjunction with the hardware itself to optimize execution. Here we describe an extensible co-design framework for solving chemistry problems on a trapped-ion quantum computer and apply it to estimating the ground-state energy of the water molecule using the variational quantum eigensolver (VQE) method. The controllability of the trapped-ion quantum computer enables robust energy estimates using the prepared VQE ansatz states. The systematic and statistical errors are comparable to the chemical accuracy, which is the target threshold necessary for predicting the rates of chemical reaction dynamics, without resorting to any error mitigation techniques based on Richardson extrapolation.
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.
Exponential scaling presents a significant challenge in electronic structure calculations performed on classical computers. This paper explores how quantum computer algorithms can accurately represent quantum systems. Variational Quantum Eigensolver (VQE) algorithm is used to compute the ground state energy of hydrogen and helium sequences by implementing variational principle and quantum gates as trial wavefunction. This technique combines classical optimization with quantum computing calculations to simulate quantum systems on noisy and resource-limited computers. The resulting calculated energy is highly consistent to the corresponding exact values and Hartree-Fock calculations with a trend of when the number of atoms increases the calculated energy becomes more negative, leading to a decrease in the percentage error. Moreover, the convergence of the ground state energy of hydrogen and helium atoms was effectively optimized. The desired energy was reached, proven by adjusting the expectation value, and gradually achieving unity in state overlap. These findings demonstrate the VQE method's accuracy in calculating simple quantum systems and its scalability for larger atomic and molecular system, such as those in quantum chemistry and material science. However, challenges in quantum computer simulations, such as limited in qubit numbers and the presence of noise, require further advancements. Therefore, implementing a larger basis sets, advanced qubit mapping, specific chemistry ansatz, and flexible optimization techniques is one way to improve overall calculation.