Distribution of kinks in an Ising ferromagnet after annealing and the generalized Kibble-Zurek mechanism

Benchmarking quantum annealing dynamics: the spin-vector Langevin model

“…Again, the SVL model reproduces the observed values in D-Wave. This is consistent with the generalized KZM [57,66] according to which the dynamics sets the correlation length out of equilibrium ξ, and defect formation can be described as the result of a sequence of ∼ N/ ξ iid discrete random variables, that yields a binomial distribution for P (n). Cumulant ratios are then set by the success probability for a kink formation, which can be expected to be weakly dependent on the underlying dynamics.…”

“…Data collected in D-Wave machines for the critical dynamics of the 1D TFIM is described by α = 0.20 in the NASA machine and by α = 0.34 in the Burnaby device [22], inconsistent with the unitary evolution of the quantum 1D TFIM. The values are also inconsistent with classical models including SVMC [22], simulated quantum annealing [56], and Glauber dynamics [57], and have been explained using a spin-boson model, coupling the quantum TFIM to an Ohmic harmonic bath. In this case, the theoretical value α KZM = 0.28 while a broader range is found numerically at zero temperature varying the spectral function [22].…”

“…134. Their study can be used to rule out models of the underlying dynamics [22,56,57]. However, cumulant ratios can be robust to decoherence induced by coupling to an external bath, as shown by simulations of the spin-boson quantum model with independent oscillators being coupled to the z component of each spin [22].…”

Coherent quantum annealing in a programmable 2000-qubit Ising chain

“…distribution can be reproduced by classical models [24]. For example, the scaling exponent −1/2 (Eq.…”

Quantum Optimization of Maximum Independent Set using Rydberg Atom Arrays

“…We now turn to a more systematic calculation of the total number of defects 1 − R. To generalize the mechanism described above, we consider that the effect of the ordering dynamics is to initially partition a system of a given size into "protodomains" (see Fig. S12) of the same length scale over which the order parameter stabilizes [73]. At the boundary between adjacent domains, kinks form with a given probability p. Conversely, with probability (1 − p), no kink is formed and the two adjacent protodomains coalesce to form a larger domain.…”