Robustness of diabatic speedup in quantum annealing

To avoid the exponential slowdown associated with closing gaps in quantum annealing, diabatic transitions to higher energy levels may be exploited in such a way that the system returns to the ground state before the end of the anneal. In certain cases, this is facilitated by the original annealing spectrum however the use of additional catalyst Hamiltonians has also been explored to produce a diabatic path to the ground state (see Feinstein et al., arXiv:2203.06779). Since the transitions depend on the evolution rate, it is important to consider the sensitivity of any potential speedup to the annealing time. We explore this sensitivity using annealing spectra containing an exponentially closing gap and an additional, tuneable, small gap created by a catalyst. We find that minimising the additional gap results in robustness to changes in the annealing time. However, as the gap size is increased, the final ground-state overlap becomes increasingly sharply peaked as a function of anneal time. This suggests a trade-off between the precision needed in the catalyst strength and the anneal time that is critical in diabatic annealing.