The role of the parameter landscape in Hartree-Fock quantum computing benchmarks

Google AI Quantum and Collaborators benchmarked the Google Sycamore quantum processor by showing that accurate estimates of the one-electron reduced density matrix could be reproduced for a classically obtained Hartree-Fock solution, thanks to extensive error mitigation strategies. However, benchmarking the Hartree-Fock algorithm on a quantum device requires not only that a given minimum can be reproduced but also that the entire orbital rotation landscape is described accurately. In this study, we aim to characterize noise-induced errors in the complete parameter landscape accessible to the single Slater determinant quantum circuit during a Hartree-Fock optimization. We find that even with error mitigation, the fidelity and the noise-induced errors of both the energy and the total spin are not homogeneous over the orbital rotation landscape, indicating that the accuracy achievable for a single state is not representative of the accuracy across the entire variational space. Our study indicates that benchmarking parameterized quantum circuits in the presence of noise requires the analysis of the complete parameter landscape to gauge the overall accuracy achievable for all states.