State preparation for molecular Hamiltonians with the quantum alternating operator ansatz (QAOA)

This work explores the use of the quantum alternating operator ansatz (QAOA) as a algorithm for state preparation for chemical systems. In our approach, the QAOA procedure is modified from its typical application in combinatorial optimization in two important ways: the initial state is chosen to be the Hartree-Fock (HF) approximation to the ground state rather than the commonly used uniform superposition and, in consistent fashion, the QAOA mixer is chosen to be the HF Hamiltonian. The algorithm is evaluated for CH2 and H2O in simple basis sets of 8 orbitals on classical hardware using traditional sparse matrix-based quantum dynamics approaches. A simple linear schedule for the usual QAOA parameters and a moderate number of iterations is shown to lead to final states with high overlap with the true ground state. This work thereby illustrates how existing quantum algorithms for combinatorial optimization can be adapted for application to chemical problems. It is anticipated that this QAOA protocol will readily extend to larger molecular systems.