Adapting the Similarity Renormalization Group to Quantum Computers

Renormalization Group (RG) methods have served as a powerful tool for increasing the tractability of the Nuclear-Many Body Problem. By applying continuous changes in resolution to our nuclear interactions, RG methods decouple low-energy and high-energy degrees of freedom while preserving low-energy observables. This allows for an effective low-energy description. While successful, classical computational implementations of the RG require a rapid growth of resources as atomic mass number increases. Here we adapt the Similarity Renormalization Group (SRG), which applies continuous unitary transformations that band-diagonalize a nuclear many-body hamiltonian, to quantum computers. As proof of concept we demonstrate the SRG evolution of a two-body nuclear hamiltonian using the Double Bracket Quantum Algorithm, and obtain it's eigenstates.