Catalyst Hamiltonians in Quantum Adiabatic Optimization: How much can they help?

Increased experimental control of quantum annealing systems has lead to a resurgence of interest in exploring different interpolation paths for quantum adiabatic optimization. In this talk, we review recent work on interpolations with a `catalyst’ Hamiltonian, corresponding to interpolations with an intermediate Hamiltonian that is different from the driver and problem Hamiltonians. For special cases, both off-diagonal and diagonal (in the computational basis) catalysts can allow for dramatic performance enhancements by eliminating exponentially closing minimum gaps along the interpolation, but we caution that these known examples have simple energy landscapes, making them poor examples of computationally hard problems. There remains no clear understanding or recipe for when these new interpolations can give performance enhancements more generally. This highlights the need for dramatically new insights and methods but also more experimental capabilities to further explore these new approaches.