Emilie Huffman: seeking to understand quantum phase transitions

Young scientists who come to Perimeter Institute as postdoctoral researchers or graduate students frequently end up with stellar careers. This year, we are interviewing several of our alumni to find out what they are doing now.

Today’s interview is with Emilie Huffman, who is currently Assistant Professor of Physics at Wake Forest University in North Carolina.

She was a postdoctoral researcher at Perimeter Institute from 2019 to 2025. She was also a Perimeter Scholars International Fellow (PSI) at Perimeter, teaching students in PSI master’s program. Her research on quantum critical behaviour may contribute to the discovery of new materials and to making quantum computers more robust.

Huffman recently returned to Perimeter for a research visit. This is a lightly edited version of our interview:

Tell us about yourself. When were you at Perimeter, and what do you study?

I was at Perimeter from 2019 to 2025, and I work on calculations that are at the intersection of particle physics and condensed matter physics.

Specifically, I’m interested in quantum critical phenomena, where you have many particles interacting at temperatures close to absolute zero. The more particles you have in a quantum system, the more computing resources are needed to study their behaviour, and this grows in an exponential way. Every time you add another particle, the number of states doubles. So if you have, for example, 300 particles, suddenly it takes longer than the age of the universe to calculate.  

Naively, you would say that would be very expensive (time wise and memory wise), and these calculations would be out of reach. But people find all kinds of clever ways to study these systems in what's called polynomial time. That's a human timescale, and it is a problem I'm fascinated with. I spend a lot of my time chipping away at new ways to study these systems in polynomial time.

Why study quantum critical behaviour? How can it be applied?

Quantum critical behaviour is related to phase transitions, but these are a little bit different from the phase transitions in our typical experience.

Typical phase transitions might include water boiling, or, for example, if you take a magnet and you heat it up enough, it stops being magnetic.

What causes these transitions are thermal fluctuations. You add heat and then because of this, the particles will be excited; they fluctuate, and eventually, the way the material behaves will change and enter a new phase. So that's the typical phase transition.

But if you were to study quantum phase transitions instead, those transitions are not due to thermal fluctuations. Instead, they're due to quantum fluctuations.

That means that even if you took a material down to absolute zero, where you could have no thermal fluctuations, you could still have a quantum phase transition due to quantum fluctuations, and that can only be explained with quantum mechanics.

Instead of changing the temperature, you can do things such as change the pressure of your system or add an external magnetic field. At some critical value, you get a phase transition.

What I do is to use numerics to study how these quantum phase transitions can be brought about and how you can get new phases.

Is this something that can be used in quantum computers?

Yes. Typically, if you have a phase that has, say, some entanglement or some fragmentation or a certain topology, there can be resistance to disturbances in the environment.

These types of phases are useful for quantum computing, because one of the big challenges in quantum computing is that qubits are very sensitive to different disturbances in the environment. If we can find ways to make them robust, then we can build on them, or scale up our quantum computer in a better way.

Does this help to solve the problem of “noise” in quantum computing systems?

Yes, and there are a few approaches to that.

One thing I don't work on as much is quantum error correction. But the other approach, which I do work on, is really trying to avoid these errors in the first place.

In topology, you may have heard about the concept of braiding. If you imagine braiding your hair, even if you don't tie it off at the end, it's resistant to going back to the unbraided state. This is the idea behind creating these states that are resistant.

Would these quantum resistant states be in hardware?

Yes, this would be the hardware, and so that's why critical phenomena are relevant to this, because the question is, what type of external things can we do to a material to put it into a phase that creates these robust states that are resistant to disturbance.

Tell us about Wake Forest University and your research group there.

Wake Forest University really specializes in the sciences in its graduate programs. It has three graduate programs in physics, biology, and chemistry. It also focuses on having strong undergraduate teaching.

My group has two students in it now, and we are looking at hiring a postdoctoral researcher.

We work on both algorithms for classical computers and quantum computers to be able to calculate critical phenomena in polynomial time (human scale time frames), to learn about how we can facilitate certain types of phases.

So, in my example of water boiling, or heating up a magnet so it is no longer magnetic --- both, in certain regimes, fall into the same universal class, which means that there's a set of numbers that describes these phase transitions. They both have the same set of universal numbers that describe them and due to some symmetry correspondences, they both have this same quantitative behaviour.

By learning about a system numerically, you can get these universal numbers that will tell you something about many other different systems.

When you were at Perimeter, you worked on something called the fuzzy sphere technique. Can you tell us about that? What is the fuzzy sphere technique and what does it do?

The fuzzy sphere technique is useful for studying critical phenomena. It is very useful for determining these universal numbers that I was discussing before.

Typically, these calculations to get universal numbers are very expensive (time-wise and memory-wise).

The typical way that you obtain these numbers is by using a computer, and you have a finite system of particles. You can imagine them as being on a piece of graph paper, where you have particles that could hop from one intersection to another on the piece of graph paper.

What you can do is make your grid tighter, make it finer, so that all those intersections are closer to each other. Then you could take that and make it finer again, so all those intersections are even closer to each other, so there are many more points. Every time you do that, you have more points, you have more sites. What you're doing is that you are getting closer and closer to continuous space. You could imagine it as having infinite intersections getting closer to each other, going toward continuous space. You can never truly get to that continuous space on a classical computer, but as you get close to it, the more you can see what the universal behaviour would be for the model.

But doing that is very expensive.

The fuzzy sphere is similar, but it does something else. It uses discrete degrees of freedom, just like those graph paper intersections, but instead of the graph paper points, it starts with a quantum mechanical phenomenon called a magnetic monopole at the center of a sphere that gives you a certain number of quantum states.

Now, a magnetic monopole is kind of an exotic idea. You can imagine it as a magnet with only a north pole, and we don't know if that can exist in real life or not.

However, it is also a mathematical tool that you can use to increase the number of quantum states you have to work with by making it stronger. Depending on its strength, you get a certain number of orbitals on your sphere, and these orbitals are like probability clouds, like the ones you would see in your chemistry class.

As you make it stronger and stronger, you have more orbitals, and you can basically approach the continuous space limit, just like you did with the graph paper. With the fuzzy sphere technique, you don't need nearly as many orbitals as you would need intersections on your graph paper. You can get away with just a few orbitals, and you can learn about the universal behaviour of a system.

What I've been working on, in general, is using the fuzzy sphere technique plus a classical technique called Quantum Monte Carlo. That will allow me to study systems with many species of particles, which is something you can’t do with the fuzzy sphere (and exact diagonalization) alone.

With the combination of this fuzzy sphere technique plus this other method for studying the system in polynomial time, I can study a class of models that seem to exhibit deconfined quantum criticality. This is a phase transition that's beyond the standard textbook understanding of phase transitions. It has enhanced symmetry, but there's a lot that's still not understood about it. These new mathematical tools can be very useful in answering questions about it.

So does this fuzzy sphere technique make the study of quantum phase transitions faster and easier?

Yes, we don't need such large system sizes to see the universal behaviour, but also, with these polynomial time methods that I develop, we're able to look at many species models that you can't study with the fuzzy sphere alone.

How did your time as a postdoctoral researcher at Perimeter help you get to Wake Forest University?

Perimeter is a fantastic place to do a postdoc because it gives you both time and freedom in what you can study. For example, with this fuzzy sphere technique, it really took over three years to get it right. This is not something that fits easily into a grant application. This is also not a technique that fits easily into one subfield of physics. This is interdisciplinary — condensed matter and particle physics — and at least in many programs, when you're applying for money, you need to be straight down the middle in a particular subfield.

Perimeter really encourages these high-risk, high reward, but long timescale projects, and projects that maybe don't fit right in the middle of a particular physics category.

The other thing is, as postdocs at Perimeter, we had the independence to study topics that we're interested in and really follow several research threads, even if they're unrelated to each other. So, I worked on both classical computing algorithms, and I developed work on quantum computing algorithms during my time there.

It really allowed me to mature these different threads of ideas and be able to start my research program at Wake Forest with a variety of research threads that are all tied together as quantum simulations.

You were also a PSI Fellow at Perimeter, meaning you were teaching graduate students. How did that help you?

That gave me a lot of confidence and skill when it came to jumping into a faculty job and teaching. It helped me in developing my lecturing skills as well as with developing tutorials and finding different ways to teach students the concepts that I talked about in the lectures.

I would also say it gave me a love of writing on blackboards and really being comfortable with the board. When I interviewed for faculty jobs, I never used slides. A lot of places are moving towards slides, but I always tried to use the whiteboard or the blackboard. I got comments from people saying, you know, that was nice. Maybe we should be doing this more often.

You are at Perimeter for a week on a research visit. What is that research visit about?

I am currently working on another polynomial time algorithm that produces what are called snapshots.

If you think about a system with many particles, you might ask: "Where are the particles?

An experimentalist could take a measurement and produce an image of where the particles are. But some of the algorithms that I work on can also produce synthetic snapshots in polynomial time.

We can get snapshots for the two main types of particles, which are called bosonic particles and fermionic particles.

With my collaborator, we've seen that at low temperature, we can get some of these interesting phases that have fragmentation properties and other kinds of properties that resist thermalization.

Perimeter postdoctoral researcher Subhayan Sahu, invited me here and I'm going to be meeting with him. He’s an expert on various ways of detecting entanglement and interesting entanglement properties in systems. So I'm going to learn from him if there are certain observables that will work well for the snapshots that I can produce with my algorithm. I am also meeting with (Perimeter research associate faculty) Roger Melko because he's really been a pioneer of working with snapshots and with machine learning based on them.

Do you use Artificial Intelligence (AI) in your research? How can that help?

When it comes to data analysis and the programs that we write, I design the algorithms, but AI is very good at suggesting improvements in implementation and tracking down bugs when it knows what I'm trying to do.

This the second in a series of Explorers profiles featuring Perimeter alumni. Read our first one here.