UPDATE – Geordie Rose, CTO of DWave, commented.
This response had nothing to do with DWave — it’s just an update on how Google feels about their experience with the machine so far. It’s only a response to anything insofar as the articles about the paper have been absolutely terrible and completely unrelated to what the paper actually showed.
A portfolio of custom solvers designed to beat the hardware on its own turf is competitive
So what do we get if we pit the hardware against these solvers designed to compete with the D-Wave hardware on its own turf? The following pattern emerges: For each solver, there are problems for which the classical solver wins or at least achieves similar performance. But the inverse is also true. For each classical solver, there are problems for which the hardware does much better.
For example, if you use random problems as a benchmark, the fast simulated annealers take about the same time as the hardware.
But importantly, if you move to problems with structure, then the hardware does much better.
This example is intriguing from a physics perspective, since it suggests co-tunneling is helping the hardware figure out that the spins in each unit cell have to to be flipped as a block to see a lower energy state.
But if we form a portfolio of the classical solvers and keep the best solution across all of them, then this portfolio is still competitive with the current version of the hardware. Again, a good example is the structured problem in Figure 3 in the slideshow. It slows down the annealers, but Alex Selby’s code has no problem with it and obtains the solution about as fast as the hardware does.
Sparse connectivity is a major limitation
A principal reason the portfolio solver is still competitive right now is actually rather mundane — the qubits in the current chip are still only sparsely connected. As the connectivity in future versions of quantum annealing processors gets denser, approaches such as Alex Selby’s will be much less effective.
One indication that sparse connectivity is a culprit also comes from well-understood examples such as the “Hamming weight function with a barrier” problem — quantum annealing tackles it easily but classical annealing fails. But we haven’t been able to implement such examples as benchmark problems yet because of the sparse connectivity.
On structured problems the behaviors of quantum annealing (QA) and simulated classical annealing (SA) are very different. QA slows down much less as the instances get larger. In this example of a structured problem, all variables within one unit cell of the Chimera graph are negatively (ferromagnetically) coupled, while unit cells are coupled randomly to each other.
A big data approach may lead to new conclusions
So will we have to wait for the next generation chip with higher connectivity before we can hope to see the hardware outperform the portfolio solver? Until very recently we thought so. But remember that these latest benchmarking results were obtained from relatively small datasets — just 1000 instances in the ones that got recent attention.
It’s easy to make premature conclusions on such small sets, as there are not enough data points from possible subsets of problem instances that might indicate a speedup. Moreover, as several groups independently discovered, such random problems tend to be too easy and don’t challenge the quantum hardware or classical solvers.
Ever since the D-Wave 2 machine became operational at NASA Ames, the head of our benchmarking efforts, Sergio Boixo, made sure we used every second of machine time to take data from running optimization problems. Simultaneously we gave the same problems to a portfolio of the best classical solvers we’re aware of. We now have data for 400,000 problem instances. This is the largest set collected to date, and it keeps growing.
Eyeballing this treasure trove of data, we’re now trying to identify a class of problems for which the current quantum hardware might outperform all known classical solvers. But it will take us a bit of time to publish firm conclusions, because as Rønnow et al’s recent work shows, you have to carefully exclude a number of factors that can mask or fake a speedup.