Energy Landscapes for the Unitary Coupled Cluster Ansatz

The unitary coupled cluster (UCC) approach has been one of the most popular wavefunction parametrizations for the variational quantum eigensolver due to the relative ease of optimization compared to hardware-efficient ansätze. In this contribution, we explore the energy landscape of the unitary coupled cluster singles and doubles (UCCSD) wavefunction for two commonly employed benchmark systems, lithium hydride and the nitrogen dimer. We investigate the organization of the solution space in terms of local minima and show how it changes as the number and order of operators of the UCC ansatz are varied. Surprisingly, we find that in all cases, the UCCSD energy has numerous low-lying minima connected by high energy transition states. Additionally, the energy spread of the minima that lie in the same band as the global minimum may exceed chemical accuracy, making the location of the true global minimum especially challenging.