Energy gap calculation on near-term quantum hardware with robust phase estimation

Can alternative approaches to phase estimation yield better results for chemical simulation on NISQ hardware? Robust phase estimation (RPE) calculates the difference in phases between two eigenstates of a unitary, provided oracular access to that unitary and the relevant eigenstates. In contrast to conventional phase estimation, it does not require a controlled-U and is naturally resistant to state preparation and measurement errors.

We evaluate the suitability of RPE on near-term hardware. In particular, we calculate the energy landscapes of H₂ and H₃ on extant quantum hardware (pre-compiling to emulate hardware with significantly higher fidelities). Resource requirements for larger molecules are considered.