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

In this study, we employ the variational quantum eigensolver algorithm with a multireference unitary coupled cluster ansatz to report the ground state energy of the BeH\(_2\) molecule in a geometry where strong correlation effects are significant. We consider the two most important determinants in the construction of the reference state for our ansatz. We remove redundancies in order to execute a redundancy-free calculation. In view of the currently available noisy quantum hardware, we carry out parameter optimization on a classical computer and measure the energy with optimized parameters on a quantum computer. Furthermore, in order to carry out our intended 12-qubit computation with error mitigation and post-selection on a noisy intermediate scale quantum era trapped ion hardware (the commercially available IonQ Forte-I), we perform a series of resource reduction techniques to a. decrease the number of two-qubit gates by \(99.84\%\) (from 12243 to 20 two-qubit gates) relative to the unoptimized circuit, and b. reduce the number of measurements via the idea of supercliques, while losing \(2.69\%\) in the obtained ground state energy relative to that computed classically for the same resource-optimized problem setting.