3Q: Scott Aaronson on Google’s New Quantum-Computing Paper

Estimated reading time: 7 minutes

A: In the current model of the D-Wave chip, there are 1,000 or so qubits [quantum bits], but they’re organized into clusters of eight qubits each. The qubits within each cluster are very tightly connected to each other, and between clusters there are only weaker connections. I think that this is the best evidence we’ve had so far for quantum tunneling behavior, at least at the level of the eight-bit clusters.

The main way that they got an advantage over simulated annealing in these results was by taking advantage of the fact that quantum tunneling — or anything that correlates all the qubits within the cluster — can flip all the bits within each cluster at the same time, whereas simulated annealing is going to try flipping the bits one by one, then see that that’s not a good idea, then flip them all back, and not realize that by flipping all eight of them, you could get something better.

The case has now clearly been made that whatever the D-Wave device is doing, it’s something that can tunnel past this eight-qubit barrier. Of course, that still doesn’t mean that you’re doing anything faster than you could do it classically.

Q: What does it mean, then?

A: In computer science, normally we care about asymptotic speedup: We care about, “What is your running time as a function of the size of the problem? Does it grow linearly? Does it grow quadratically?” The constant that’s in front — Does it take 5N steps? Does it take 10N steps? — we don’t care that much about. We just care that it’s linear in N.

In the Google paper, they discuss two classical algorithms that do match the asymptotic performance — and one of them beats the real-world performance — of the D-Wave machine. So besides simulated annealing, there are two more classical algorithms that are actors in this story. One of them is quantum Monte Carlo, which is actually a classical optimization method, but it’s one that’s inspired by quantum mechanics.

In this new Google paper, they say that even though quantum Monte Carlo has the same asymptotic performance, the constant is way, way better for the D-Wave machine. The constant is about 100 million times better.

There are two huge issues that I would have with that. The first issue is that the problem instances where the comparison is being done are basically for the problem of simulating the D-Wave machine itself. There were $150 million dollars that went into designing this special-purpose hardware for this D-Wave machine and making it as fast possible. So in some sense, it’s no surprise that this special-purpose hardware could get a constant-factor speedup over a classical computer for the problem of simulating itself.

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