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Towards a Description of the Ground State Properties of LiHm Complexes and Reaction Energetics of Hydrogenation of Small Li Clusters using VQE-based Quantum Chemical Calculations

Dominic R. Alfonso, Benjamin Avramidis, Hari P. Paudel, Yuhua Duan, Kenneth D. Jordan

Published Mar 3, 2024• 0 citations
Publisher

Abstract

This presentation describes the utilization of the variational quantum eigensolver (VQE) using a unitary coupled cluster with singles and doubles (UCCSD) ansatz to simulate a series of LiHn molecules (n=1-3), including their singly charged ions. The performance is considered using a simulator by systematically increasing system size, providing data to compare against future VQE calculations. The predicted energy profiles are in semi-quantitative agreement with highly accurate CCSD/FCI methods.

DOI
10.2172/2560284

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This presentation describes the utilization of the variational quantum eigensolver (VQE) using a unitary coupled cluster with singles and doubles (UCCSD) ansatz to simulate a series of LiHn molecules (n=1-3), including their singly charged ions. The performance is considered using a simulator by systematically increasing system size, providing data to compare against future VQE calculations. The predicted energy profiles are in semi-quantitative agreement with highly accurate CCSD/FCI methods.
In this study, the variational quantum eigensolver (VQE) on a quantum simulator is used in calculating ground state electronic structure properties of the LiHn, n = 1–3, complexes including their singly charged ions. Results calculated using classical electronic structure algorithms are also included. We investigate the use of the unitary coupled cluster with singles and doubles (UCCSD) Ansatz using VQE within Qiskit and compare results to full configuration interaction (FCI) calculations. Computed ground state energies, electron affinities, ionization potentials, and dipole moments are considered. We report the first-of-its-kind simulated quantum computing results of selected LiHn species and use the parity orbital to qubit mapping scheme. We find that VQE/UCCSD results are comparable to classical coupled clusters with singles and doubles for all considered systems with respect to FCI. A VQE calculation cost evaluation is included in which we evaluate performance using both Jordan–Wigner and parity orbital to qubit mapping schemes. We also discuss some of the current limitations of utilizing VQE for the study of chemical systems.
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.
Abstract The fragmentation-based method has attracted interest as a way to reduce the computational cost of quantum chemical computations. Using the variational quantum eigensolver (VQE) of unitary coupled cluster singles and doubles (UCCSD), concurrent processing was used alongside the fragment molecular orbital scheme for the Li(I)–(H₂)n (n = 4 and 6) clusters on a supercomputer with a graphical processing unit (GPU)-accelerated quantum simulator. Energy and timing data of VQE-UCCSD are presented to highlight issues in practical applications.
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.
Variational quantum eigensolver (VQE) is a hybrid quantum-classical technique that leverages noisy intermediate scale quantum (NISQ) hardware to obtain the minimum eigenvalue of a model Hamiltonian. VQE has so far been used to simulate condensed matter systems as well as quantum chemistry of small molecules. In this work, we employ VQE methods to obtain the ground-state energy of LiCoO2_22​, a candidate transition metal oxide used for battery cathodes. We simulate Li2_22​Co2_22​O4_44​ and Co2_22​O4_44​ gas-phase models, which represent the lithiated and delithiated states during the discharge and the charge of the Li-ion battery, respectively. Computations are performed using a statevector simulator with a single reference state for three different trial wavefunctions: unitary coupled-cluster singles and doubles (UCCSD), unitary coupled-cluster generalized singles and doubles (UCCGSD) and k-unitary pair coupled-cluster generalized singles and doubles (k-UpCCGSD). The resources in terms of circuit depth, two-qubit entangling gates and wavefunction parameters are analyzed. We find that the k-UpCCGSD with k=5 produces results similar to UCCSD but at a lower cost. Finally, the performance of VQE methods is benchmarked against the classical wavefunction-based methods, such as coupled-cluster singles and doubles (CCSD) and complete active space configuration interaction (CASCI). Our results show that VQE methods quantitatively agree with the results obtained from CCSD. However, the comparison against the CASCI results clearly suggests that advanced trial wavefunctions are likely necessary to capture the multi-reference characteristics as well as the correlations emerging from high-level electronic excitations.
We present computational chemistry data for small molecules (COCOCO, HClHClHCl, F2F_2F2​, NH4+NH_4^+NH4+​, CH4CH_4CH4​, NH3NH_{3}NH3​, H3O+H_3O^+H3​O+, H2OH{_2}OH2​O, BeH2BeH_{2}BeH2​, LiHLiHLiH, OH−OH^-OH−, HFHFHF, HeH+HeH^+HeH+, H2H_2H2​), obtained by implementing the Unitary Coupled Cluster method with Single and Double excitations (UCCSD) on a quantum computer simulator. We have used the Variational Quantum Eigensolver (VQE) algorithm to extract the ground state energies of these molecules. This energy data represents the expected ground state energy that a quantum computer will produce for the given molecules, on the STO-3G basis. Since there is a lot of interest in the implementation of UCCSD on quantum computers, we hope that our work will serve as a benchmark for future experimental implementations.