Non-adiabatic Optimisation via Localisation-Delocalisation Transitions

arXiv:2610.30301v1 Announce Type: cross Abstract: The promise of efficiently solving classical optimisation problems on quantum computers is tantalizing. As many such problems can be mapped to approximating the ground state of spin-glasses, paradigmatic models for studying many-body localisation, it is natural to ask if some of the intuition coming from quantum statistical mechanics can help guide the construction of novel quantum optimisation algorithms. In this work, we discuss how continuous reverse quantum annealing crossing a many-body localisation transition can be accelerated by considering the density of Landau-Zener crossings as the system is quenched. We provide an interpretation of this behaviour in terms of an effective Fokker-Planck equation for the success probability of the algorithm. This interpretation suggests an improvement in the required annealing time as a function of the system size $N$, which goes from $\mathcal{O}({\rm poly}(N))$ to $\mathcal{O}(1)$ for reference states with non-vanishing energy density. We show that the continuous dynamics can be Trotterised with a number of steps that remains modest as system size increases, making it appealing for near-term devices. For the resulting circuit implementation, we provide a quantitative strategy for determining the parameters of the time-dependent Hamiltonian. We compare the performance of our digitised algorithm, which we call FRIO, against that of the QAOA for finding the ground state of spin-glass problems, in particular the SK model. The numerical results suggest that with suitably selected circuit parameters which can be efficiently found using thermalizing dynamics, FRIO almost always outperforms the conventional QAOA ansatz with pre-optimized angles.