On the robustness of Quantum Phase Estimation to compute ground properties of many-electron systems

We propose an analysis of the Quantum Phase Estimation (QPE) algorithm applied to electronic systems by investigating its free parameters such as the time step, number of phase qubits, initial state preparation, number of measurement shots, and parameters related to the unitary operators implementation. A deep understanding of these parameters is crucial to pave the way towards more automation of QPE applied to predictive computational chemistry and material science. To our knowledge, aspects remain to be investigated and a holistic method to coherently set these parameters to be clearly stated. After reviewing key QPE features, we propose a constructive method to set the QPE free parameters for ground energy estimation and ground state projection. We gather and refine, among other things, explicit conditions for achieving chemical accuracy in ground energy estimation. We also demonstrate that, using our conditions, the complexity of the Trotterized version of QPE tends to depend mostly on physical system properties and weakly on the number of phase qubits. Numerical simulations on the H2 molecule provide a first validation of our approach.