Unitary Coupled-Cluster for Quantum Computation of Molecular Properties in a Strong Magnetic Field

Abstract: In truncated coupled-cluster (CC) theories, non-variational and/or generally complex ground-state energies can occur. This is due to the non-Hermitian nature of the similarity transformed Hamiltonian matrix in combination with CC truncation. For chemical problems that deal with real-valued Hamiltonian matrices, complex CC energies rarely occur. However, for complex-valued Hamiltonian matrices, such as those that arise in the presence of strong magnetic fields, complex CC energies can be regularly observed unless certain symmetry conditions are fulfilled. Therefore, in the presence of magnetic fields, it is desirable to pursue CC methods that are guaranteed to give upper-bound, real-valued energies. In this work, we present the first application of unitary CC (UCC) to chemical systems in a strong magnetic field. This is achieved utilizing the variational quantum eigensolver (VQE) algorithm applied to the unitary coupled-cluster singles and doubles (UCCSD) method. We benchmark the method on the H$_2$ molecule in a strong magnetic field, and then calculate UCCSD energies for the H$_4$ molecule as a function of both geometry and field angle. We show that while standard CCSD can yield generally complex energies that are not an upper-bound to the true energy, UCCSD always results in variational and real-valued energies. We also show that the imaginary components of the CCSD energy are largest in the strongly correlated region. Lastly, the UCCSD calculations capture a large percentage of the correlation energy.