Notes Toward "Quantum Computing for Dogs"

Maybe the start of something to work on

Back when I was working on How to Teach [Quantum] Physics to Your Dog, I joked about doing a chapter on quantum computing, but that never happened. I just could not for the life of me think of a way to make quantum computing relevant to Emmy’s interests, namely trying to catch the squirrels and bunnies in our back yard, and trying to get me to give her more treats. The best I could come up with was cracking RSA encryption to unlock infinite money for the purchase of treats, but that was, y’know, a little dark for the otherwise cheerful vibe of the books.

I mention that because I have a light teaching load this fall term, and have been kicking around ideas of some sort of relatively limited project I could take on in that time¹. One possibility, following on teaching Quantum Optics and Quantum Information last winter, would be to do something on that topic: quantum computing for a general audience.

Photo by Markus Winkler on Unsplash

This is a somewhat tricky undertaking for me, since I’m not really a quantum computing guy. I’ve followed the field from outside, and taught it to undergrads, but it’s not like I’m doing cutting-edge research on the subject. There are lots of people out there whose formal credentials are way better than mine when it comes to establishing credibility as an Expert.

I do, however, have a particular set of skills, in the area of breaking down complex mathematical subjects and making them seem more approachable to non-physicists. And this is a place where that might well be highly useful: The field has advanced considerably in the years since I was writing funny dialogue for the Queen of Niskayuna, and it’s drawn investment from governments and major corporations at a level that ought to get public attention². There’s not a ton of good material out there on the subject, though— the stuff that’s correct tends to be a bit too technical, and the stuff that’s non-technical too often slides toward batshit crazy. So this might be worth taking a run at, using the undergrad courses I’ve taught as a starting point.

This is not a book-length project, but it’s not going to be just blog posts, either— I’m hoping to get somebody to pay me for this at a higher rate than what I get from here³. I do have this space, though, so will use it for a bit of thinking-out-loud about the general subject and how to break it down.

So, quantum computing for non-mathematically-inclined humans: What’s essential, here? I’ve got a public talk on this that I dust off from time to time, and still haven’t really come up with a better summation of the core idea than the one-sentence description I use for that:

A quantum computer exploits properties of quantum physics to perform certain types of calculations more efficiently than any classical computer

That captures both of the elements I regard as really essential to communicate about quantum computing: 1) it’s based on the clever manipulation of very general features of quantum physics, and 2) it’s only really useful within a fairly limited space of problems.

Of course, it works as a one-sentence summary because there’s a lot packed into those words. When I use this to frame a public lecture I do it in three parts⁴:

1. “Properties of Quantum Physics”: This can, to a large extent, be boiled down to the single observation that everything has both particle and wave nature. When you prepare a quantum system in a particular state, it will evolve into the future in a manner that is fundamentally wave-like, and when you measure its state at a later time, those waves determine the probability of each possible outcome. The whole business of quantum computing comes down to engineering ways to make those waves come together in a way that gives you a very high probability that the measurement result is the correct answer to whatever computation you’re trying to do⁵.

   

   All is waves with nothing waving across no distance at all.

2. “Certain Types of Calculations”: The engineering-of-wave-evolution framing leads very nicely into the observation that this only works some of the time. There are classes of problems where those wave properties allow for the kind of evolution that you’re looking for, generally problems involving collective properties of some kind. The two killer apps of the field have this character: factoring numbers is about figuring out which two small numbers multiply together to get the big one you have, and database search is about identifying which members of a large set of states have a particular property of interest. It’s somewhat obvious that these are situations where having a wavefunction that’s exploring a little bit of everything is a net win.

3. “More Efficiently Than Any Classical Computer”: This one’s a tiny bit of a cheat, in that it breaks into two sub-points, corresponding to two different meanings of “efficient.” One has to do with the number of steps required to do a particular computation, which is the core of classical computing theory: for the right kind of problems, you can get to an answer with fewer steps using a quantum computer. The other meaning has to do with physical resources, and leads to the notion of “analog(ue) quantum computing”: if you’re trying to simulate a collection of quantum objects on a classical computer, the same wave properties that power quantum computing become a major headache, as you need extra memory and extra operations to keep track of them. If you can find a way to make the qubits of your quantum computer evolve in the exact same way that the quantum objects you’re interested in do, you can reduce that overhead dramatically.

I think this works well as a way to structure a discussion of the subject— obviously, because I keep giving that talk⁶. For something going into greater detail than a one-hour public lecture, each of these break down further: separate discussions of superposition, measurement and probability, and entanglement; problems where access to those quantum resources make otherwise impossible things possible (teleportation, dense coding); individual algorithms that reduces computational complexity (Shor, Grover); systems where quantum simulation is a useful thing to do.

There are two other chunks to the story, as well:

4. Physical Implementations: If you’re going to make a quantum computer, you need a particular physical system, and at present there isn’t a super clear winner— there are multiple potential platforms (superconducting junctions, trapped ions, neutral atoms, maybe color centers in solids) under active development, and other options in a more speculative state. These are each worth some individual discussion.

5. Errors and the Correction Thereof: Reality is messy, and there will inevitably be undesirable interactions that screw with the states of the qubits in your computer. A working system will either need to be inherently robust, or employ some clever scheme to fix errors on the fly. That’s a much trickier business than in a classical computer, and worth some discussion.

I think those five high-level bullet points capture the essence of what a worthwhile “Quantum Computing for Dogs” sort of project would need to cover. Which is both kind of a lot, and probably a manageable amount? The trick is getting the ordering right, both for the high-level groups of topics and the subparts of each topic.

But this post is just meant to be a sketch of the outline of the idea, so that’s probably enough for today…

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And if you either think I’m crazy or see a huge gap in my high-level overview, the comments will be open:

1. “Relatively limited” because my teaching load gets heavy again in the Winter term, and I’m still Chair, with all the administrative headaches that entails. So the ideal project here would be something that might feasibly wrap up the heavy-lifting phase by December.

2. Though that interest may be fading a bit now, thanks to competition from a different roiling cauldron of linear algebra.

3. Though, you know, if you have a few hundred friends you can talk into buying subscriptions to this Substack, I might reconsider…

4. Three, after all, is the magic number.

5. A tip of the hat to Shelby Kimmel, who was the first person I heard frame it this way.

6. Speaking of which, if you’re in a position where you book speakers for things, I’m generally happy to go places and talk to people…