Quantum annealing speedup of embedded problems via suppression of Griffiths singularities

The integration of quantum annealing (QA) into practical applications necessitates optimal parameter settings for problems embedded within hardware graphs. We explore the implications of Griffiths phases on embedding chains, indicating that rather than posing a hindrance, they can effectively balance singularities in logical problems, thus changing their universality class. By employing a judicious selection of embedding parameters, we significantly reduce the time complexity for a random Ising chain from O(exp[c√N]) to O(N²). This reduction is supported by numerical results obtained through the development of a custom integrator designed to tackle convergence challenges. The impact of our results suggests substantial performance improvements in QA applications, highlighting the utility of precise parameter tuning in mitigating the effects of non-adiabatic excitations and underutilization of qubits during the annealing process. This research offers a novel perspective on the intersection of quantum mechanics and computational optimization, paving the way for enhanced applications in quantum computing and related fields.