What may or may not be the world's first commercial quantum computer was put to the test recently with optimization problems from Ramsey Theory.
As was reported on September 25 in Physical Review Letters, a machine made by Canadian company D-Wave Systems and running (according to D-Wave) a 128-qubit processor successfully implemented an algorithm to calculate Ramsey numbers, though it did not arrive at any previously unknown results.
Skeptics doubt the coherence of the D-Wave computer's qubits, and suggest that Ramsey number problems may not be the best way to gauge the computing power of a supposed quantum computer. Wired's coverage paraphrases an analogy it credits to physicist Frank Gaitan (University of Maryland):
Imagine a company says they built a self-driving car and then placed it on top of a hill. They start the car and it rolls to the bottom of the hill. You could say the car drove itself down or you could say it was carried downhill by gravity, and it might be hard to determine which one it is.