Eiichiro Mori

Preparing low-energy eigenstates, such as excited states, in quantum systems is a central challenge. Previous method reduces this to a ground-state preparation problem by modifying the system Hamiltonian using an approximate energy of the target state. However, this approach results in a large Hamiltonian simulation cost. Here, by adding a penalty term based on a system-size-independent conserved quantity, we successfully reduce this cost by a square-root factor. We confirm this through numerical simulations on the transverse-field Ising model and the Hubbard model.