Quantum Adiabatic Perturbation Theory

The growing field of quantum computing shows potential for studying nuclear many-body systems. Unfortunately, current quantum-computational costs do not scale well even for the leading orders of nuclear effective field theories. We present a two-step quantum algorithm for solving hard-to-simulate Hamiltonians. First, we solve the simplest part of the Hamiltonian as a zeroth-order step, which can be done using methods such as the Rodeo Algorithm. Second, we leverage the adiabatic theorem to find perturbative corrections from the easily-computable Hamiltonian to a difficult Hamiltonian of interest. This algorithm can be scaled to find increasingly higher order corrections. Used in tandem with methods such as Wavefunction Matching, quantum adiabatic perturbation theory can be a powerful tool for solving nuclear many-body problems.