  The number of topological defects created in a system driven through a
quantum phase transition exhibits a power-law scaling with the driving time.
This universal scaling law is the key prediction of the Kibble-Zurek mechanism
(KZM), and testing it using a hardware-based quantum simulator is a coveted
goal of quantum information science. Here we provide such a test using quantum
annealing. Specifically, we report on extensive experimental tests of
topological defect formation via the one-dimensional transverse-field Ising
model on two different D-Wave quantum annealing devices. We find that the
quantum simulator results can indeed be explained by the KZM for open-system
quantum dynamics with phase-flip errors, with certain quantitative deviations
from the theory likely caused by factors such as random control errors and
transient effects. In addition, we probe physics beyond the KZM by identifying
signatures of universality in the distribution and cumulants of the number of
kinks and their decay, and again find agreement with the quantum simulator
results. This implies that the theoretical predictions of the generalized KZM
theory, which assumes isolation from the environment, applies beyond its
original scope to an open system. We support this result by extensive numerical
computations. To check whether an alternative, classical interpretation of
these results is possible, we used the spin-vector Monte Carlo model, a
candidate classical description of the D-Wave device. We find that the degree
of agreement with the experimental data from the D-Wave annealing devices is
better for the KZM, a quantum theory, than for the classical spin-vector Monte
Carlo model, thus favoring a quantum description of the device. Our work
provides an experimental test of quantum critical dynamics in an open quantum
system, and paves the way to new directions in quantum simulation experiments.
