  The observation of an unequivocal quantum speedup remains an elusive
objective for quantum computing. The D-Wave quantum annealing processors have
been at the forefront of experimental attempts to address this goal, given
their relatively large numbers of qubits and programmability. A complete
determination of the optimal time-to-solution (TTS) using these processors has
not been possible to date, preventing definitive conclusions about the presence
of a scaling advantage. The main technical obstacle has been the inability to
verify an optimal annealing time within the available range. Here we overcome
this obstacle and present a class of problem instances for which we observe an
optimal annealing time using a D-Wave 2000Q processor over a range spanning up
to more than $2000$ qubits. This allows us to perform an optimal TTS
benchmarking analysis and perform a comparison to several classical algorithms,
including simulated annealing, spin-vector Monte Carlo, and discrete-time
simulated quantum annealing. We establish the first example of a scaling
advantage for an experimental quantum annealer over classical simulated
annealing: we find that the D-Wave device exhibits certifiably better scaling
than simulated annealing, with $95\%$ confidence, over the range of problem
sizes that we can test. However, we do not find evidence for a quantum speedup:
simulated quantum annealing exhibits the best scaling by a significant margin.
Our construction of instance classes with verifiably optimal annealing times
opens up the possibility of generating many new such classes, paving the way
for further definitive assessments of scaling advantages using current and
future quantum annealing devices.

Quantum Physics