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The European Physical Journal Plus

Trapped ion quantum hardware demonstration of energy calculations using a multireference unitary coupled cluster ansatz: application to the BeH$$_2$$ insertion problem

Palak Chawla, Disha Shetty, Peniel Bertrand Tsemo, Kenji Sugisaki, Jordi Riu, Jan Nogué, Debashis Mukherjee, V. S. Prasannaa

Published Sep 27, 2025• 3 citations
Publisher
DOI
10.1140/epjp/s13360-025-06876-y

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In this paper we calculate the ground-state energy of benzene under spatial deformations by using the variational quantum eigensolver. The primary goal of the study is to estimate the feasibility of using quantum computing Ans\"atze on near-term devices to solve problems with a large number of orbitals in regions where classical methods are known to fail. Furthermore, by combining our advanced simulation platform with real quantum computers, we provide an analysis of how the noise, inherent to quantum computers, affects the results. At the center of our study are the hardware efficient and quantum unitary coupled-cluster (QUCC) Ans\"atze. First, we find that the hardware efficient Ansatz has the potential to outperform mean-field methods for extreme deformations of benzene. However, key problems remain at equilibrium, preventing real chemical application. Moreover, the hardware efficient Ansatz yields results that strongly depend on the initial guess of parameters (in both noisy and noiseless cases) and optimization issues have a higher impact on their convergence than noise. This is confirmed by comparison with real quantum computing demonstrations. On the other hand, the QUCC Ansatz alternative exhibits deeper circuits. Therefore, noise effects increase and are so extreme that the method never outperform mean-field theories. Our dual simulator, (8--16)-qubit QPU computations of QUCC Ansatz appears to be much more sensitive to hardware noise than shot noise, which further indicates where the noise-reduction efforts should be directed. Finally, the study shows that the QUCC method better captures the physics of the system as the QUCC method can be utilized together with the H\"uckel approximation. We discussed how going beyond this approximation sharply increases the optimization complexity of such a difficult problem.
Abstract The variational quantum eigensolver (VQE) algorithm, designed to calculate the energy of molecular ground states on near‐term quantum computers, requires specification of symmetries that describe the system, for example, spin state and number of electrons. This opens the possibility of using VQE to obtain excited states as the lowest‐energy solutions of a given set of symmetries. In this paper, the performances of various unitary coupled cluster (UCC) ansätze applied to VQE calculations on excited states are investigated using quantum circuits designed to represent single reference and multireference wavefunctions to calculate energy curves with respect to variations in the molecular geometry. These ansätze include standard Unitary Coupled Cluster Singles and Doubles (UCCSD), as well as modified versions of Unitary Coupled Cluster Generalized Singles and Doubles (UCCGSD) and k‐UpCCGSD, which are engineered to tackle excited states without undesired spin symmetry crossover to lower states during VQE optimization. These studies are carried out on a range of systems, including H2, H3, H4, NH, OH+, CH2, and , covering examples of spin singlet, doublet, and triplet molecular ground states with single and multireference excited states. In most cases, our calculations are in excellent agreement with results from full‐configuration interaction calculations on classical machines, thus showing that the VQE algorithm is capable of calculating the lowest excited state at a certain symmetry, including multireference closed‐ and open‐shell states, by setting appropriate restrictions on the excitations considered in the cluster operator and appropriate constraints in the qubit register encoding the starting mean field state.
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.