Preserving Symmetries for Variational Quantum Eigensolvers in the Presence of Noise

One of the most promising applications of noisy intermediate scale quantum computers (NISQ) is the simulation of molecular Hamiltonians using the variational quantum eigensolver (VQE) algorithm, which has already been demonstrated on small molecules. We show that encoding symmetries of the simulated Hamiltonian at the level of the ansatz used in the VQE provides improvements to both classical and quantum resources. We further verify that these improvements persist in the presence of noise by simulating such variational forms in noisy environments and evaluating their ability to find the correct ground state. To further improve the quality of our results, we implement state of the art error mitigation techniques. Finally, we demonstrate our results in experiment by using IBMQ quantum processors.