Reshaping quantum annealing landscapes with diagonal catalysts
arXiv:2607.14063
The paper introduces a framework linking energy to Hamming distance in optimization problems and proposes diagonal ZZ-catalysts derived from small frustration‑free subproblems to reshape quantum annealing landscapes, boosting the probability of finding near‑optimal solutions.
Abstract
Quantum annealing is often limited by population trapped in local minima many spin flips from the solution. We introduce a mathematical framework to understand the connection between energy and Hamming distance in optimization problems. Using this, we build ZZ-catalysts from ground-state patterns of small frustration-free subproblems that make configurations far from the solution less energetically competitive. On sparse problems they multiply the near-solution probability at short sweeps, with gains persisting on fully-connected models and tunable via subproblem choice.
20 pages, 13 figures and 2 tables