Sufficiency of Hartree–Fock-type input states for ground-state energy estimation

Determine whether commonly adopted initial states for electronic-structure quantum simulations—such as the Hartree–Fock state—have sufficiently large overlap with the true ground state to enable reliable and accurate ground-state energy estimation (e.g., via quantum phase estimation or qubitization-based phase estimation) for molecular Hamiltonians on fault-tolerant quantum computers, and characterize for which classes of molecules or active-space selections this sufficiency holds.

Background

Quantum phase estimation and related phase-estimation techniques used for electronic-structure simulations require an input state with non-negligible overlap with the target ground state to ensure efficient convergence and accurate eigenvalue estimation.

Despite the common practice of using the Hartree–Fock state as an initial state, the adequacy of such choices is uncertain in general, particularly for strongly correlated systems and large active spaces. The paper highlights this uncertainty and notes that ground-state preparation itself is QMA-hard, motivating the need to establish when standard initial states suffice.

References

For example, quantum computation of electronic spectra of molecules relies on preparation of input states with significant overlap with the ground state (whose energy is to be estimated). However, is it unclear whether the commonly adopted choices (e.g., the Hartree--Fock state) will be sufficient.

— How to Build a Quantum Supercomputer: Scaling from Hundreds to Millions of Qubits (2411.10406 - Mohseni et al., 15 Nov 2024) in Section: Validation of quantum algorithms