  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.
