Monthly Archives: February 2025

Some FAQ for Microsoft’s Majorana 1 Chip

Recently, Microsoft announced a fancy new quantum computing chip called Majorana 1. I’ve noticed quite a bit of confusion about what they actually announced, and while there’s a great FAQ page about it on the quantum computing blog Shtetl Optimized, the post there aims at a higher level, assuming you already know the basics. You can think of this post as a complement to that one, that tries to cover some basic things Shtetl Optimized took for granted.

Q: In the announcement, Microsoft said:

“It leverages the world’s first topoconductor, a breakthrough type of material which can observe and control Majorana particles to produce more reliable and scalable qubits, which are the building blocks for quantum computers.”

That sounds wild! Are they really using particles in a computer?

A: All computers use particles. Electrons are particles!

Q: You know what I mean!

A: You’re asking if these are “particle physics” particles, like the weird types they try to observe at the LHC?

No, they’re not.

Particle physicists use a mathematical framework called quantum field theory, where particles are ripples in things called quantum fields that describe properties of the universe. But they aren’t the only people to use that framework. Instead of studying properties of the universe you can study properties of materials, weird alloys and layers of metal and crystal that do weird and useful things. The properties of these materials can be approximately described with the same math, with quantum fields. Just as the properties of the universe ripple to produce particles, these properties of materials ripple to produce what are called quasiparticles. Ultimately, these quasiparticles come down to movements of ordinary matter, usually electrons in the original material. They’re just described with a kind of math that makes them look like their own particles.

Q: So, what are these Majorana particles supposed to be?

A: In quantum field theory, most particles come with an antimatter partner. Electrons, for example, have partners called positrons, with a positive electric charge instead of a negative one. These antimatter partners have to exist due to the math of quantum field theory, but there is a way out: some particles are their own antimatter partner, letting one particle cover both roles. This happens for some “particle physics particles”, but all the examples we’ve found are a type of particle called a “boson”, particles related to forces. In 1937, the physicist Ettore Majorana figured out the math you would need to make a particle like this that was a fermion instead, the other main type of particle that includes electrons and protons. So far, we haven’t found one of these Majorana fermions in nature, though some people think the elusive neutrino particles could be an example. Others, though, have tried instead to find a material described by Majorana’s theory. This should in principle be easier, you can build a lot of different materials after all. But it’s proven quite hard for people to do. Back in 2018, Microsoft claimed they’d managed this, but had to retract the claim. This time, they seem more confident, though the scientific community is still not convinced.

Q: And what’s this topoconductor they’re talking about?

A: Topoconductor is short for topological superconductor. Superconductors are materials that conduct electricity much better than ordinary metals.

Q: And, topological means? Something about donuts, right?

A: If you’ve heard anything about topology, you’ve heard that it’s a type of mathematics where donuts are equivalent to coffee cups. You might have seen an animation of a coffee cup being squished and mushed around until the ring of the handle becomes the ring of a donut.

This isn’t actually the important part of topology. The important part is that, in topology, a ball is not equivalent to a donut.

Topology is the study of which things can change smoothly into one another. If you want to change a donut into a ball, you have to slice through the donut’s ring or break the surface inside. You can’t smoothly change one to another. Topologists study shapes of different kinds of things, figuring out which ones can be changed into each other smoothly and which can’t.

Q: What does any of that have to do with quantum computers?

A: The shapes topologists study aren’t always as simple as donuts and coffee cups. They can also study the shape of quantum fields, figuring out which types of quantum fields can change smoothly into each other and which can’t.

The idea of topological quantum computation is to use those rules about what can change into each other to encode information. You can imagine a ball encoding zero, and a donut encoding one. A coffee cup would then also encode one, because it can change smoothly into a donut, while a box would encode zero because you can squash the corners to make it a ball. This helps, because it means that you don’t screw up your information by making smooth changes. If you accidentally drop your box that encodes zero and squish a corner, it will still encode zero.

This matters in quantum computing because it is very easy to screw up quantum information. Quantum computers are very delicate, and making them work reliably has been immensely challenging, requiring people to build much bigger quantum computers so they can do each calculation with many redundant backups. The hope is that topological superconductors would make this easier, by encoding information in a way that is hard to accidentally change.

Q: Cool. So does that mean Microsoft has the best quantum computer now?

A: The machine Microsoft just announced has only a single qubit, the quantum equivalent of just a single bit of computer memory. At this point, it can’t do any calculations. It can just be read, giving one or zero. The hope is that the power of the new method will let Microsoft catch up with companies that have computers with hundred of qubits, and help them arrive faster at the millions of qubits that will be needed to do anything useful.

Q: Ah, ok. But it sounds like they accomplished some crazy Majorana stuff at least, right?

A: Umm…

Read the Shtetl-Optimized FAQ if you want more details. The short answer is that this is still controversial. So far, the evidence they’ve made public isn’t enough to show that they found these Majorana quasiparticles, or that they made a topological superconductor. They say they have more recent evidence that they haven’t published yet. We’ll see.

Bonus Material for “How Hans Bethe Stumbled Upon Perfect Quantum Theories”

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I had an article last week in Quanta Magazine. It’s a piece about something called the Bethe ansatz, a method in mathematical physics that was discovered by Hans Bethe in the 1930’s, but which only really started being understood and appreciated around the 1960’s. Since then it’s become a key tool, used in theoretical investigations in areas from condensed matter to quantum gravity. In this post, I thought I’d say a bit about the story behind the piece and give some bonus material that didn’t fit.

When I first decided to do the piece I reached out to Jules Lamers. We were briefly office-mates when I worked in France, where he was giving a short course on the Bethe ansatz and the methods that sprung from it. It turned out he had also been thinking about writing a piece on the subject, and we considered co-writing for a bit, but that didn’t work for Quanta. He helped me a huge amount with understanding the history of the subject and tracking down the right sources. If you’re a physicist who wants to learn about these things, I recommend his lecture notes. And if you’re a non-physicist who wants to know more, I hope he gets a chance to write a longer popular-audience piece on the topic!

If you clicked through to Jules’s lecture notes, you’d see the word “Bethe ansatz” doesn’t appear in the title. Instead, you’d see the phrase “quantum integrability”. In classical physics, an “integrable” system is one where you can calculate what will happen by doing an integral, essentially letting you “solve” any problem completely. Systems you can describe with the Bethe ansatz are solvable in a more complicated quantum sense, so they get called “quantum integrable”. There’s a whole research field that studies these quantum integrable systems.

My piece ended up rushing through the history of the field. After talking about Bethe’s original discovery, I jumped ahead to ice. The Bethe ansatz was first used to think about ice in the 1960’s, but the developments I mentioned leading up to it, where experimenters noticed extra variability and theorists explained it with the positions of hydrogen atoms, happened earlier, in the 1930’s. (Thanks to the commenter who pointed out that this was confusing!) Baxter gets a starring role in this section and had an important role in tying things together, but other people (Lieb and Sutherland) were involved earlier, showing that the Bethe ansatz indeed could be used with thin sheets of ice. This era had a bunch of other big names that I didn’t have space to talk about: C. N. Yang makes an appearance, and while Faddeev comes up later, I didn’t mention that he had a starring role in the 1970’s in understanding the connection to classical integrability and proposing a mathematical structure to understand what links all these different integrable theories together.

I vaguely gestured at black holes and quantum gravity, but didn’t have space for more than that. The connection there is to a topic you might have heard of before if you’ve read about string theory, called AdS/CFT, a connection between two kinds of world that are secretly the same: a toy model of gravity called Anti-de Sitter space (AdS) and a theory without gravity that looks the same at any scale (called a Conformal Field Theory, or CFT). It turns out that in the most prominent example of this, the theory without gravity is integrable! In fact, it’s a theory I spent a lot of time working with back in my research days, called N=4 super Yang-Mills. This theory is kind of like QCD, and in some sense it has integrability for similar reasons to those that Feynman hoped for and Korchemsky and Faddeev found. But it actually goes much farther, outside of the high-energy approximation where Korchemsky and Faddeev’s result works, and in principle seems to include everything you might want to know about the theory. Nowadays, people are using it to investigate the toy model of quantum gravity, hoping to get insights about quantum gravity in general.

One thing I didn’t get a chance to mention at all is the connection to quantum computing. People are trying to build a quantum computer with carefully-cooled atoms. It’s important to test whether the quantum computer functions well enough, or if the quantum states aren’t as perfect as they need to be. One way people have been testing this is with the Bethe ansatz: because it lets you calculate the behavior of special systems perfectly, you can set up your quantum computer to model a Bethe ansatz, and then check how close to the prediction your results are. You know that the theoretical result is complete, so any failure has to be due to an imperfection in your experiment.

I gave a quick teaser to a very active field, one that has fascinated a lot of prominent physicists and been applied in a wide variety of areas. I hope I’ve inspired you to learn more!

Valentine’s Day Physics Poem 2025

Integration by Parts, Evolved

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I posted what may be my last academic paper today, about a project I’ve been working on with Matthias Wilhelm for most of the last year. The paper is now online here. For me, the project has been a chance to broaden my horizons, learn new skills, and start to step out of my academic comfort zone. For Matthias, I hope it was grant money well spent.

I wanted to work on something related to machine learning, for the usual trendy employability reasons. Matthias was already working with machine learning, but was interested in pursuing a different question.

When is machine learning worthwhile? Machine learning methods are heuristics, unreliable methods that sometimes work well. You don’t use a heuristic if you have a reliable method that runs fast enough. But if all you have are heuristics to begin with, then machine learning can give you a better heuristic.

Matthias noticed a heuristic embedded deep in how we do particle physics, and guessed that we could do better. In particle physics, we use pictures called Feynman diagrams to predict the probabilities for different outcomes of collisions, comparing those predictions to observation to look for evidence of new physics. Each Feynman diagram corresponds to an integral, and for each calculation there are hundreds, thousands, or even millions of those integrals to do.

Luckily, physicists don’t actually have to do all those integrals. It turns out that most of them are related, by a slightly more advanced version of that calculus class mainstay, integration by parts. Using integration by parts you can solve a list of equations, finding out how to write your integrals in terms of a much smaller list.

How big a list of equations do you need, and which ones? Twenty-five years ago, Stefano Laporta proposed a “golden rule” to choose, based on his own experience, and people have been using it (more or less, with their own tweaks) since then.

Laporta’s rule is a heuristic, with no proof that it is the best option, or even that it will always work. So we probably shouldn’t have been surprised when someone came up with a better heuristic. Watching talks at a December 2023 conference, Matthias saw a presentation by Johann Usovitsch on a curious new rule. The rule was surprisingly simple, just one extra condition on top of Laporta’s. But it was enough to reduce the number of equations by a factor of twenty.

That’s great progress, but it’s also a bit frustrating. Over almost twenty-five years, no-one had guessed this one simple change?

Maybe, thought Matthias and I, we need to get better at guessing.

We started out thinking we’d try reinforcement learning, a technique where a machine is trained by playing a game again and again, changing its strategy when that strategy brings it a reward. We thought we could have the machine learn to cut away extra equations, getting rewarded if it could cut more while still getting the right answer. We didn’t end up pursuing this very far before realizing another strategy would be a better fit.

What is a rule, but a program? Laporta’s golden rule and Johann’s new rule could both be expressed as simple programs. So we decided to use a method that could guess programs.

One method stood out for sheer trendiness and audacity: FunSearch. FunSearch is a type of algorithm called a genetic algorithm, which tries to mimic evolution. It makes a population of different programs, “breeds” them with each other to create new programs, and periodically selects out the ones that perform best. That’s not the trendy or audacious part, though, people have been doing that sort of genetic programming for a long time.

The trendy, audacious part is that FunSearch generates these programs with a Large Language Model, or LLM (the type of technology behind ChatGPT). Using an LLM trained to complete code, FunSearch presents the model with two programs labeled v0 and v1 and asks it to complete v2. In general, program v2 will have some traits from v0 and v1, but also a lot of variation due to the unpredictable output of LLMs. The inventors of FunSearch used this to contribute the variation needed for evolution, using it to evolve programs to find better solutions to math problems.

We decided to try FunSearch on our problem, modifying it a bit to fit the case. We asked it to find a shorter list of equations, giving a better score for a shorter list but a penalty if the list wasn’t able to solve the problem fully.

Some tinkering and headaches later, it worked! After a few days and thousands of program guesses, FunSearch was able to find a program that reproduced the new rule Johann had presented. A few hours more, and it even found a rule that was slightly better!

But then we started wondering: do we actually need days of GPU time to do this?

An expert on heuristics we knew had insisted, at the beginning, that we try something simpler. The approach we tried then didn’t work. But after running into some people using genetic programming at a conference last year, we decided to try again, using a Python package they used in their work. This time, it worked like a charm, taking hours rather than days to find good rules.

This was all pretty cool, a great opportunity for me to cut my teeth on Python programming and its various attendant skills. And it’s been inspiring, with Matthias drawing together more people interested in seeing just how much these kinds of heuristic methods can do there. I should be clear though, that so far I don’t think our result is useful. We did better than the state of the art on an example, but only slightly, and in a way that I’d guess doesn’t generalize. And we needed quite a bit of overhead to do it. Ultimately, while I suspect there’s something useful to find in this direction, it’s going to require more collaboration, both with people using the existing methods who know better what the bottlenecks are, and with experts in these, and other, kinds of heuristics.

So I’m curious to see what the future holds. And for the moment, happy that I got to try this out!

4 gravitons

Stories about physics from someone who's been there