Effects of XX-Catalysts on Annealing Spectra with a Scalable Weighted Maximum-Independent-SetProblem*

Quantum annealing is an algorithm designed to solve optimisation problems by initialising a system in the ground state of a simple driver Hamiltonian and evolving to a Hamiltonian whose ground state encodes the solution to the problem. To prevent excitations, the evolution time must scale inversely with the square of the minimum gap between the instantaneous ground and first excited states - which generally closes exponentially with the problem size. A promising solution is the introduction of a catalyst Hamiltonian that modifies the evolution, either softening the scaling of the minimum gap, or producing a spectrum that enables diabatic annealing. To controllably manipulate annealing spectra, it is vital to study the impact of catalyst Hamiltonians in various settings. Using the weighted MIS problem, we examine how catalysts containing carefully chosen XX-couplings can be introduced to predictably alter the annealing spectrum. We show how, depending on the properties of the original spectrum, the same catalyst will either increase the gap or introduce an additional, tuneable, small gap. This additional gap shows potential for exploitation in diabatic annealing protocols.