Feasibility of variational quantum preparation of low-energy states for Anderson impurity models

Determine whether variational quantum algorithms implemented on quantum processors can successfully prepare low-energy (including ground) states of the Anderson impurity model as problem sizes increase to regimes where variational optimization challenges such as barren plateaus and hardware decoherence become significant, thereby establishing conditions or evidence for scalability beyond small test cases.

Background

The paper surveys quantum algorithms for solving dynamical mean-field theory (DMFT) impurity problems and reviews early implementations that predominantly use variational quantum eigensolver (VQE) approaches with small impurity and bath sizes. While these demonstrations are promising, they do not yet probe regimes where known issues of variational training (e.g., barren plateaus) are severe.

Because the Anderson impurity model (AIM) is the central Hamiltonian used as the DMFT impurity solver, establishing whether variational methods can reliably generate its low-energy states at larger bath sizes is critical for assessing the long-term viability of quantum-accelerated DMFT. The authors explicitly flag this as an unresolved question.