Symmetry Breaking Slows Convergence of the ADAPT Variational Quantum Eigensolver

The accurate treatment of molecular systems exhibiting strong electronic correlations has long been a target of quantum simulation. Strong correlation often results in symmetry-breaking of the mean-field reference, leading to Löwdin's “symmetry dilemma”[1] whereby accuracy in the energy can be increased by breaking intrinsic symmetries of the system. We explore the impact of symmetry breaking on the performance of ADAPT-VQE using two strongly correlated systems where increasing correlation leads to spontaneous symmetry breaking of the mean-field solutions. We analyze the role that symmetry breaking in the reference states and orbital mappings of the fermionic Hamiltonians have on the performance of ADAPT-VQE. We observe that breaking symmetry has a deleterious effect on ADAPT-VQE by increasing the length of the ansatz necessary for energy convergence and exacerbating the problem of “gradient troughs”.