# The recent “How Quantum is the D-Wave Machine?” Shin et.al. paper

Generally I try to avoid commenting on ongoing scientific debates. My view is that good explanations survive scrutiny, and bad explanations do not, and that our role in bringing quantum computers kicking and screaming into the world is to, well, build quantum computers. If people love what we build, and we do everything we can to adjust our approach to make better and better gear for the people who love our computers, we have succeeded and I sleep well.

I am going to make an exception here. Many people have asked me specifically about the recent Shin et. al. paper, and I’d like to give you my perspective on it.

In my world view, science is fundamentally about good explanations.

What does this mean? David Deutsch eloquently describes this point of view in this TED talk.  There is a transcript here. He proposes and defends the idea that progress comes from discovering good explanations for why things are the way they are. You would not be reading this right now if we had not come up with good explanations for what electrons are.

We can and should directly apply these ideas to the question of whether D-Wave processors are quantum or classical. From my perspective, if the correct explanation were ‘it’s classical’, that would be critical to know as quickly as possible, because we could then identify why this was so, and attempt to fix whatever was going wrong. That’s kind of my job. So I need to really understand this sort of thing.

Here are two competing explanations for experiments performed on D-Wave processors.

Explanation #1. D-Wave processors are inherently quantum mechanical, and described by open quantum systems models where the energy scale of the noise is much less than the energy scale of the central quantum system.

Explanation #2. D-Wave processors are inherently classical, and can be described by a classical model with no need to invoke quantum mechanics.

The Shin et. al. paper claims that Explanation #2 is a correct explanation of D-Wave processors. Let’s examine that claim.

Finding good explanations for experimental results

It is common practice that whenever an experiment is reported demonstrating quantum mechanical (or in general non-classical) effects, researchers look for classical models that can provide the same results. A successful theory, however, needs to explain all existing experimental results and not just a few select ones. For example, the classical model of light with the assumption of ether could successfully explain many experiments at the beginning of the 20th century. Only a few unexplained experiments were enough to lead to the emergence of special relativity.

In the case of finding good explanations for the experimental results available for D-Wave hardware, there is a treasure trove of experimental data available. Here is just a small sample. There are experimental results available on single qubits (Macroscopic Resonant Tunneling & Landau-Zener), two qubits (cotunneling) and multiple qubits (now up to about 500) (the eight qubit Nature paper, entanglementresults at 16 qubits, the Boixo et.al. paper).

Let’s see what we get when we apply our two competing explanations of what’s going on inside D-Wave processors to all of this data.

If we assume Explanation #1, we find that a single simple quantum model perfectly describes every single experiment ever done. In the case of the simpler data sets, experimental results agree with quantum mechanics with no free parameters, as it is possible to characterize every single term in the system’s Hamiltonian, including the noise terms.

Explanation #2 however completely fails on every single experiment listed above, except for the Boixo et.al. data (I’ll give you an explanation of why this is shortly). In particular, the eight qubit quantum entanglement measured in Lanting et al. can never be explained by such a model, which rules it out as an explanation of the underlying behavior of the device. Note that this is a stronger result than it’s simply a bad explanation — the model proposed in Shin et. al. makes a prediction about an experiment that you can easily perform on D-Wave processors that contradicts what is observed.

Why the model proposed works in describing the Boixo et.al. data

Because the Shin et. al. model makes predictions that contradict the experimental data for most of the experiments that have been performed on D-Wave chips, it is clearly not a correct explanation of what’s going on inside the processors. So what’s the explanation for the agreement in the case of the Boixo paper? Here’s a possibility, which we can test.

The experiment performed in the Boixo et. al. paper considered a specific use of the processors. This use involved solving a specifically chosen type of problem. It turns out that for this type of problem, multi-qubit quantum dynamics and therefore entanglement are not necessary for the hardware to reach good solutions. In other words, for this experiment, a Bad Explanation (a classical model) can be concocted that matches the results of a fully quantum system.

To be more specific, the Shin et. al. model replaces terms like $J_{ij} \sigma^z_i \sigma^z_j$ with $J_{ij} <\sigma^z_i><\sigma ^z_j>$, where $\sigma^z_i$ is a Pauli matrix and $<\sigma^z_i>$ is the quantum average of $\sigma^z_i$. Since all quantum correlations are gone after such averaging, you can model $<\sigma^z_i>$ as a classical magnetic moment in a 2D plane. But now it is clear that any experiments relying on multi-qubit quantum correlation and entanglement cannot be explained by this simple model.

I’ve proposed an explanation for the agreement between the Shin et.al. model and this particular experiment — that the hardware is fundamentally quantum, but for the particular problem type run, this won’t show up because the problem type is ‘easy’ (in the sense that good solutions can be found without requiring multi-qubit dynamics, and an incorrect classical model can be proposed that nevertheless agrees with the experimental data).

How do we test this explanation? We change the problem type to one where a fundamental difference in experimental outcome between the processor hardware and any classical model is expected. If the Shin et. al. model continues to describe what is observed in that situation, then we have a meaningful result that disagrees with the ‘hardware is quantum’ explanation. If it disagrees with experiment, that supports the ‘hardware is quantum’ and the ‘type of problem originally studied is expected to show the same experimental results for quantum and classical models so it’s just a bad choice if that’s your objective’ explanations.

So a very important test to help determine what is truly going on is to make this change, measure the results and see what’s up. I believe that some of the folks working on our systems are doing this now. Looking forward to seeing the results!

The best explanation we have now is that D-Wave processors are beautifully quantum mechanical

The explanation that D-Wave processors are fundamentally quantum mechanical beautifully explains every single experiment that has ever been performed on them. The degree of agreement is astonishing. The results on the smallest systems, such as the individual qubits, are like nothing I’ve ever seen in terms of agreement of theory and experiment. Some day these will be in textbooks as examples of open quantum systems.

No classical model has ever been proposed that simultaneously explains all of the experiments listed above.

The specific model proposed in Shin et.al. focuses only on one experiment for which there was no expectation of an experimental difference between quantum and classical models and completely (and from my perspective disingenuously) ignores the entire remainder of the mountains of experimental data on the device.

For these reasons, the Shin et.al. results have no validity and no importance.

As an aside, I was disappointed when I saw what they were proposing. I had heard through the grapevine that Umesh Vazirani was preparing some really cool classical model that described the data referred to above and I was actually pretty excited to see it.

When I saw how trivially wrong it was it was like opening a Christmas present and getting socks.

# NASA Experts Available For Interviews About Quantum Computing | NASA

This is cool! Check out the link for a resource that can help answer questions about D-Wave quantum computers from the perspective of our users at NASA.