Asymptotic scaling of coherent quantum annealing in 3D spin glasses
In plain words
A quantum annealer slowly removes a sideways field so that the spins settle into a low-energy arrangement, and the leftover energy falls as a power of the anneal time. Whether that power keeps the value predicted from the critical point, and what happens at long anneal times, is not known.
Precise statement
For the 3D Edwards-Anderson model (cubic lattice, $\pm J$ or Gaussian couplings) under coherent unitary annealing of $\Gamma(t)$ from $\Gamma >> \Gamma_c$ to 0 in time $t_a$, determine the exponent $\kappa$ of the residual energy per spin $\epsilon(t_a) \sim t_a^{-\kappa}$, whether it equals the Kibble-Zurek value fixed by $z$ and $\nu$ of the 3D quantum critical point, and the anneal time beyond which avoided crossings inside the glass phase change it. An answer gives $\kappa$ with error bars in each regime.
What would settle it
Exact unitary or tensor-network simulations and coherent hardware anneals over at least two decades of $t_a$ on lattices of increasing $L$, compared with independently computed $z$ and $\nu$.
Status in the literature
King et al. (Nature 2023) observed Kibble-Zurek scaling of coherent annealing in 3D spin glasses on about 5000 qubits over a limited window of short anneal times; the long-time regime is untested.