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Physical Chemistry Chemical Physics

Variational quantum eigensolver simulations with the multireference unitary coupled cluster ansatz: a case study of the C 2 v quasi-reaction pathway of beryllium insertion into a H 2 molecule

Kenji Sugisaki, Takumi Kato, Yuichiro Minato, Koji Okuwaki, Yuji Mochizuki

Published Jan 1, 2022• 29 citations
Publisher

Abstract

reaction pathway, resulting in a large discrepancy of the simulated VQE energy from the full-configuration interaction (full-CI) value. By contrast, the MR-UCCpGSD ansatz can give more reliable results with respect to total energy and the overlap with the full-CI solution, insisting the importance of multiconfigurational treatments in the calculations of strongly correlated systems. The MR-UCCpGSD ansatz allows us to compute the energy with the same accuracy regardless of the strength of multiconfigurational character, which is an essential property to discuss energy differences of various molecular systems.

DOI
10.1039/d1cp04318h

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Towards Accurate Description of Chemical Reaction Energetics by Using Variational Quantum Eigensolver: A Case Study of the C2v Quasi-Reaction Pathway of Beryllium Insertion to H2 Molecule

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We have examined the performance of variational quantum eigensolver along the quasi-reaction pathway of Be insertion to H2 molecule, in which avoided crossing occurs at the transition structure. Numerical simulations revealed that the multireference unitary coupled cluster with partially generalized singles and doubles (MR-UCCpGSD) is a powerful tool to describe the electronic structure of strongly correlated systems.

•Jun 25, 2021•0 citations

Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz

Jonathan Romero, Ryan Babbush, Jarrod R. McClean +3 more

Abstract The variational quantum eigensolver (VQE) algorithm combines the ability of quantum computers to efficiently compute expectation values with a classical optimization routine in order to approximate ground state energies of quantum systems. In this paper, we study the application of VQE to the simulation of molecular energies using the unitary coupled cluster (UCC) ansatz. We introduce new strategies to reduce the circuit depth for the implementation of UCC and improve the optimization of the wavefunction based on efficient classical approximations of the cluster amplitudes. Additionally, we propose an analytical method to compute the energy gradient that reduces the sampling cost for gradient estimation by several orders of magnitude compared to numerical gradients. We illustrate our methodology with numerical simulations for a system of four hydrogen atoms that exhibit strong correlation and show that the circuit depth of VQE using a UCC ansatz can be reduced without introducing significant loss of accuracy in the final wavefunctions and energies.

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Quantum computer specification for nuclear structure calculations

Ching-Hwa Wee, Meng-Hock Koh, Yung Szen Yap

Recent studies to solve nuclear structure problems using quantum computers rely on a quantum algorithm known as Variational Quantum Eigensolver (VQE). In this study, we calculate the correlation energy in Helium-6 using VQE, with a \textit{full-term} unitary-paired-coupled-cluster-doubles (UpCCD) ansatz on a quantum computer simulator and implement a set of custom termination criteria to shorten the optimization time. Using this setup, we test out noisy quantum computer simulators of various coherence times and quantum errors to find the required specification for such calculations. We also look into the contribution of errors from the quantum computers and optimization process. We find that the minimal specification of 5~ms coherence times and $10^{-4}$ quantum errors is required to reliably reproduce state-vector results within 8\% discrepancy. Our study indicates the possibility of performing VQE calculations using a full-term UpCCD ansatz on a slightly noisy quantum computer, without implementing quantum error correction.

arXiv:2406.16165•Jun 23, 2024•0 citations

Molecular Ground-State Energy Estimation Using VQE

Enoth Kumar N, Irene S, Vinod Jani +2 more

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:$\mathrm{H}_{2}, \mathrm{H}_{3}^{+}, \text{LiH}, \text{HF}, \text{OH}^{-}, \mathrm{H}_{2} \mathrm{O}, \text{BH}_{3}, \text{CH}_{4}$, and$\text{NH}_{3}$. 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.

IEEE Pune Section International Conference (PuneCon)•Dec 12, 2025•0 citations

Multicomponent Unitary Coupled Cluster and Equation-of-Motion for Quantum Computation

Fabijan Pavošević, Sharon Hammes‐Schiffer

The variational quantum eigensolver (VQE) algorithm combined with the unitary coupled cluster (UCC) ansatz has been developed for the quantum computation of molecular energies and wave functions within the Born–Oppenheimer approximation. Herein, this approach is extended to multicomponent systems to enable the quantum mechanical treatment of more than one type of particle, such as electrons and positrons or electrons and nuclei, without invoking the Born–Oppenheimer approximation. Specifically, we introduce the multicomponent unitary coupled cluster (mcUCC) method combined with the VQE algorithm for the calculation of ground-state energies and wave functions as well as the multicomponent equation-of-motion (mcEOM) method for the calculation of excitation energies. These methods are developed within the nuclear-electronic orbital (NEO) framework and are formulated in the qubit basis to enable implementations on quantum computers. Moreover, these methods are used to calculate the ground-state energy and excitation energies of positronium hydride, where both electrons and the positron are treated quantum mechanically, as well as the H 2 molecule, where both electrons and one proton are treated quantum mechanically. These applications validate the implementation and provide benchmark data for future calculations. The errors due to Trotterization of the mcUCC ansatz are also analyzed. This formalism, as well as the accompanying computer code, will serve as the basis for applications to more complex multicomponent systems, such as simulations of photoinduced nonadiabatic molecular processes, on both classical and quantum computers.

Journal of Chemical Theory and Computation•May 4, 2021•37 citations

Evaluating Variational Quantum Eigensolver Approaches for Simplified Models of Molecular Systems: A Case Study on Protocatechuic Acid

Gleydson Fernandes de Jesus, Erico S. Teixeira, Lucas Queiroz Galvão +6 more

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.

Molecules•Dec 31, 2024•6 citations
reaction pathway, resulting in a large discrepancy of the simulated VQE energy from the full-configuration interaction (full-CI) value. By contrast, the MR-UCCpGSD ansatz can give more reliable results with respect to total energy and the overlap with the full-CI solution, insisting the importance of multiconfigurational treatments in the calculations of strongly correlated systems. The MR-UCCpGSD ansatz allows us to compute the energy with the same accuracy regardless of the strength of multiconfigurational character, which is an essential property to discuss energy differences of various molecular systems.
Abstract The variational quantum eigensolver (VQE) algorithm combines the ability of quantum computers to efficiently compute expectation values with a classical optimization routine in order to approximate ground state energies of quantum systems. In this paper, we study the application of VQE to the simulation of molecular energies using the unitary coupled cluster (UCC) ansatz. We introduce new strategies to reduce the circuit depth for the implementation of UCC and improve the optimization of the wavefunction based on efficient classical approximations of the cluster amplitudes. Additionally, we propose an analytical method to compute the energy gradient that reduces the sampling cost for gradient estimation by several orders of magnitude compared to numerical gradients. We illustrate our methodology with numerical simulations for a system of four hydrogen atoms that exhibit strong correlation and show that the circuit depth of VQE using a UCC ansatz can be reduced without introducing significant loss of accuracy in the final wavefunctions and energies.
Recent studies to solve nuclear structure problems using quantum computers rely on a quantum algorithm known as Variational Quantum Eigensolver (VQE). In this study, we calculate the correlation energy in Helium-6 using VQE, with a \textit{full-term} unitary-paired-coupled-cluster-doubles (UpCCD) ansatz on a quantum computer simulator and implement a set of custom termination criteria to shorten the optimization time. Using this setup, we test out noisy quantum computer simulators of various coherence times and quantum errors to find the required specification for such calculations. We also look into the contribution of errors from the quantum computers and optimization process. We find that the minimal specification of 5~ms coherence times and 10−410^{-4}10−4 quantum errors is required to reliably reproduce state-vector results within 8\% discrepancy. Our study indicates the possibility of performing VQE calculations using a full-term UpCCD ansatz on a slightly noisy quantum computer, without implementing quantum error correction.
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\mathrm{H}_{2}, \mathrm{H}_{3}^{+}, \text{LiH}, \text{HF}, \text{OH}^{-}, \mathrm{H}_{2} \mathrm{O}, \text{BH}_{3}, \text{CH}_{4}H2​,H3+​,LiH,HF,OH−,H2​O,BH3​,CH4​, andNH3\text{NH}_{3}NH3​. 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.
The variational quantum eigensolver (VQE) algorithm combined with the unitary coupled cluster (UCC) ansatz has been developed for the quantum computation of molecular energies and wave functions within the Born–Oppenheimer approximation. Herein, this approach is extended to multicomponent systems to enable the quantum mechanical treatment of more than one type of particle, such as electrons and positrons or electrons and nuclei, without invoking the Born–Oppenheimer approximation. Specifically, we introduce the multicomponent unitary coupled cluster (mcUCC) method combined with the VQE algorithm for the calculation of ground-state energies and wave functions as well as the multicomponent equation-of-motion (mcEOM) method for the calculation of excitation energies. These methods are developed within the nuclear-electronic orbital (NEO) framework and are formulated in the qubit basis to enable implementations on quantum computers. Moreover, these methods are used to calculate the ground-state energy and excitation energies of positronium hydride, where both electrons and the positron are treated quantum mechanically, as well as the H 2 molecule, where both electrons and one proton are treated quantum mechanically. These applications validate the implementation and provide benchmark data for future calculations. The errors due to Trotterization of the mcUCC ansatz are also analyzed. This formalism, as well as the accompanying computer code, will serve as the basis for applications to more complex multicomponent systems, such as simulations of photoinduced nonadiabatic molecular processes, on both classical and quantum computers.
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.